1. H1 is provided on p.85 of the article. What would be H0 for this study?2. Of all participants in the study (described in the Participants section), what percentage were Instagram users? Provide the number of Instagram users and total number of participants in the answer.3. In Table 1, what does the frequency value of “13” represent? Variable names from the table alone will not be sufficient.4. According to Table 1, how many people with public accounts had personal information on their bio? How many did not?5. Of the 11 Grandiose variables listed in Table 2, which have scores that are negatively skewed? (OK, I can hear you groaning! Hint: There are 4 of them; refer back to your Measures of Central Tendency handout/notes to refresh as to which should be larger, the mean or the median).6. Of the 11 Grandiose variables listed in Table 2, which has the lowest variability?7. In the Correlations results of Section 3.7, which Instagram behavior had the highest correlation with grandiose narcissism? With vulnerable narcissism? (Hint: they are in para. 2 of the Correlations section; look for rho values).8. In Figure 2, which two variables had the strongest correlation? The weakest? (This figure has correlation values on the top part of the diagonal; along the diagonal are the histograms for each variable and below the diagonal are the scatterplots for each relationship.) Social Networking, 2016, 5, 82-92

Published Online April 2016 in SciRes. http://www.scirp.org/journal/sn

http://dx.doi.org/10.4236/sn.2016.52009

An Exploratory Study of the Relationships

between Narcissism, Self-Esteem and

Instagram Use

Olga Paramboukis, Jason Skues, Lisa Wise

Department of Psychological Sciences, Faculty of Health, Arts and Design, Swinburne University of Technology,

Hawthorn, Australia

Received 21 March 2016; accepted 25 April 2016; published 28 April 2016

Copyright © 2016 by authors and Scientific Research Publishing Inc.

This work is licensed under the Creative Commons Attribution International License (CC BY).

http://creativecommons.org/licenses/by/4.0/

Abstract

The aim of this mixed-methods exploratory study was to examine the relationship between narcissism, self-esteem and Instagram usage and was motivated by unsubstantiated media claims of

increasing narcissism due to excessive use of social networks. A sample of 200 participants responded to an online survey which consisted of the Five Factor Narcissism Inventory (FFNI), the

Rosenberg Self-Esteem scale, and the Instagram Usage, Behaviours, and Affective Responses Questionnaire (IUBARQ) constructed specifically for the purposes of this study. There was only weak

evidence for any relationship between narcissism and Instagram usage, suggesting that media

concerns are somewhat exaggerated. However the negative correlation between vulnerable narcissism and self-esteem warrants further examination.

Keywords

Narcissism, Vulnerable Narcissism, Grandiose Narcissism, Instagram, Self-Esteem, Social Media

1. Narcissism, Self-Esteem and Social Media

Recent research has suggested that young people today are more narcissistic compared to previous generations

[1]. This statistical increase in scores on narcissism measures has coincided with the introduction, uptake, and

widespread use of social networking sites such as Facebook and Twitter. Several researchers have investigated

the simultaneous increase in narcissism and social media use and note that self-reported narcissism tends to be

associated with different motivations and patterns of usage for social media [2]-[10]. Yet few studies have investigated whether social networking sites other than Facebook or Twitter are related to high levels of selfHow to cite this paper: Paramboukis, O., Skues, J. and Wise, L. (2016) An Exploratory Study of the Relationships between

Narcissism, Self-Esteem and Instagram Use. Social Networking, 5, 82-92. http://dx.doi.org/10.4236/sn.2016.52009

O. Paramboukis et al.

reported narcissism. This study contributes to the current research by investigating how Instagram, a social networking site focusing on editing, posting, and commenting on images, is associated with the personality trait of

narcissism.

1.1. Measures of Narcissism

Although narcissism has been investigated for around 40 years (see [11] for a review), there is still ongoing debate about whether narcissism should be conceptualised as a psychiatrically diagnosed personality disorder or a

subclinical personality trait [12]-[14]. Narcissism has been viewed from a social and personality psychology

perspective as a trait comprising multiple dimensions shaped from the earlier clinical construct. A common distinction in both the clinical and social/personality psychology literature is between grandiose and vulnerable

narcissism [15]. The grandiose dimension refers to traits such as exhibitionism, callousness, extraversion, manipulativeness, superiority, aggression, indifference and seeking of acclaim, whereas the vulnerable dimension is

believed to reflect feelings of inadequacy, emptiness and shame, reactive anger, helplessness, hypervigilance to

insult, excessive shyness and interpersonal avoidance [16] [17]. In general, more emphasis has been placed on

the grandiose aspect of narcissism compared to the vulnerable aspect. The current study defines narcissism from

the social and personality perspective as a sub-clinical trait with two factors, grandiose and vulnerable narcissism respectively.

1.2. Narcissism and Self-Esteem

Some researchers have posited significant conceptual overlap between narcissism and self-esteem with individuals high in both traits having a higher opinion of themselves [18]-[20]. In contrast, others have argued that,

while self-esteem is considered to be an intrapersonal trait, narcissism is primarily interpersonal [21]. Narcissistic individuals may present a false mask of high self-esteem, scoring high on explicit measures of self-esteem,

but showing much lower scores on implicit measures of the same trait [21].

Another possible explanation for the equivocal findings relates to the notion of different aspects of the self,

e.g., agentic versus communal self-views [18] [19]. Campbell et al. [19] found that narcissists and people with

high self-esteem report positive, albeit distinct, self-views. That is, narcissists perceive themselves as better than

average primarily on traits reflecting agency (e.g., competence), whereas individuals with high self-esteem hold

superior beliefs regarding both agency and communal traits. In this regard, the self-regulatory strategies employed by narcissists involve seeking attention and admiration by comparing themselves to others, and by defending their competence to others. Given the multiple alternative explanations relating to the relationship between narcissism and self-esteem, this study will contribute to this research by exploring the relationship between these two constructs in the context of social network use.

1.3. Narcissism and Social Networking Sites

Several researchers have investigated the relationship between narcissism and social media with studies ranging

from testing simple correlations between narcissism scores and basic usage and descriptive data, to studies that

have examined how different dimensions of narcissism relate to motivations and behaviours associated with

different social network sites including MySpace, Facebook, and Twitter. Not surprisingly, the findings have

been mixed. The early studies focused primarily on Facebook and reported significant correlations between narcissism and time per day spent using Facebook, number of Facebook friends, numbers of photos and the selection of specific profile photos, and status updates [3] [8]. Bergman et al. [2] did not find narcissism to be related

to actual social media usage, but instead that it was positively associated with motivations such as wanting to

have a lot of online friends, believing others are interested in what they are doing, and wanting to show others

what they were doing. This highlights that researchers need to look beyond simplistic quantitative variables in

relation to social media use.

In one of the first studies to separate narcissism into different factors and relate these factors to Facebook use,

Carpenter [4] found Grandiose-Exhibitionism to be associated with self-promoting behaviours, number of

Facebook friends, seeking social support and retaliating against perceived mean comments, while Entitlement/

Exploitativeness was related to more anti-social behaviours such as retaliation and checking up on whether he or

she is being talked about by others.

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Panek et al. [10] also examined how different aspects of narcissism were related to Facebook and Twitter use

in a study of both undergraduate students and adults. For university students, exhibitionism was related to time

spent and number of Facebook status posts, and entitlement was related to time spent per day. For adults, superiority and authority were related to Facebook checking, and vanity was associated with Facebook posting and

Twitter checking. According to Panek et al., university students use Twitter as a “technologically augmented

megaphone” that allows them to demonstrate their superiority to others. For adults, it appears to be Facebook

that is used in this manner. Davenport et al. [5] also examined the role of narcissism and motives in relation to

Facebook and Twitter in university and adult samples. Similarly to Panek et al. [10], Twitter was found to be

associated with narcissistic university students for whom tweeting was the preferred mode of communication.

However, it was more important for narcissists in both samples to have more Facebook friends than Twitter followers, which is probably a reflection of the different affordances and relationships with people in the audience

for both of the social network sites. Ong et al. [9] also found in their sample of secondary school students that

after controlling for extraversion, narcissism was positively associated with self-generated content on Facebook

(e.g., profile picture selection etc), but not system-generated content (e.g., number of friends or photos etc).

However, Ong et al. acknowledged that they did not consider privacy settings, which can limit the size and intended audience.

It may be that the expression of narcissistic behaviour through social networking sites is more of a by-product

of a society that is becoming increasingly more “self-centred”, and social media merely provide another arena in

which narcissistic tendencies can be displayed. Alternatively, social media may facilitate, encourage and applaud narcissistic behaviours in a problematic spiral that magnifies the degree of narcissism even further. A further possibility is that this association is merely the result of changes in the way people respond to narcissism

and self-esteem scale items on the respective scales (i.e., with less false modesty than in previous generations),

rather than a actual change in the nature of the personality traits themselves.

1.4. Instagram

Instagram is a photo and video sharing social networking site that is becoming increasingly popular among

young people1. Instagram prompts users to edit photos using inbuilt, easily-applied filters and special effects,

before posting these images onto the Instagram site [22]. Instagram differs from Facebook and Twitter through

being entirely focused on images. According to Instagram Press [22], 300 million of its users have an Instagram

account that they regularly use (monthly). There is also an average of 70 million photos being posted daily

worldwide, attracting 2.5 billion “likes” [22]. Nonetheless, in spite of its widespread usage and specific focus on

posting images, there is a dearth of research on Instagram, and how it relates to narcissism.

Based on the integration of previous research on other social networking sites and the affordances that Instagram provides to users, it is argued that narcissistic tendencies such as attention-seeking and exhibitionism may

be facilitated by Instagram usage due to its specific image-based applications and functions. Firstly, Instagram

facilitates the selection and editing of photos that can be used to make a specific impression to others by glamorizing their portrayal of themselves or their lives. Such behaviour aligns with grandiose narcissism traits such as

attention-seeking, vanity, self-promotion and exhibitionism. Secondly, “liking” and “commenting” functions are

available on Instagram for followers and do not require the formation of a deeper relationship (which may be

achieved via instant messaging functions). This aspect of the site may greatly appeal to highly narcissistic individuals (both grandiose and vulnerable) as they tend to not retain close relationships despite their desire for social contact [23] [24]. Thirdly, “hash tagging” may also be used as a form of self-promotion by both highly vulnerable and grandiose narcissistic individuals as a user may choose to hash tag their photo with popular search

terms with the intention of their photo being seen by a larger audience.

