Heiman G. Basic Statistics for the Behavioral Sciences

Подождите немного. Документ загружается.

408 APPENDIX B / Using SPSS

SCREEN B.15

One-Way ANOVA Summary Table

SCREEN B.16

Output for Tukey’s HSD Test

Select the graph: While at the “Options” box, checkmark Means plot to produce a

line graph. Click Continue.

The output: Click OK. In the “Descriptives” table, the first three rows give the ,

and confidence interval for in each level.

The ANOVA summary table is shown in Screen B.15 above. Our is 17.452.

Under “Sig.” is the minimum needed for to be significant, so interpret this as in

previous procedures. Here the results are significant, with .

In Screen B.16 is the “Multiple Comparisons” table, showing the Tukey HSD proce-

dure. Under “(I) color” is first Blue, and in the rows here are the comparisons between

Blue and the other conditions. Thus, the first row compares the mean of Blue to the

mean of Green and the difference is . The asterisk indicates that this difference is

larger than the HSD value when , and under “Sig.” we see that . The

confidence interval is for the difference between the represented by these two level

means. Under “(I) color” at Green are the comparisons involving the mean of Green,

including again comparing it with Blue. And so on.

Note in your output the line graph of the means, which may be exported to a report

you are writing. Compute effect size using our formula for .␩

␮s

␣ 5 .001␣ 5 .05

28.6

p 6 .001

obt

␣

obt

␮

For Practice

Perform the ANOVA in Application Question 19 in Chapter 13. Confirm that your

answers match those in Appendix D.

B.8 THE TWO-WAY, BETWEEN-SUBJECTS ANOVA

This section describes how to perform the two-way, between-subjects ANOVA, as

described in Chapter 14. This includes Tukey’s HSD comparisons for main effects only,

descriptive statistics for the cells and main effects, and graphing. (These instructions

assume equal ns in all cells.) As an example, in Chapter 14, we tested the factors of vol-

ume of a message and gender on the dependent variable of persuasiveness. We had the

data shown in Table B.1.

Name the variables: In the Data Editor, name three variables: one for factor A

(Volume), one for factor B (Gender), and one for the dependent variable (Persuasion).

Arbitrarily assign a number to each level in each factor. Let’s use 1, 2, and 3 for soft,

medium, and loud, and 1 and 2 for male and female, respectively.

Label the output: Enter word labels for each factor as described in the independent-

samples t-test (B.6). Otherwise, the output is mind-boggling!

Enter the data: We must identify the cell in which each score belongs. In the Data

Editor, enter a participant’s level of A in the Volume column and, in the same row, enter

that participant’s level of B in the Gender column. While still in the same row, enter

that participant’s dependent score in the Persuasion column. Thus, in the male-soft cell

is the score of 9, so we enter 1 under Volume, 1 under Gender, and 9 under Persuasion.

See Screen B.17. Enter all scores from a cell together, so in the second row enter 1, 1,

and 4. In the third row, enter 1, 1, and 11. For the next cell, change only one factor.

Let’s change to medium volume. In row 4 of the Data Editor, for the first male-medium

score, enter 2 under Volume, 1 under Gender, and 8 under Persuasion, and so on. In row

10, go back to 1 for Volume, but enter 2 for Gender (females), and so on.

Select the ANOVA: On the Menu Bar, select Analyze, General Linear Model, and

Univariate. The “Univariate” box appears.

Select the variables: Move your dependent variable (Persuasion) to “Dependent

variable.” Move both factors to “Fixed Factors.”

Select the post hoc test: Click Post Hoc and, in the box that appears, move each fac-

tor, to “Post Hoc Test for.” Checkmark Tukey. Click Continue.

Select Descriptives: Click Options and, in the box that appears, checkmark Descrip-

tive Statistics. This will give the and for all levels and cells. Click Continue.s

B.8 The Two-Way, Between-Subjects ANOVA 409

USING SPSS

TABLE B.1

A 3 ⫻ 2 Design for the

Factors of Volume and

Gender

Each column represents a

level of the volume factor;

each row represents a

level of the gender factor.

Factor A: Volume

Level A

: Level A

Soft Medium Loud

9818

Level B

41217

Male

11 13 15

Factor B:

Gender

296

Level B

610 8

Female

417 4

N ⫽ 18

Select graphs: Click Plots. In the box that appears, to plot the main effect means,

move a factor to “Horizontal Axis” and click Add. Do the same with the other factor.