1.5. The Current Study

The current study aims to explore the relationships between narcissism and its subtypes, self-esteem, and Instagram use. The main motivation for the study was to investigate the relationship between narcissism and social

1

Although typically considered a separate social networking site in its own right, it is important to highlight that Instagram is often linked to

Facebook and Twitter, which means that content and communication on these sites is not necessarily mutually exclusive and will depend on

whether one has linked the respective profiles. Indeed since this study was undertaken, Facebook has purchased Instagram, making the

boundary between them even more difficult to define.

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media use by targeting a social networking site (i.e., Instagram) that specifically facilitates the type of behaviour

that has been shown to be associated with narcissism in previous research (i.e., photo-sharing).

H1: Individuals who score high on narcissism will engage in more Instagram behaviours.

We anticipate that some aspects of narcissism may be related to self-esteem and that both narcissism and

self-esteem may influence patterns of Instagram use. These relationships are best investigated as research questions, in keeping with the exploratory nature of the study.

RQ1: How do different aspects of narcissism relate to self-esteem and Instagram use?

RQ2: Is there a difference in the pattern of Instagram use for individuals who are classified as grandiose narcissists compared to those classified as vulnerable narcissists?

2. Method

2.1. Participants

After preliminary data screening, during which participants with missing data were deleted listwise, a total of

200 participants completed the study. There were 148 female and 52 male participants, with ages ranging from

18 to 51 (M = 22.41, Med = 21, SD = 6.15). Of these participants, only 154 had Instagram accounts, and the

majority of data will be reported from the demographic of interest, constituting 141 of the 154 Instagram users

who were under the age of 26.

2.2. Measures

Five Factor Narcissism Inventory (FFNI [25]). The Five Factor Narcissism Inventory is a 148-item narcissism

personality trait measure that was designed from a theoretical framework that views narcissistic traits as maladaptive extensions of traits from the Five Factor Model of personality. The FFNI contains 15 different facets

which form two subtypes of narcissism, namely Grandiose Narcissism (Indifference, Exhibitionism, Thrill

Seeking, Authoritativeness, Grandiose Fantasies, Manipulativeness, Exploitativeness, Entitlement, Arrogance,

Lack of Empathy and Acclaim Seeking) and Vulnerable Narcissism (Reactive Anger, Shame, Need for Admiration and Cynicism/Distrust). Participants were asked to respond on a five point Likert scale ranging from (1)

Strongly Disagree to (5) Strongly Agree with higher scores corresponding to more of a particular trait.

Rosenberg Self-Esteem Scale (RSS [26]). Participants completed the Rosenberg self-esteem scale which is a

measure of global self-esteem that consists of 10 items which are measured on a four point Likert scale ranging

from (1) Strongly Disagree to (4) Strongly Agree [26].

Instagram Usage, Behaviour, and Emotional Reactions Questionnaire (IUBRQ). Participants completed

the Instagram Usage, Behaviour, and Emotional Reactions Questionnaire (IUBRQ), which was designed for the

purpose of the current study. Since no specific scale is currently available to operationalise Instagram usage, the

following questionnaire was created to investigate only the areas of interest in this study, which included frequency of usage, frequency of Instagram-specific behaviours and the attitudes and affective reactions towards

Instagram usage. The selection of the content for this scale was formed via informal focus groups with a small

cohort of research students from our laboratory, along observations of online forums regarding behaviours on

Instagram undertaken by the first author.

Instagram Usage. This section comprised 12 questions ranging from open-ended estimates of time or frequency to yes/no responses or 4-point likert scale responses.

Instagram Behaviours. This section consisted of 16 questions relating to ways of interacting with Instagram.

Participants responded on a five point scale (1 = Never; 2 = Rarely; 3 = Sometimes, 4 = Often; and 5 = Very

Often) based on their recollection of activities over the past month.

Instagram Attitudes. This section consisted of 5 questions relating to motivations for interacting with Instagram. Participants responded on a four point scale (1 = Not at all important; 2 = Slightly important; 3 = Kind of

important; and 4 = Very important).

Instagram Emotional Reactions. The section consisted of 3 open-ended questions where participants were

invited to respond to questions about how they characterised some aspects of Instagram usage, and also how

they emotionally reacted to positive and potentially negative feedback they may receive on Instagram posts.

2.2. Procedure

Participants were invited to complete a 30-minute online survey which consisted of the FFNI, the RSES, and the

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IBURQ. Participants completed the survey at a time and location that was convenient to them, and they were

provided with a debriefing statement immediately upon the completion of the survey. The study was approved

by Swinburne University’s ethical review committee. Data were analysed using Microsoft Excel, SPSS Version

23.0, and R Version 3.2.3.

3. Results and Discussion

3.1. Instagram and Other Social Networks

Of the 200 participants recruited for the study, 154 had Instagram accounts, of whom 122 were female and 32

were male. Of the 154 participants with Instagram accounts, 62 participants linked their Instagram account to

another social network. Of these, 53 linked their Instagram account to Facebook, 9 to Twitter, 8 to Tumblr.

Some linked to more than one social network, with 8 linking to both Facebook and Twitter, 6 linking to both

Facebook and Tumbler, 3 linking to both Twitter and Tumblr. No participants linked to all three. Thirty six of

the remaining 46 non-Instagram users reported having a Facebook account, and only 5 did not report any use of

social networking sites at all.

Within our sample, it appeared that Facebook was still the most popular social networking site, and that Instagram was often used in conjunction with other social media sites. Since our data were collected for this study,

Facebook has purchased Instagram, underscoring the transient nature of usage/behaviour patterns for specific

social network sites.

3.2. Instagram Privacy Settings

We asked participants three questions relating to privacy: 1) was their account publically available?; 2) did they

accept follower requests from people unknown to them?; and 3) did their bio page contain personal information?

(see Table 1). While it might be expected that users would maintain consistency between different privacy settings (for example, keeping their content private, accepting follower requests only from people they know and

restricting personal information in their bio), this was not always the case. For example, as can be seen from

Table 1, 24 participants who kept their accounts private accepted follower requests from strangers. The inconsistency in privacy settings is more likely to reflect a lack of knowledge of account settings and how they operate than any deliberate strategy for information dissemination.

3.3. Instagram Usage, Behaviours and Emotional Reactions Questionnaire

The vast majority of the sample of Instagram users were university students under the age of 26 (141 of 154 Instagram users) and this was the demographic targeted for our analysis of relationships between personality traits

and Instagram behaviours and attitudes. The IUBRQ survey attempted to quantify aspects of Instagram usage in

terms of frequency of interaction with Instagram, the types of behaviours engaged in through Instagram, and the

motives and attitudes surrounding Instagram interactions.

3.4. Instagram Usage

While half of the participants (51%) visited their Instagram site often or very often, the majority of the sample

posted photos occasionally or rarely (77%). This suggests that the majority of Instagram users are consumers

rather than creators of content.

Table 1. Privacy settings on Instagram: cross-tabulation of participants who accept followers

who are unknown to them, have personal information in their bio sections and have their

accounts publically available.

Accept Unknown

Bio with Personal Info

Account Public

Yes

No

Yes

No

Yes

69

13

33

49

No

24

48

19

53

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3.5. Instagram Behaviours

The Behaviours section of the IUBRQ survey addressed ways in which users could interact via Instagram and

reflects features of Instagram at the time when the research was undertaken.

As can be seen from the top panel of Figure 1, most participants rarely used the Instagram features listed,

consistent with finding that very few Instagram users regularly post photos. The most frequent behaviour was

use of hashtags, which was the only listed behaviour that the majority of Instagram users performed at least

sometimes.

In order to generate possible metrics to capture the degree of interaction with Instagram, a Principal Components Analysis was conducted on the 16 Instagram Behaviour items of the IUBRQ. A one-factor solution was

revealed to be the best fitting model in which 13 of the 16 items had primary loadings above 0.3 on a single factor and explained 25% of the variance. On the basis of this analysis, we compiled a single Instagram Behaviours

score from all the items of this section for use in the correlational analyses with personality traits.

3.6. Instagram Attitudes

The Attitudes section of the IUBRQ survey addressed attitudes towards Instagram usage. As can be seen from

the bottom panel of Figure 1, being portrayed and recognised in a positive light was important to the majority of

participants. However it should be noted that positive acclaim was not purely reflected through getting “likes”,

something that 35% of the participants did not find particularly important. Achieving symmetry in the layout of

images on the screen was also not particularly important to most participants.

3.7. Narcissism, Self-Esteem and Instagram Behaviours

In order to test whether narcissism relates to self-esteem and Instagram use, summary data were first calculated

for each of the narcissism and self-esteem scales and relevant subscales used in this study and reported in Table

2.

Narcissism. The median values for both grandiose and vulnerable narcissism scores were approximately at

the midpoint of the scoring, with some participants scoring toward the upper limit of possible scores. At the trait

level, the highest-scoring trait was “acclaim seeking” (M = 36.33, SD = 6.85), whilst the lowest scoring trait was

Figure 1. Likert scales for each item on the Instagram Behaviours and Instagram

Attitudes sections of the IUBARQ.

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Table 2. Means, SDs, medians and ranges for scales and subscales from the FFNI and the

Rosenberg Self-Esteem Scale.

Descriptive Statistics

Personality variable

Mean

SD

Median

Range

Indifference

26.90

8.55

26

10 – 49

Exhibitionism

32.35

6.81

33

15 – 49

Thrill seeking

21.13

6.87

21

8 – 36

Arrogance

22.10

6.19

21

10 – 48

Entitlement

20.23

5.41

20

10 – 48

Manipulativeness

24.80

7.16

23

10 – 47

Exploitativeness

20.94

7.29

20

10 – 47

Authoritativeness

31.99

7.62

33

10 – 50

Grandiose fantasies

31.44

7.02

32

11 – 49

Lack of empathy

17.72

5.22

17

10 – 42

Acclaim seeking

36.33

6.85

37

11 – 50

Grandiose Total

285.80

283

155 – 462

Reactive anger

27.53

6.56

28

11 – 46

Shame

31.78

8.12

32

12 – 50

Need for admiration

28.39

6.22

28

10 – 44

Distrust

26.46

5.72

27

12 – 39

Vulnerable Total

114.20

116

51 – 168

FFNI Total

400.00

401

269 – 622

Rosenberg Self-Esteem

29.33

29

11 – 39

5.34

“lack of empathy” (M = 17.72, SD = 5.22).

Self-esteem. Self-esteem scores were found to be high in the sample with more than 75% of the sample scoring more than the midpoint of the scale.

Correlations. Spearman’s rank order correlations were used to test the significance of associations between

narcissism, self-esteem, Instagram Behaviours as measured by a composite score from the IUBRQ Behaviours

items and Instagram Attitudes as measured by a composite score from the IUBRQ Attitudes items. As can be

seen in Figure 2, overall narcissism (FFNI Total) did not correlate with self-esteem (RSS). However when narcissism was separated into grandiose and vulnerable dimensions, a weak positive correlation was found between