To plot the interaction, click the factor with the most levels (Volume) and move it to

“Horizontal Axis.” Click the other factor (Gender) and move it to “Separate Lines.”

Click Add and then Continue.

The output: Click OK. The ANOVA summary table is in Screen B.18.

In the row at the name of each factor is the relevant information. For Volume, the

is 7.142, which is significant . For Gender, is 11.358, which is significant

. SPSS describes the interaction here as “Volume * Gender.” The interaction1p 5 .0062

obt

1p 5 .0092

obt

410 APPENDIX B / Using SPSS

SCREEN B.17

Data Editor for the

Two-Way ANOVA

SCREEN B.18

Two-Way ANOVA Summary Table

is 6.250, and it is significant . The is in the row labeled “Error”

(8.222) and . Use these numbers when computing the HSD for the interaction.

Use the “Corrected Total” sum of squares when computing squared.

Screen B.19 above shows the “Descriptive Statistics” table. First are the cells under

soft volume. The first row is labeled “Male,” so for the cell of male-soft,

and . The second row, “Female,” describes the female-soft cell. The row

labeled “Total” has the and for the main effect of soft volume, after collapsing

across gender. In the next group of rows labeled “Medium” are the male-medium cell,

the female-medium cell, and the main effect for medium volume, and so on. In the bot-

tom rows labeled “Total” are the main effect means for gender.

Your output will also include the “Multiple Comparisons” table which shows

Tukey’s HSD test for the main effect of Volume. Interpret this as we did for the one-

way ANOVA. If the Gender factor had involved more than two levels, a separate “Mul-

tiple Comparisons” table for it would appear.

Remember that SPSS does not compute Tukey’s HSD for the interaction effect, so

use the procedure described in Chapter 14. Likewise, compute effect size—using our

formula for —for each significant effect.

For Practice

Perform the two-way ANOVAs in Application Questions 19 and 21 in Chapter 14.

Confirm that your answers match those in Appendix D.

B.9 CHI SQUARE PROCEDURES

This section describes how to perform the one-way and two-way chi square procedure,

as described in Chapter 15.

The One-Way Chi Square

In Chapter 15, we discussed a study involving the frequency of left- or right-handed

geniuses. There we had a total 10 left-handers and 40 right-handers. However, we must

let SPSS count the participants in each category. For example, let’s look at a small

␩

5 3.60555

X 5 8.0000

␩

5 12

1p 5 .0142F

obt

B.9 Chi Square Procedures 411

USING SPSS

SCREEN B. 19

Descriptive Statistics

Output for the

Two-Way ANOVA

portion of the original handedness data before the totals. We used a 1 to indicate left-

handed and a 2 to indicate right-handed.

Participant Handedness

10 2

11 1

12 2

Enter the data: In the Data Editor, name one variable (for example, Handedness).

(Label the output as in previous procedures.) Then enter the scores.

Select Chi Square: On the Menu Bar, select Analyze, Nonparametric Tests, and Chi-

Square. The “Chi-Square Test” box appears.

Select the variables: Move your variable to “Test Variable List.” (If your is not

that all frequencies are equal, under “Expected values” check Values. Then type in the

expected frequency for the lowest labeling score: We’d enter the for the number

of 1s. Click Add. Enter the for the second labeling score (2s), click Add, and so on.)

The output: Click OK. As in Screen B.20, the “Handedness” table shows the and

for each category. The “Test Statistics” table shows that with . The

“Asymp. Sig.” is , which is interpreted as in previous procedures: This is sig-

nificant, with .

The Two-Way Chi Square

Here SPSS must count the participants in each category of two variables. For example,

let’s examine the study comparing Type A or B personalities and the incidence of heart

attacks from Chapter 15. We’ll violate the assumptions and look at a very small .N

p 5 .021

␹

obt

.021

df 5 1␹

obt

5 5.33f

412 APPENDIX B / Using SPSS

SCREEN B.20

Output for the One-Way Chi Square

Participant Type Attack

111

222

322

412

511

621

711

822

911

10 2 2

11 1 1

12 2 2

Enter the data: Name the two variables (for example, Type and Attack). For each,

determine the scores that will indicate the categories. Above, a 1 is Type A and a 2 is

Type B. Also, a 1 indicates a heart attack, and a 2 indicates no attack. (Label the output

as we’ve done for previous procedures.) Then, for each participant, enter in the same

row the scores that indicate category membership on each variable: For participant 1,

enter 1 under Type and 1 under Attack. For participant 2, enter 2 and 2, and so on.