grandiose narcissism and self-esteem (ρ = 0.35, p < 0.001), whilst a negative moderate strength correlation was
found between vulnerable narcissism and self-esteem (ρ = −0.59, p < 0.001). That is, those Instagram users with
higher levels of grandiose narcissism tended to report higher self-esteem levels, whilst vulnerable narcissists reported lower self-esteem levels. All three narcissism scores were positively associated with both Instagram Attitudes and Instagram Behaviours, but the relationships between self-esteem and both Instagram Attitudes and
Instagram Behaviours were not significant.
An inspection of the item level data for selected Instagram behaviours revealed significant correlations between grandiose narcissism and Instagram behaviours such as “Hashtagging popular or expensive brands” (ρ =
0.29, p < 0.001), “Posting photos of things you want, but do not have” (ρ = 0.19, p < 0.001), “Posting photos of
celebrities or people you admire” (ρ = 0.18, p < 0.05), and “Posting photos of progress towards physical health,
fitness and wellbeing” (ρ = 0.20, p < 0.05). Moreover, vulnerable narcissism correlated with “Hashtagging
popular or expensive brands (ρ = 0.24, p < 0.001), “Posting photos of things you want, but do not have” (ρ =
0.21, p < 0.05), “Posting photos of celebrities or people you admire” (ρ = 0.34, p < 0.001), “Posting photos of
yourself at impressive events or functions” (ρ = 0.23, p < 0.001), and “Request for followers” (e.g. #follow4follow)
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Figure 2. Scatterplots, frequency histograms and correlations for narcissism
scores, self-esteem scores, Instagram Behaviours and Instagram Attitudes.
Ranges of values for scatterplots and histograms can be identified from the range
column of Table 2.
(ρ = 0.17, p < 0.05). For the most part, the pattern of correlations were similar for grandiose and vulnerable narcissism, with the only differences being a significant association between grandiose narcissism and posting
photos of physical health, fitness and wellbeing, and a significant relationship between vulnerable narcissism
and requests for followers.
3.8. Qualitative Analyses
The similarities and differences between grandiose and vulnerable narcissism were also explored using openended questions exploring emotional reactions to feedback received from other people in response to a participant’s Instagram behaviours. Prior to performing a content analysis on the open-ended responses, three groups
of participants were identified according to their combined Grandiose and Vulnerable Narcissism scores, namely
1) a High Grandiose/Low Vulnerable group; 2) a High Vulnerable/Low Grandiose; group; and 3) a High Grandiose/High Vulnerable group. Responses to three questions were compared across the three groups. The first
question was 1) “Do you feel happy or elated when you receive a lot of feedback on a post?” The most common
response to this question across all three groups was “Yes, because it gives a sense of validation and/or approval”. According to one participant, “…I feel that people are ‘liking’ an aspect of my life and further more are
showing approval of me as a person”.
In response to the second question, “If your post receives no feedback, how does that make you feel?”, participants classified in the high grandiose groups typically responded with indifference, whilst the most common
responses for participants in the high vulnerable/low grandiose group were experienced negative emotions
(32.1%) and deleted the post (17.9%).
For the last question, “If someone is critical of your post, how does that make you feel?”, the most common
response for the high vulnerable, low grandiose group was “Block/Delete the post and/or the person whom was
critical” (28.6%), with the second most common response relating to feeling defensive (25%). Indeed, one participant states “I react negatively and defensively. It makes me feel judged and unintelligent”. In contrast, both
high grandiose groups tended to be neutral in their responses.
In sum, the content analysis revealed that participants who were simultaneously high in vulnerable narcissism
and low in grandiose narcissism reacted more strongly to both negative and positive interactions on Instagram in
comparison to participants who scored either high on grandiose narcissism exclusively or scored high on both
grandiose and vulnerable narcissism.
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4. General Discussion
This study aimed to explore the interrelationships between narcissism, self-esteem and Instagram usage. Although there were differences in how grandiose and vulnerable narcissism related to self-esteem, neither types
of narcissism were strongly associated with Instagram usage as identified via the IUBRQ.
4.1. Narcissism and Self-Esteem
The FFNI total score for narcissism was not correlated with self-esteem, however vulnerable narcissism was
negatively correlated with self-esteem, while grandiose narcissism was positively correlated with self-esteem,
albeit at a lower level. This finding provides further evidence for the distinction between grandiose and vulnerable narcissism and supports the view that self-esteem is an important factor that distinguishes between those
subtypes of grandiose and vulnerable narcissism (see [18] [19]). Moreover the data suggest that vulnerable narcissism may have more of an intrapersonal component compared to grandiose narcissism, and that internal feelings of inadequacy and helplessness are more closely related to self-esteem compared to feelings of superiority
over others. However, it still remains unclear whether those with high grandiose narcissism levels do in fact
have higher self-esteem levels, or whether their underlying need for superiority and exhibitionism results in presenting an overly inflated self view on a self-report measure of self-esteem.
4.2. Narcissism and Instagram Behaviours
Vulnerable narcissism also had the highest degree of correlation with both Instagram Behaviours and Instagram
Attitudes although these relationships were not strong. In terms of specific Instagram behaviours, posting up
photos of one’s physical appearance was more associated with grandiose narcissism, while requests for followers was more associated with vulnerable narcissism. The qualitative data identified those who were high in vulnerable but low in grandiose narcissism showed stronger emotional reactions to Instagram feedback. These
findings are broadly consistent with past research that suggests that narcissism is related to self-generated content on social network sites, rather than system-generated content [9]. Those high on vulnerable narcissism appeared to be more interested in increasing their popularity and seeking the approval of others, whereas grandiose
narcissists used overt attempts of drawing attention to themselves in order to be admired. That vulnerable narcissists use Instagram as a platform to seek out positive feedback aligns with the notion that people seek validation from others in order to help boost self-esteem [27]. This would also help to explain the strong emotional
reactions to negative feedback for individuals high on vulnerable narcissism, which includes the dimensions of
reactive anger, need for admiration and shame. In contrast, grandiose narcissists appear to seek out opportunities
to engage in behaviours that afford self-promotion (see [4] [6]) in order to maintain their elevated positive selfview [3], which fits with the grandiose dimensions of exhibitionism and seeking of acclaim.
4.3. Implications
The findings from this study have provided theoretical, methodological and practical implications. Firstly, this
study provides further evidence for distinguishing between grandiose and vulnerable narcissism, and that these
two subtypes are differentially related to self-esteem. Secondly, this study has expanded the research on narcissism subtypes and social network use, targeting a social network that specifically focuses on posting images.
However despite this specific focus, the study has shown only weak evidence for any relationship between narcissism and Instagram use. This study also developed a survey that aimed to quantify specific Instagram behaviours in an attempt to uncover more nuanced patterns of behaviour relating both to reasons for posting content,
and reactions to feedback on content. Even with detailed quantitative and qualitative data on Instagram usage,
the weak evidence for any association between narcissism and Instagram suggests that Instagram offers a platform for expression of existing narcissistic tendencies rather than a medium that encourages extremes of narcissistic behaviour in people who do not normally show such tendencies.
4.4. Limitations and Future Research
Although this study was one of the very studies to have attempted to operationalise Instagram behaviours by
developing a specific measure that quantifies some of the common Instagram behaviours, it should be noted that
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the frequency of particular Instagram behaviours may not accurately reflect the importance placed on these behaviours by the individual participants. The qualitative data collected in this study provided some insights into
the way individual participants interpret and react to Instagram content but did not really provide a coherent
narrative on why people use Instagram, nor is it clear that such a narrative exists at a psychological level (i.e., at
a deeper level than that it offers an easy way to share photos with friends and family).
It is important to note that this study targeted Instagram for its specific emphasis on posting and sharing photos rather than on providing instant messaging for communicating with others. However our data suggest that
Instagram is often used in conjunction with other social network sites and most participants had more followers
on Facebook than on Instagram. The fact that Facebook has now purchased Instagram may result in a tighter integration of Instagram features into Facebook, or a change in Instagram features that renders some items of the
IUBRQ irrelevant. Indeed the primary limitation of most studies on social networking sites is that they only provide a transient snapshot of behaviour patterns as both the technologies and user bases evolve.
4.5. Conclusion
In conclusion, the primary finding from this study is that there is only weak evidence for any relationship between narcissism and Instagram usage, suggesting that media concerns about social media giving rise to unprecedented narcissistic behaviour are somewhat exaggerated. However, it appears that there is a complex relationship between narcissism and self-esteem such that vulnerable narcissism is negatively correlated with selfesteem and grandiose narcissism is positively associated with self-esteem albeit more weakly. Vulnerable narcissism appears to be more strongly associated with Instagram usage, with vulnerable narcissists seeking acclaim and being more sensitive to feedback on their posts. In contrast grandiose narcissists appear to use Instagram to exhibit their superiority over others but are not overly sensitive to feedback. Despite the limitations of
the study, the findings have provided a better understanding of the associations between narcissism subtypes,
self-esteem and Instagram use, and highlight the need for further exploration of the relationship between selfesteem and vulnerable narcissism, which has typically received less attention by researchers than grandiose narcissism.
References
[1]
Twenge, J.M., Konrath, S., Foster, J.D., Campbell, W.K. and Bushman, B.J. (2008) Egos Inflating over TIme: A Cross
Temporal Meta-Analysis of the Narcissistic Personality Inventory. Journal of Personality, 76, 875-902.
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[2]
Bergman, S., Fearrington, M.E., Davenport, S.W. and Bergman, J.Z. (2011) Millenials, Narcissism and Social Networking: What Narcissists do on Social Networks and Why. Personality and Individual Differences, 50, 706-711.
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[4]
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[5]
Davenport, S.W., Bergman, S.M., Bergman, J.Z. and Fearrington, M.E. (2014) Twitter versus Facebook: Exploring the
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212-220. http://dx.doi.org/10.1016/j.chb.2013.12.011
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Positive Self-Views: An Experimental Investigation. Computers in Human Behaviour, 28, 1929-1933.
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Mehdizadeh, S. (2010) Self-Presentation 2.0: Narcissism and Self-Esteem on Facebook. Cyberpsychology, Behaviour
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Ong, E.Y.L., Ang, R.P., Ho, J.C.M., Lim, J.C.Y., Goh, D.H. and Lee, C.S. (2011) Narcissism, Extraversion and Adolescents’ Self-Presentation on Facebook. Personality and Individual Differences, 50, 180-185.
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[11] Cain, N.M., Pincus, A.L. and Ansell, E.B. (2008) Narcissism at the Crossroads: Phenotypic Description of Pathological
Narcissism across Clinical Theory, Social/Personality Psychology and Psychiatric Diagnosis. Clinical Psychology Review, 28, 638-656. http://dx.doi.org/10.1016/j.cpr.2007.09.006
[12] Kohut, H. (1971) The Analysis of the Self: A Systematic Psychoanalytic Approach to the Treatment of Narcissistic
Personality Disorders. International Press, New York.
[13] Kernberg, O.F., (1984) Severe Personality Disorders: Psychotherapeutic Strategies. Yale University, New Haven.
[14] Kernberg, O.F. (1985) Borderline Conditions and Pathological Narcissism. Rowman and Littlefield, Lanham, MD.
[15] Pincus, A.L, and Lukowitsky, M.R. (2010) Pathological Narcissism and Narcissistic Personality Disorder. Annual Review of Clinical Psychology, 6, 421-446. http://dx.doi.org/10.1146/annurev.clinpsy.121208.131215
[16] Ackerman, R.A., Witt, E.A., Donnellan, M.B., Tzresniewski, K.H., Robbins, R.W. and Kashy, D.A. (2011) What Does
the Narcissistic Personality Inventory Really Measure? Assessment, 18, 67-87.
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[17] Miller, J.D. and Campbell, K. (2008) Comparing Clinical and Social Personality Conceptualizations of Narcissism.
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[18] Bosson, J.K., Lakey, C. E., Campbell, W.K., Zeigler-Hill, V., Jordan, C.H. and Kernis, M.H. (2008) Untangling the
Links between Narcissism and Self-Esteem: A Theoretical and Empirical Review. Personality and Social Psychology
Compass, 2, 1415-1439. http://dx.doi.org/10.1111/j.1751-9004.2008.00089.x
[19] Campbell, W.K., Rudich, E.A. and Sedikides, C. (2002) Narcissism, Self-Esteem, and the Positivity of Self-Views:
Two Portraits of Self-Love. Personality and Social Psychology Bulletin, 28, 358-368.
http://dx.doi.org/10.1177/0146167202286007
[20] Hovrath, S. and Morf, C.C. (2010) To Be Grandiose or Not To Be Worthless: Different Routes to Self-Enhancement
for Narcissism and Self-Esteem. Journal of Research in Personality, 44, 585-592.
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[21] Zeigler-Hill, V. (2006) Discrepancies between Implicit and Explicit Self-Esteem: Implications for Narcissism and SelfEsteem Instability. Journal of Personality, 74, 119-144. http://dx.doi.org/10.1111/j.1467-6494.2005.00371.x
[22] Instagram Press (2015, 13th of January) Retrieved from http://Instagram.com/press/
[23] Kealy, D. and Rasmussen, B. (2012) Veiled and Vulnerable: The Other Side of Grandiose Narcissism. Clinical Social
Work Journal, 40, 356-365. http://dx.doi.org/10.1007/s10615-011-0370-1
[24] McGregor, I., Nail, P.R., Kocalar, D. and Haji, R. (2013) I’m OK, I’m OK: Praise Makes Narcissists with Low Implicit
Self-Esteem Indifferent to the Suffering of Others. Personality and Individual Differences, 55, 655-659.
http://dx.doi.org/10.1016/j.paid.2013.05.007
[25] Glover, N., Miller, J.D., Lynam, D.R., Crego, C. and Widiger, T.A. (2012) The Five-Factor Narcissism Inventory: A
Five-Factor Measure of Narcissistic Personality Traits. Journal of Personality Assessment, 94, 500-512.
http://dx.doi.org/10.1080/00223891.2012.670680
[26] Rosenberg, M. (1965) Society and the Adolescent Self-image. Princeton University Press, Princeton, NJ.
[27] Krämer, N.C. and Winter, S. (2008) Impression Management 2.0: The Relationship of Self-Esteem, Extraversion, SelfEfficacy, and Self-Presentation within Social Networking Sites. Journal of Media Psychology, 20, 106-116.
http://dx.doi.org/10.1027/1864-1105.20.3.106
92
Ed iti o n
© Deborah Batt
10
Statistics for the
Behavioral Sciences
Frederick J Gravetter
The College at Brockport, State University of New York
Larry B. WaLLnau
The College at Brockport, State University of New York
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Printed in Canada
Print Number: 01
Print Year: 2015
B RiEF Co n tEn t S
CHAPtER
1
Introduction to Statistics 1
CHAPtER
2
Frequency Distributions
CHAPtER
3
Central Tendency
CHAPtER
4
Variability
CHAPtER
5
z-Scores: Location of Scores and Standardized Distributions 131
CHAPtER
6
Probability
CHAPtER
7
Probability and Samples: The Distribution of Sample Means 193
CHAPtER
8
Introduction to Hypothesis Testing 223
CHAPtER
9
Introduction to the t Statistic
C H A P t E R 10
CHAPtER
11
33
67
99
159
267
The t Test for Two Independent Samples 299
The t Test for Two Related Samples 335
C H A P t E R 12
Introduction to Analysis of Variance 365
C H A P t E R 13
Repeated-Measures Analysis of Variance 413
C H A P t E R 14
Two-Factor Analysis of Variance (Independent Measures) 447
CHAPtER
15
Correlation
485
C H A P t E R 16
Introduction to Regression 529
C H A P t E R 17
The Chi-Square Statistic: Tests for Goodness of Fit and Independence 559
C H A P t E R 18
The Binomial Test
603
iii
Co n tEn t S
CHAPtER
1 Introduction to Statistics
PREVIEW
1
2
1.1 Statistics, Science, and Observations 2
1.2 Data Structures, Research Methods, and Statistics 10
1.3 Variables and Measurement 18
1.4 Statistical Notation 25
Summary
29
Focus on Problem Solving 30
Demonstration 1.1 30
Problems 31
CHAPtER
2 Frequency Distributions
PREVIEW
33
34
2.1 Frequency Distributions and Frequency Distribution Tables 35
2.2 Grouped Frequency Distribution Tables 38
2.3 Frequency Distribution Graphs 42
2.4 Percentiles, Percentile Ranks, and Interpolation 49
2.5 Stem and Leaf Displays 56
Summary
58
Focus on Problem Solving 59
Demonstration 2.1 60
Demonstration 2.2 61
Problems 62
v
vi
CONTENTS
CHAPtER
3 Central Tendency
PREVIEW
67
68
3.1 Overview 68
3.2 The Mean 70
3.3 The Median 79
3.4 The Mode 83
3.5 Selecting a Measure of Central Tendency 86
3.6 Central Tendency and the Shape of the Distribution 92
Summary
94
Focus on Problem Solving 95
Demonstration 3.1 96
Problems 96
CHAPtER
4 Variability
PREVIEW
99
100
4.1 Introduction to Variability 101
4.2 Defining Standard Deviation and Variance 103
4.3 Measuring Variance and Standard Deviation for a Population 108
4.4 Measuring Standard Deviation and Variance for a Sample 111
4.5 Sample Variance as an Unbiased Statistic 117
4.6 More about Variance and Standard Deviation 119
Summary
125
Focus on Problem Solving 127
Demonstration 4.1 128
Problems 128
z-Scores: Location of Scores
C H A P t E R 5 and Standardized Distributions
PREVIEW
132
5.1 Introduction to z-Scores 133
5.2 z-Scores and Locations in a Distribution 135
5.3 Other Relationships Between z, X, 𝛍, and 𝛔 138
131
CONTENTS
vii
5.4 Using z-Scores to Standardize a Distribution 141
5.5 Other Standardized Distributions Based on z-Scores 145
5.6 Computing z-Scores for Samples 148
5.7 Looking Ahead to Inferential Statistics 150
Summary
153
Focus on Problem Solving 154
Demonstration 5.1 155
Demonstration 5.2 155
Problems 156
CHAPtER
6 Probability
PREVIEW
159
160
6.1 Introduction to Probability 160
6.2 Probability and the Normal Distribution 165
6.3 Probabilities and Proportions for Scores
from a Normal Distribution
172
6.4 Probability and the Binomial Distribution 179
6.5 Looking Ahead to Inferential Statistics 184
Summary
186
Focus on Problem Solving 187
Demonstration 6.1 188
Demonstration 6.2 188
Problems 189
Probability and Samples: The Distribution
C H A P t E R 7 of Sample Means
PREVIEW
194
7.1 Samples, Populations, and the Distribution
of Sample Means
194
7.2 The Distribution of Sample Means for any Population
and any Sample Size
199
7.3 Probability and the Distribution of Sample Means 206
7.4 More about Standard Error 210
7.5 Looking Ahead to Inferential Statistics
215
193
viii
CONTENTS
Summary
219
Focus on Problem Solving 219
Demonstration 7.1 220
Problems 221
CHAPtER
8 Introduction to Hypothesis Testing
PREVIEW
223
224
8.1 The Logic of Hypothesis Testing 225
8.2 Uncertainty and Errors in Hypothesis Testing 236
8.3 More about Hypothesis Tests 240
8.4 Directional (One-Tailed) Hypothesis Tests 245
8.5 Concerns about Hypothesis Testing: Measuring Effect Size 250
8.6 Statistical Power 254
Summary
260
Focus on Problem Solving 261
Demonstration 8.1 262
Demonstration 8.2 263
Problems 263
CHAPtER
9 Introduction to the t Statistic
PREVIEW
268
9.1 The t Statistic: An Alternative to z 268
9.2 Hypothesis Tests with the t Statistic 274
9.3 Measuring Effect Size for the t Statistic 279
9.4 Directional Hypotheses and One-Tailed Tests 288
Summary
291
Focus on Problem Solving 293
Demonstration 9.1 293
Demonstration 9.2 294
Problems 295
267
CONTENTS
CHAPtER
10 The t Test for Two Independent Samples
PREVIEW
ix
299
300
10.1 Introduction to the Independent-Measures Design 300
10.2 The Null Hypothesis and the Independent-Measures t Statistic 302
10.3 Hypothesis Tests with the Independent-Measures t Statistic 310
10.4 Effect Size and Confidence Intervals for the
Independent-Measures t
316
10.5 The Role of Sample Variance and Sample Size in the
Independent-Measures t Test
Summary
322
325
Focus on Problem Solving 327
Demonstration 10.1 328
Demonstration 10.2 329
Problems 329
CHAPtER
11 The t Test for Two Related Samples
PREVIEW
335
336
11.1 Introduction to Repeated-Measures Designs 336
11.2 The t Statistic for a Repeated-Measures Research Design 339
11.3 Hypothesis Tests for the Repeated-Measures Design 343
11.4 Effect Size and Confidence Intervals for the Repeated-Measures t 347
11.5 Comparing Repeated- and Independent-Measures Designs 352
Summary
355
Focus on Problem Solving 358
Demonstration 11.1 358
Demonstration 11.2 359
Problems 360
CHAPtER
12 Introduction to Analysis of Variance
PREVIEW
366
12.1 Introduction (An Overview of Analysis of Variance) 366
12.2 The Logic of Analysis of Variance 372
12.3 ANOVA Notation and Formulas 375
365
x
CONTENTS
12.4 Examples of Hypothesis Testing and Effect Size with ANOVA 383
12.5 Post Hoc Tests 393
12.6 More about ANOVA 397
Summary
403
Focus on Problem Solving 406
Demonstration 12.1 406
Demonstration 12.2 408
Problems 408
CHAPtER
13 Repeated-Measures Analysis of Variance
PREVIEW
413
414
13.1 Overview of the Repeated-Measures ANOVA 415
13.2 Hypothesis Testing and Effect Size with the
Repeated-Measures ANOVA
420
13.3 More about the Repeated-Measures Design 429
Summary
436
Focus on Problem Solving 438
Demonstration 13.1 439
Demonstration 13.2 440
Problems 441
Two-Factor Analysis of Variance
C H A P t E R 14 (Independent Measures)
PREVIEW
447
448
14.1 An Overview of the Two-Factor, Independent-Measures, ANOVA: Main
Effects and Interactions
448
14.2 An Example of the Two-Factor ANOVA and Effect Size 458
14.3 More about the Two-Factor ANOVA 467
Summary
473
Focus on Problem Solving 475
Demonstration 14.1 476
Demonstration 14.2 478
Problems 479
CONTENTS
CHAPtER
15 Correlation
PREVIEW
xi
485
486
15.1 Introduction 487
15.2 The Pearson Correlation 489
15.3 Using and Interpreting the Pearson Correlation 495
15.4 Hypothesis Tests with the Pearson Correlation 506
15.5 Alternatives to the Pearson Correlation 510
Summary
520
Focus on Problem Solving 522
Demonstration 15.1 523
Problems 524
CHAPtER
16 Introduction to Regression
PREVIEW
529
530
16.1 Introduction to Linear Equations and Regression 530
16.2 The Standard Error of Estimate and Analysis of Regression:
The Significance of the Regression Equation
538
16.3 Introduction to Multiple Regression with Two Predictor Variables 544
Summary
552
Linear and Multiple Regression
554
Focus on Problem Solving 554
Demonstration 16.1 555
Problems 556
The Chi-Square Statistic: Tests for Goodness
C H A P t E R 17 of Fit and Independence
PREVIEW
560
17.1 Introduction to Chi-Square: The Test for Goodness of Fit 561
17.2 An Example of the Chi-Square Test for Goodness of Fit 567
17.3 The Chi-Square Test for Independence 573
17.4 Effect Size and Assumptions for the Chi-Square Tests
17.5 Special Applications of the Chi-Square Tests 587
582
559
xii
CONTENTS
Summary
591
Focus on Problem Solving 595
Demonstration 17.1 595
Demonstration 17.2 597
Problems 597
CHAPtER
18 The Binomial Test
PREVIEW
603
604
18.1 Introduction to the Binomial Test 604
18.2 An Example of the Binomial Test 608
18.3 More about the Binomial Test: Relationship with Chi-Square
and the Sign Test
Summary
612
617
Focus on Problem Solving 619
Demonstration 18.1 619
Problems 620
A PPE N D IX E S
A Basic Mathematics Review 625
A.1
A.2
A.3
A.4
A.5
Symbols and Notation 627
Proportions: Fractions, Decimals, and Percentages 629
Negative Numbers 635
Basic Algebra: Solving Equations 637
Exponents and Square Roots 640
B Statistical Tables 647
C Solutions for Odd-Numbered Problems in the Text 663
D General Instructions for Using SPSS 683
E Hypothesis Tests for Ordinal Data: Mann-Whitney,
Wilcoxon, Kruskal-Wallis, and Friedman Tests
687
Statistics Organizer: Finding the Right Statistics for Your Data
References
717
Name Index
723
Subject Index
725
701
PREFACE
M
any students in the behavioral sciences view the required statistics course as an
intimidating obstacle that has been placed in the middle of an otherwise interesting curriculum. They want to learn about human behavior—not about math and science.
As a result, the statistics course is seen as irrelevant to their education and career goals.
However, as long as the behavioral sciences are founded in science, knowledge of statistics
will be necessary. Statistical procedures provide researchers with objective and systematic
methods for describing and interpreting their research results. Scientific research is the
system that we use to gather information, and statistics are the tools that we use to distill
the information into sensible and justified conclusions. The goal of this book is not only
to teach the methods of statistics, but also to convey the basic principles of objectivity and
logic that are essential for science and valuable for decision making in everyday life.
Those of you who are familiar with previous editions of Statistics for the Behavioral
Sciences will notice that some changes have been made. These changes are summarized
in the section entitled “To the Instructor.” In revising this text, our students have been
foremost in our minds. Over the years, they have provided honest and useful feedback.
Their hard work and perseverance has made our writing and teaching most rewarding. We
sincerely thank them. Students who are using this edition should please read the section of
the preface entitled “To the Student.”
The book chapters are organized in the sequence that we use for our own statistics
courses. We begin with descriptive statistics, and then examine a variety of statistical procedures focused on sample means and variance before moving on to correlational methods
and nonparametric statistics. Information about modifying this sequence is presented in the
To The Instructor section for individuals who prefer a different organization. Each chapter
contains numerous examples, many based on actual research studies, learning checks, a
summary and list of key terms, and a set of 20–30 problems.
Ancillaries
Ancillaries for this edition include the following.
■■
MindTap® Psychology: MindTap® Psychology for Gravetter/Wallnau’s Statistics
for The Behavioral Sciences, 10th Edition is the digital learning solution that helps
instructors engage and transform today’s students into critical thinkers. Through paths
of dynamic assignments and applications that you can personalize, real-time course
analytics, and an accessible reader, MindTap helps you turn cookie cutter into cutting
edge, apathy into engagement, and memorizers into higher-level thinkers.
As an instructor using MindTap you have at your fingertips the right content and
unique set of tools curated specifically for your course, such as video tutorials that
walk students through various concepts and interactive problem tutorials that provide
students opportunities to practice what they have learned, all in an interface designed
to improve workflow and save time when planning lessons and course structure. The
control to build and personalize your course is all yours, focusing on the most relevant
xiii
xiv
PREFACE
■■
■■
■■
material while also lowering costs for your students. Stay connected and informed in
your course through real time student tracking that provides the opportunity to adjust
the course as needed based on analytics of interactivity in the course.
Online Instructor’s Manual: The manual includes learning objectives, key terms,
a detailed chapter outline, a chapter summary, lesson plans, discussion topics, student
activities, “What If” scenarios, media tools, a sample syllabus and an expanded test
bank. The learning objectives are correlated with the discussion topics, student
activities, and media tools.
Online PowerPoints: Helping you make your lectures more engaging while effectively reaching your visually oriented students, these handy Microsoft PowerPoint®
slides outline the chapters of the main text in a classroom-ready presentation. The
PowerPoint® slides are updated to reflect the content and organization of the new
edition of the text.
Cengage Learning Testing, powered by Cognero®: Cengage Learning Testing,
Powered by Cognero®, is a flexible online system that allows you to author, edit,
and manage test bank content. You can create multiple test versions in an instant and
deliver tests from your LMS in your classroom.
Acknowledgments
It takes a lot of good, hard-working people to produce a book. Our friends at Cengage
have made enormous contributions to this textbook. We thank: Jon-David Hague, Product
Director; Timothy Matray, Product Team Director; Jasmin Tokatlian, Content Development Manager; Kimiya Hojjat, Product Assistant; and Vernon Boes, Art Director. Special
thanks go to Stefanie Chase, our Content Developer and to Lynn Lustberg who led us
through production at MPS.
Reviewers play a very important role in the development of a manuscript. Accordingly,
we offer our appreciation to the following colleagues for their assistance: Patricia Case,
University of Toledo; Kevin David, Northeastern State University; Adia Garrett, University of Maryland, Baltimore County; Carrie E. Hall, Miami University; Deletha Hardin,
University of Tampa; Angela Heads, Prairie View A&M University; Roberto Heredia,
Texas A&M International University; Alisha Janowski, University of Central Florida;
Matthew Mulvaney, The College at Brockport (SUNY); Nicholas Von Glahn, California
State Polytechnic University, Pomona; and Ronald Yockey, Fresno State University.
To the Instructor
Those of you familiar with the previous edition of Statistics for the Behavioral Sciences will
notice a number of changes in the 10th edition. Throughout this book, research examples
have been updated, real world examples have been added, and the end-of-chapter problems
have been extensively revised. Major revisions for this edition include the following:
1. Each section of every chapter begins with a list of Learning Objectives for that
specific section.
2. Each section ends with a Learning Check consisting of multiple-choice questions
with at least one question for each Learning Objective.
PREFACE
xv
3. The former Chapter 19, Choosing the Right Statistics, has been eliminated and
an abridged version is now an Appendix replacing the Statistics Organizer, which
appeared in earlier editions.
Other examples of specific and noteworthy revisions include the following.
Chapter 1 The section on data structures and research methods parallels the new
Appendix, Choosing the Right Statistics.
Chapter 2 The chapter opens with a new Preview to introduce the concept and purpose
of frequency distributions.
Chapter 3
Minor editing clarifies and simplifies the discussion the median.
Chapter 4 The chapter opens with a new Preview to introduce the topic of Central
Tendency. The sections on standard deviation and variance have been edited to increase
emphasis on concepts rather than calculations.
The section discussion relationships between z, X, μ, and σ has been
expanded and includes a new demonstration example.
Chapter 5
Chapter 6
The chapter opens with a new Preview to introduce the topic of Probability.
The section, Looking Ahead to Inferential Statistics, has been substantially shortened and
simplified.
Chapter 7
The former Box explaining difference between standard deviation and
standard error was deleted and the content incorporated into Section 7.4 with editing to
emphasize that the standard error is the primary new element introduced in the chapter.
The final section, Looking Ahead to Inferential Statistics, was simplified and shortened to
be consistent with the changes in Chapter 6.
Chapter 8
A redundant example was deleted which shortened and streamlined the
remaining material so that most of the chapter is focused on the same research example.
Chapter 9 The chapter opens with a new Preview to introduce the t statistic and explain
why a new test statistic is needed. The section introducing Confidence Intervals was edited
to clarify the origin of the confidence interval equation and to emphasize that the interval
is constructed at the sample mean.
Chapter 10
The chapter opens with a new Preview introducing the independent-measures t statistic. The section presenting the estimated standard error of (M1 – M2) has been
simplified and shortened.
Chapter 11
The chapter opens with a new Preview introducing the repeated-measures t
statistic. The section discussing hypothesis testing has been separated from the section on
effect size and confidence intervals to be consistent with the other two chapters on t tests.
The section comparing independent- and repeated-measures designs has been expanded.
Chapter 12 The chapter opens with a new Preview introducing ANOVA and explaining
why a new hypothesis testing procedure is necessary. Sections in the chapter have been
reorganized to allow flow directly from hypothesis tests and effect size to post tests.
xvi
PREFACE
Chapter 13
Substantially expanded the section discussing factors that influence the
outcome of a repeated-measures hypothesis test and associated measures of effect size.
Chapter 14
The chapter opens with a new Preview presenting a two-factor research
example and introducing the associated ANOVA. Sections have been reorganized so that
simple main effects and the idea of using a second factor to reduce variance from individual differences are now presented as extra material related to the two-factor ANOVA.
Chapter 15
The chapter opens with a new Preview presenting a correlational research
study and the concept of a correlation. A new section introduces the t statistic for evaluating the significance of a correlation and the section on partial correlations has been simplified and shortened.
Chapter 16 The chapter opens with a new Preview introducing the concept of regression and
its purpose. A new section demonstrates the equivalence of testing the significance of a correlation and testing the significance of a regression equation with one predictor variable. The section on residuals for the multiple-regression equation has been edited to simplify and shorten.
Chapter 17
A new chapter Preview presents an experimental study with data consisting
of frequencies, which are not compatible with computing means and variances. Chi-square
tests are introduced as a solution to this problem. A new section introduces Cohen’s w as
a means of measuring effect size for both chi-square tests.
Chapter 18
Substantial editing clarifies the section explaining how the real limits for
each score can influence the conclusion from a binomial test.
The former Chapter 19 covering the task of matching statistical methods to specific
types of data has been substantially shortened and converted into an Appendix.
■■Matching the Text to Your Syllabus
The book chapters are organized in the sequence that we use for our own statistics courses.
However, different instructors may prefer different organizations and probably will choose
to omit or deemphasize specific topics. We have tried to make separate chapters, and even
sections of chapters, completely self-contained, so they can be deleted or reorganized to fit
the syllabus for nearly any instructor. Some common examples are as follows.
■■
■■
■■
It is common for instructors to choose between emphasizing analysis of variance
(Chapters 12, 13, and 14) or emphasizing correlation/regression (Chapters 15 and 16).
It is rare for a one-semester course to complete coverage of both topics.
Although we choose to complete all the hypothesis tests for means and mean
differences before introducing correlation (Chapter 15), many instructors prefer to
place correlation much earlier in the sequence of course topics. To accommodate
this, Sections 15.1, 15.2, and 15.3 present the calculation and interpretation of
the Pearson correlation and can be introduced immediately following Chapter 4
(variability). Other sections of Chapter 15 refer to hypothesis testing and should be
delayed until the process of hypothesis testing (Chapter 8) has been introduced.
It is also possible for instructors to present the chi-square tests (Chapter 17) much
earlier in the sequence of course topics. Chapter 17, which presents hypothesis tests
for proportions, can be presented immediately after Chapter 8, which introduces the
process of hypothesis testing. If this is done, we also recommend that the Pearson
correlation (Sections 15.1, 15.2, and 15.3) be presented early to provide a foundation
for the chi-square test for independence.
PREFACE
xvii
To the Student
A primary goal of this book is to make the task of learning statistics as easy and painless
as possible. Among other things, you will notice that the book provides you with a number
of opportunities to practice the techniques you will be learning in the form of Learning
Checks, Examples, Demonstrations, and end-of-chapter problems. We encourage you to
take advantage of these opportunities. Read the text rather than just memorizing the formulas. We have taken care to present each statistical procedure in a conceptual context that
explains why the procedure was developed and when it should be used. If you read this
material and gain an understanding of the basic concepts underlying a statistical formula,
you will find that learning the formula and how to use it will be much easier. In the “Study
Hints,” that follow, we provide advice that we give our own students. Ask your instructor
for advice as well; we are sure that other instructors will have ideas of their own.
Over the years, the students in our classes and other students using our book have given
us valuable feedback. If you have any suggestions or comments about this book, you can
write to either Professor Emeritus Frederick Gravetter or Professor Emeritus Larry Wallnau
at the Department of Psychology, SUNY College at Brockport, 350 New Campus Drive,
Brockport, New York 14420. You can also contact Professor Emeritus Gravetter directly at
fgravett@brockport.edu.
■■Study Hints
You may find some of these tips helpful, as our own students have reported.
■■
■■
■■
■■
■■
The key to success in a statistics course is to keep up with the material. Each new
topic builds on previous topics. If you have learned the previous material, then the
new topic is just one small step forward. Without the proper background, however,
the new topic can be a complete mystery. If you find that you are falling behind, get
help immediately.
You will learn (and remember) much more if you study for short periods several
times per week rather than try to condense all of your studying into one long session.
For example, it is far more effective to study half an hour every night than to have
a single 3½-hour study session once a week. We cannot even work on writing this
book without frequent rest breaks.
Do some work before class. Keep a little ahead of the instructor by reading the appropriate sections before they are presented in class. Although you may not fully understand what you read, you will have a general idea of the topic, which will make the
lecture easier to follow. Also, you can identify material that is particularly confusing
and then be sure the topic is clarified in class.
Pay attention and think during class. Although this advice seems obvious, often it is
not practiced. Many students spend so much time trying to write down every example
presented or every word spoken by the instructor that they do not actually understand
and process what is being said. Check with your instructor—there may not be a need
to copy every example presented in class, especially if there are many examples like
it in the text. Sometimes, we tell our students to put their pens and pencils down for a
moment and just listen.
Test yourself regularly. Do not wait until the end of the chapter or the end of the
week to check your knowledge. After each lecture, work some of the end-of-chapter
problems and do the Learning Checks. Review the Demonstration Problems, and
be sure you can define the Key Terms. If you are having trouble, get your questions
answered immediately—reread the section, go to your instructor, or ask questions in
class. By doing so, you will be able to move ahead to new material.
xviii
PREFACE
■■
■■
Do not kid yourself! Avoid denial. Many students observe their instructor solve
problems in class and think to themselves, “This looks easy, I understand it.” Do
you really understand it? Can you really do the problem on your own without having
to leaf through the pages of a chapter? Although there is nothing wrong with using
examples in the text as models for solving problems, you should try working a problem with your book closed to test your level of mastery.
We realize that many students are embarrassed to ask for help. It is our biggest challenge as instructors. You must find a way to overcome this aversion. Perhaps contacting the instructor directly would be a good starting point, if asking questions in class
is too anxiety-provoking. You could be pleasantly surprised to find that your instructor does not yell, scold, or bite! Also, your instructor might know of another student
who can offer assistance. Peer tutoring can be very helpful.
Frederick J Gravetter
Larry B. Wallnau
A B o U t tH E AU tH o R S
Frederick Gravetter
Frederick J Gravetter is Professor Emeritus of Psychology at the
State University of New York College at Brockport. While teaching at
Brockport, Dr. Gravetter specialized in statistics, experimental design, and
cognitive psychology. He received his bachelor’s degree in mathematics from
M.I.T. and his Ph.D in psychology from Duke University. In addition to publishing this textbook and several research articles, Dr. Gravetter co-authored
Research Methods for the Behavioral Science and Essentials of Statistics for
the Behavioral Sciences.
Larry B. Wallnau
Larry B. WaLLnau is Professor Emeritus of Psychology at the State
University of New York College at Brockport. While teaching at Brockport,
he published numerous research articles in biopsychology. With
Dr. Gravetter, he co-authored Essentials of Statistics for the Behavioral
Sciences. Dr. Wallnau also has provided editorial consulting for numerous
publishers and journals. He has taken up running and has competed in 5K
races in New York and Connecticut. He takes great pleasure in adopting
neglected and rescued dogs.
xix
CH A P T ER
Introduction to Statistics
1
© Deborah Batt
PREVIEW
1.1 Statistics, Science, and Observations
1.2 Data Structures, Research Methods, and Statistics
1.3 Variables and Measurement
1.4 Statistical Notation
Summary
Focus on Problem Solving
Demonstration 1.1
Problems
1
PREVIEW
Before we begin our discussion of statistics, we ask you
to read the following paragraph taken from the philosophy of Wrong Shui (Candappa, 2000).
The Journey to Enlightenment
In Wrong Shui, life is seen as a cosmic journey,
a struggle to overcome unseen and unexpected
obstacles at the end of which the traveler will find
illumination and enlightenment. Replicate this quest
in your home by moving light switches away from
doors and over to the far side of each room.*
Why did we begin a statistics book with a bit of twisted
philosophy? In part, we simply wanted to lighten the
mood with a bit of humor—starting a statistics course is
typically not viewed as one of life’s joyous moments. In
addition, the paragraph is an excellent counterexample for
the purpose of this book. Specifically, our goal is to do
everything possible to prevent you from stumbling around
in the dark by providing lots of help and illumination as
you journey through the world of statistics. To accomplish
this, we begin each section of the book with clearly stated
learning objectives and end each section with a brief quiz
to test your mastery of the new material. We also introduce each new statistical procedure by explaining the purpose it is intended to serve. If you understand why a new
procedure is needed, you will find it much easier to learn.
1.1
The objectives for this first chapter are to provide
an introduction to the topic of statistics and to give you
some background for the rest of the book. We discuss
the role of statistics within the general field of scientific
inquiry, and we introduce some of the vocabulary and
notation that are necessary for the statistical methods
that follow.
As you read through the following chapters, keep
in mind that the general topic of statistics follows a
well-organized, logically developed progression that
leads from basic concepts and definitions to increasingly sophisticated techniques. Thus, each new topic
serves as a foundation for the material that follows. The
content of the first nine chapters, for example, provides
an essential background and context for the statistical
methods presented in Chapter 10. If you turn directly
to Chapter 10 without reading the first nine chapters,
you will find the material confusing and incomprehensible. However, if you learn and use the background
material, you will have a good frame of reference for
understanding and incorporating new concepts as they
are presented.
*Candappa, R. (2000). The little book of wrong shui. Kansas City:
Andrews McMeel Publishing. Reprinted by permission.
Statistics, Science, and Observations
LEARNING OBJECTIVEs
1. Define the terms population, sample, parameter, and statistic, and describe the
relationships between them.
2. Define descriptive and inferential statistics and describe how these two general
categories of statistics are used in a typical research study.
3. Describe the concept of sampling error and explain how this concept creates the
fundamental problem that inferential statistics must address.
■■Definitions of Statistics
By one definition, statistics consist of facts and figures such as the average annual snowfall
in Denver or Derrick Jeter’s lifetime batting average. These statistics are usually informative
and time-saving because they condense large quantities of information into a few simple figures. Later in this chapter we return to the notion of calculating statistics (facts and figures)
but, for now, we concentrate on a much broader definition of statistics. Specifically, we use
the term statistics to refer to a general field of mathematics. In this case, we are using the
term statistics as a shortened version of statistical procedures. For example, you are probably using this book for a statistics course in which you will learn about the statistical techniques that are used to summarize and evaluate research results in the behavioral sciences.
2
SEctIon 1.1 | Statistics, Science, and Observations
3
Research in the behavioral sciences (and other fields) involves gathering information.
To determine, for example, whether college students learn better by reading material on
printed pages or on a computer screen, you would need to gather information about students’ study habits and their academic performance. When researchers finish the task of
gathering information, they typically find themselves with pages and pages of measurements such as preferences, personality scores, opinions, and so on. In this book, we present
the statistics that researchers use to analyze and interpret the information that they gather.
Specifically, statistics serve two general purposes:
1. Statistics are used to organize and summarize the information so that the researcher can
see what happened in the research study and can communicate the results to others.
2. Statistics help the researcher to answer the questions that initiated the research by
determining exactly what general conclusions are justified based on the specific
results that were obtained.
DEFInItIon
The term statistics refers to a set of mathematical procedures for organizing, summarizing, and interpreting information.
Statistical procedures help ensure that the information or observations are presented
and interpreted in an accurate and informative way. In somewhat grandiose terms, statistics
help researchers bring order out of chaos. In addition, statistics provide researchers with a
set of standardized techniques that are recognized and understood throughout the scientific
community. Thus, the statistical methods used by one researcher will be familiar to other
researchers, who can accurately interpret the statistical analyses with a full understanding
of how the analysis was done and what the results signify.
■■Populations and Samples
Research in the behavioral sciences typically begins with a general question about a specific
group (or groups) of individuals. For example, a researcher may want to know what factors
are associated with academic dishonesty among college students. Or a researcher may want
to examine the amount of time spent in the bathroom for men compared to women. In the
first example, the researcher is interested in the group of college students. In the second
example, the researcher wants to compare the group of men with the group of women. In statistical terminology, the entire group that a researcher wishes to study is called a population.
DEFInItIon
A population is the set of all the individuals of interest in a particular study.
As you can well imagine, a population can be quite large—for example, the entire set
of women on the planet Earth. A researcher might be more specific, limiting the population
for study to women who are registered voters in the United States. Perhaps the investigator
would like to study the population consisting of women who are heads of state. Populations
can obviously vary in size from extremely large to very small, depending on how the investigator defines the population. The population being studied should always be identified by
the researcher. In addition, the population need not consist of people—it could be a population of rats, corporations, parts produced in a factory, or anything else an investigator wants
to study. In practice, populations are typically very large, such as the population of college
sophomores in the United States or the population of small businesses.
Because populations tend to be very large, it usually is impossible for a researcher to
examine every individual in the population of interest. Therefore, researchers typically select
4
chaPtER 1 | Introduction to Statistics
a smaller, more manageable group from the population and limit their studies to the individuals in the selected group. In statistical terms, a set of individuals selected from a population
is called a sample. A sample is intended to be representative of its population, and a sample
should always be identified in terms of the population from which it was selected.
A sample is a set of individuals selected from a population, usually intended to
represent the population in a research study.
DEFInItIon
Just as we saw with populations, samples can vary in size. For example, one study might
examine a sample of only 10 students in a graduate program and another study might use a
sample of more than 10,000 people who take a specific cholesterol medication.
So far we have talked about a sample being selected from a population. However, this is
actually only half of the full relationship between a sample and its population. Specifically,
when a researcher finishes examining the sample, the goal is to generalize the results back
to the entire population. Remember that the research started with a general question about
the population. To answer the question, a researcher studies a sample and then generalizes
the results from the sample to the population. The full relationship between a sample and a
population is shown in Figure 1.1.
■■Variables and Data
Typically, researchers are interested in specific characteristics of the individuals in the population (or in the sample), or they are interested in outside factors that may influence the
individuals. For example, a researcher may be interested in the influence of the weather on
people’s moods. As the weather changes, do people’s moods also change? Something that
can change or have different values is called a variable.
DEFInItIon
A variable is a characteristic or condition that changes or has different values for
different individuals.
THE POPULATION
All of the individuals of interest
The results
from the sample
are generalized
to the population
F I G U R E 1.1
The relationship between a
population and a sample.
The sample
is selected from
the population
THE SAMPLE
The individuals selected to
participate in the research study
SEctIon 1.1 | Statistics, Science, and Observations
5
Once again, variables can be characteristics that differ from one individual to another,
such as height, weight, gender, or personality. Also, variables can be environmental conditions that change such as temperature, time of day, or the size of the room in which the
research is being conducted.
To demonstrate changes in variables, it is necessary to make measurements of the variables
being examined. The measurement obtained for each individual is called a datum, or more commonly, a score or raw score. The complete set of scores is called the data set or simply the data.
DEFInItIon
Data (plural) are measurements or observations. A data set is a collection of measurements or observations. A datum (singular) is a single measurement or observation and is commonly called a score or raw score.
Before we move on, we should make one more point about samples, populations, and
data. Earlier, we defined populations and samples in terms of individuals. For example,
we discussed a population of graduate students and a sample of cholesterol patients. Be
forewarned, however, that we will also refer to populations or samples of scores. Because
research typically involves measuring each individual to obtain a score, every sample (or
population) of individuals produces a corresponding sample (or population) of scores.
■■Parameters and Statistics
When describing data it is necessary to distinguish whether the data come from a population or a sample. A characteristic that describes a population—for example, the average
score for the population—is called a parameter. A characteristic that describes a sample is
called a statistic. Thus, the average score for a sample is an example of a statistic. Typically,
the research process begins with a question about a population parameter. However, the
actual data come from a sample and are used to compute sample statistics.
DEFInItIon
A parameter is a value, usually a numerical value, that describes a population. A
parameter is usually derived from measurements of the individuals in the population.
A statistic is a value, usually a numerical value, that describes a sample. A statistic
is usually derived from measurements of the individuals in the sample.
Every population parameter has a corresponding sample statistic, and most research
studies involve using statistics from samples as the basis for answering questions about
population parameters. As a result, much of this book is concerned with the relationship
between sample statistics and the corresponding population parameters. In Chapter 7, for
example, we examine the relationship between the mean obtained for a sample and the
mean for the population from which the sample was obtained.
■■Descriptive and Inferential Statistical Methods
Although researchers have developed a variety of different statistical procedures to organize and interpret data, these different procedures can be classified into two general categories. The first category, descriptive statistics, consists of statistical procedures that are used
to simplify and summarize data.
DEFInItIon
Descriptive statistics are statistical procedures used to summarize, organize, and
simplify data.
6
chaPtER 1 | Introduction to Statistics
Descriptive statistics are techniques that take raw scores and organize or summarize
them in a form that is more manageable. Often the scores are organized in a table or a graph
so that it is possible to see the entire set of scores. Another common technique is to summarize a set of scores by computing an average. Note that even if the data set has hundreds
of scores, the average provides a single descriptive value for the entire set.
The second general category of statistical techniques is called inferential statistics.
Inferential statistics are methods that use sample data to make general statements about a
population.
DEFInItIon
Inferential statistics consist of techniques that allow us to study samples and then
make generalizations about the populations from which they were selected.
Because populations are typically very large, it usually is not possible to measure
everyone in the population. Therefore, a sample is selected to represent the population.
By analyzing the results from the sample, we hope to make general statements about the
population. Typically, researchers use sample statistics as the basis for drawing conclusions
about population parameters. One problem with using samples, however, is that a sample
provides only limited information about the population. Although samples are generally
representative of their populations, a sample is not expected to give a perfectly accurate
picture of the whole population. There usually is some discrepancy between a sample statistic and the corresponding population parameter. This discrepancy is called sampling
error, and it creates the fundamental problem inferential statistics must always address.
DEFInItIon
Sampling error is the naturally occurring discrepancy, or error, that exists between
a sample statistic and the corresponding population parameter.
The concept of sampling error is illustrated in Figure 1.2. The figure shows a population of 1,000 college students and 2 samples, each with 5 students who were selected from
the population. Notice that each sample contains different individuals who have different
characteristics. Because the characteristics of each sample depend on the specific people in
the sample, statistics will vary from one sample to another. For example, the five students
in sample 1 have an average age of 19.8 years and the students in sample 2 have an average
age of 20.4 years.
It is also very unlikely that the statistics obtained for a sample will be identical to the
parameters for the entire population. In Figure 1.2, for example, neither sample has statistics that are exactly the same as the population parameters. You should also realize that
Figure 1.2 shows only two of the hundreds of possible samples. Each sample would contain
different individuals and would produce different statistics. This is the basic concept of
sampling error: sample statistics vary from one sample to another and typically are different from the corresponding population parameters.
One common example of sampling error is the error associated with a sample proportion. For example, in newspaper articles reporting results from political polls, you frequently find statements such as this:
Candidate Brown leads the poll with 51% of the vote. Candidate Jones has 42%
approval, and the remaining 7% are undecided. This poll was taken from a sample of registered voters and has a margin of error of plus-or-minus 4 percentage points.
The “margin of error” is the sampling error. In this case, the percentages that are reported
were obtained from a sample and are being generalized to the whole population. As always,
you do not expect the statistics from a sample to be perfect. There always will be some
“margin of error” when sample statistics are used to represent population parameters.
SEctIon 1.1 | Statistics, Science, and Observations
7
F I G U R E 1. 2
A demonstration of sampling error. Two
samples are selected from the same population.
Notice that the sample statistics are different
from one sample to another and all the sample
statistics are different from the corresponding
population parameters. The natural differences that exist, by chance, between a sample
statistic and population parameter are called
sampling error.
Population
of 1000 college students
Population Parameters
Average Age 5 21.3 years
Average IQ 5 112.5
65% Female, 35% Male
Sample #1
Sample #2
Eric
Jessica
Laura
Karen
Brian
Tom
Kristen
Sara
Andrew
John
Sample Statistics
Average Age 5 19.8
Average IQ 5 104.6
60% Female, 40% Male
Sample Statistics
Average Age 5 20.4
Average IQ 5 114.2
40% Female, 60% Male
As a further demonstration of sampling error, imagine that your statistics class is separated into two groups by drawing a line from front to back through the middle of the room.
Now imagine that you compute the average age (or height, or IQ) for each group. Will the
two groups have exactly the same average? Almost certainly they will not. No matter what
you chose to measure, you will probably find some difference between the two groups.
However, the difference you obtain does not necessarily mean that there is a systematic
difference between the two groups. For example, if the average age for students on the
right-hand side of the room is higher than the average for students on the left, it is unlikely
that some mysterious force has caused the older people to gravitate to the right side of
the room. Instead, the difference is probably the result of random factors such as chance.
The unpredictable, unsystematic differences that exist from one sample to another are an
example of sampling error.
■■Statistics in the Context of Research
The following example shows the general stages of a research study and demonstrates
how descriptive statistics and inferential statistics are used to organize and interpret the
data. At the end of the example, note how sampling error can affect the interpretation of
experimental results, and consider why inferential statistical methods are needed to deal
with this problem.
8
chaPtER 1 | Introduction to Statistics
ExamplE 1.1
Figure 1.3 shows an overview of a general research situation and demonstrates the roles that
descriptive and inferential statistics play. The purpose of the research study is to address a
question that we posed earlier: Do college students learn better by studying text on printed
pages or on a computer screen? Two samples are selected from the population of college
students. The students in sample A are given printed pages of text to study for 30 minutes
and the students in sample B study the same text on a computer screen. Next, all of the
students are given a multiple-choice test to evaluate their knowledge of the material. At this
point, the researcher has two sets of data: the scores for sample A and the scores for sample
B (see the figure). Now is the time to begin using statistics.
First, descriptive statistics are used to simplify the pages of data. For example, the
researcher could draw a graph showing the scores for each sample or compute the average score for each sample. Note that descriptive methods provide a simplified, organized
Step 1
Experiment:
Compare two
studying methods
Data
Test scores for the
students in each
sample
Step 2
Descriptive statistics:
Organize and simplify
Population of
College
Students
Sample A
Read from printed
pages
25
27
30
19
29
26
21
28
23
26
20
25
28
27
24
26
22
30
Average
Score = 26
Step 3
Inferential statistics:
Interpret results
F i g u r E 1. 3
The role of statistics in experimental
research.
Sample B
Read from computer
screen
20
20
23
25
22
18
22
17
28
19
24
25
30
27
23
21
22
19
Average
Score = 22
The sample data show a 4-point difference
between the two methods of studying. However,
there are two ways to interpret the results.
1. There actually is no difference between
the two studying methods, and the sample
difference is due to chance (sampling error).
2. There really is a difference between
the two methods, and the sample data
accurately reflect this difference.
The goal of inferential statistics is to help researchers
decide between the two interpretations.
SEctIon 1.1 | Statistics, Science, and Observations
9
description of the scores. In this example, the students who studied printed pages had an average score of 26 on the test, and the students who studied text on the computer averaged 22.
Once the researcher has described the results, the next step is to interpret the outcome.
This is the role of inferential statistics. In this example, the researcher has found a difference
of 4 points between the two samples (sample A averaged 26 and sample B averaged 22). The
problem for inferential statistics is to differentiate between the following two interpretations:
1. There is no real difference between the printed page and a computer screen, and
the 4-point difference between the samples is just an example of sampling error
(like the samples in Figure 1.2).
2. There really is a difference between the printed page and a computer screen, and
the 4-point difference between the samples was caused by the different methods
of studying.
In simple English, does the 4-point difference between samples provide convincing
evidence of a difference between the two studying methods, or is the 4-point difference just
chance? The purpose of inferential statistics is to answer this question.
■
lE arn in g Ch ECk
1. A researcher is interested in the sleeping habits of American college students.
A group of 50 students is interviewed and the researcher finds that these students
sleep an average of 6.7 hours per day. For this study, the average of 6.7 hours is an
example of a(n)
.
a. parameter
b. statistic
c. population
d. sample
2. A researcher is curious about the average IQ of registered voters in the state of Florida.
The entire group of registered voters in the state is an example of a
.
a. sample
b. statistic
c. population
d. parameter
3. Statistical techniques that summarize, organize, and simplify data are classified
as
.
a. population statistics
b. sample statistics
c. descriptive statistics
d. inferential statistics
4. In general,
statistical techniques are used to summarize the data from
a research study and
statistical techniques are used to determine what
conclusions are justified by the results.
a. inferential, descriptive
b. descriptive, inferential
c. sample, population
d. population, sample
10
chaPtER 1 | Introduction to Statistics
5. IQ tests are standardized so that the average score is 100 for the entire group of
people who take the test each year. However, if you selected a group of 20 people
who took the test and computed their average IQ score you probably would not get
100. What statistical concept explains the difference between your mean and the
mean for the entire group?
a. statistical error
b. inferential error
c. descriptive error
d. sampling error
an s wE r s
1. B, 2. C, 3. C, 4. B, 5. D
1.2 Data Structures, Research Methods, and Statistics
LEARNING OBJECTIVEs
4. Differentiate correlational, experimental, and nonexperimental research and describe
the data structures associated with each.
5. Define independent, dependent, and quasi-independent variables and recognize
examples of each.
■■Individual Variables: Descriptive Research
Some research studies are conducted simply to describe individual variables as they exist
naturally. For example, a college official may conduct a survey to describe the eating, sleeping, and study habits of a group of college students. When the results consist of numerical
scores, such as the number of hours spent studying each day, they are typically described
by the statistical techniques that are presented in Chapters 3 and 4. Non-numerical scores
are typically described by computing the proportion or percentage in each category. For
example, a recent newspaper article reported that 34.9% of Americans are obese, which is
roughly 35 pounds over a healthy weight.
■■Relationships Between Variables
Most research, however, is intended to examine relationships between two or more variables. For example, is there a relationship between the amount of violence in the video
games played by children and the amount of aggressive behavior they display? Is there a
relationship between the quality of breakfast and academic performance for elementary
school children? Is there a relationship between the number of hours of sleep and grade
point average for college students? To establish the existence of a relationship, researchers must make observations—that is, measurements of the two variables. The resulting
measurements can be classified into two distinct data structures that also help to classify
different research methods and different statistical techniques. In the following section we
identify and discuss these two data structures.
I. One Group with Two Variables Measured for Each Individual: The Correlational Method One method for examining the relationship between variables is to
observe the two variables as they...

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