Select the Chi Square: On the Menu Bar, select Analyze, Descriptive Statistics, and

Crosstabs. The “Crosstabs” box appears.

Select the variables: This design forms a matrix. Move the variable

you want to form the rows of the matrix to “Rows.” Move the variable that forms the

columns to “Columns.”

Select a bar chart: Checkmark Display clustered bar charts.

Select the statistics: Click Statistics. In the box that appears, checkmark Chi-square.

Below that, checkmark Contingency coefficient or Phi and . . . (in this example, its the

latter). Click Continue.

Select the expected frequencies: To see the in each cell, click Cells. In the box

that appears, under “Counts” checkmark Expected. Click Continue.

The output: Click OK. In your output is the table labeled “HeartAttack*Type

Crosstabulation.” In it is the matrix containing the observed and expected fre-

quencies (count). In the “Chi-square Tests” table, at “Pearson Chi-Square,” is the

of 5.333, with . The “Asymp. Sig.” is , which is interpreted as in previous

procedures, so is significant . In the “Symmetric Measures” table, the

phi coefficient is .

For Practice

1. In a survey, Foofy finds that three people prefer country music, nine prefer hip-

hop, and two prefer classical. Compute the for these data. (a) What is and

(b) Are the results significant? (c) What is ?

2. In another survey, Foofy asks if people like (1) or dislike (2) country music and if

they like (1) or dislike (2) classical music. Compute the on the following data:␹

pdf ?

␹

obt

␹

.667

1p 5 .0212␹

obt

.021df 5 1

␹

obt

2 3 2

2 3 22 3 2

B.9 Chi Square Procedures 413

USING SPSS

Participant Country Classical

121

212

322

412

521

621

712

822

911

10 2 2

11 2 2

12 2 2

(a) What is and ? (b) Are the results significant? (c) What is ? (d) Does

the bar chart show an interaction?

Answers

1. (a) , ; (b) Significant; (c)

2. (a) , ; (b) Not significant; (c) ; (d) No: Connecting the

tops of the “Like” (blue) bars with one line, and the tops of the “Dislike” (green)

bars with another produces close to parallel lines.

B.10 NONPARAMETRIC TESTS FOR RANKED SCORES

The following describes how to compute the Mann–Whitney , the Wilcoxon , the

Kruskal–Wallis , and the Friedman tests, which are discussed in Chapter 15. How-

ever, use our formulas for computing effect size and post hoc tests. For each, the

dependent scores can be ranks, or they can be interval or ratio scores that SPSS will

automatically convert to ranks. You can compute descriptive statistics for these raw

interval/ratio scores by selecting Options and then checking Descriptive.

The Mann–Whitney U Test

Enter the data: Create the Data Editor as in the independent-samples t-test (B.6).

Select the nonparametric test: On the Menu Bar, select Analyze, Nonparametric

Tests, and 2 Independent Samples. The “Two Independent Samples” box appears.

Under “Test Type” check Mann-Whitney .

Select the variables: Move your dependent variable to “Test Variable List.” Move

your independent variable to “Grouping Variable.”

Define the groups: Click Define groups and, in the box that appears, enter the num-

ber that you used to identify each condition. Click Continue.

The output: Click OK. In the “Test Statistics” table, is at “Mann–Whitney .”

The minimum needed to be significant is at “Asymp. Sig. (2-tailed).”␣

obt

␹

p 5 .665df 5 1␹

obt

5 .188

p 5 .046df 5 2␹

obt

5 6.143

pdf␹

obt

414 APPENDIX B / Using SPSS

The Wilcoxon T Test

Enter the data: Create the Data Editor as in the related-samples t-test (B.6).

Select the nonparametric test: On the Menu Bar, select Analyze, Nonparametric

Tests, and 2 Related Samples. The “Two Related Samples” box appears. Under “Test

Type” check Wilcoxon.

Select the variables: In the area under “Test Pairs,” drag and drop each of your vari-

ables into the highlighted row labeled “1.” Drop one variable under “Variable 1” and

the other under “Variable 2.”

The output: Click OK. In the “Ranks” table are the sums of the positive and nega-

tive ranks. You may use the smaller sum as as described in Chapter 15 and com-

pare it to . Or, in the output’s “Test Statistics” table, the smaller sum is transformed

to a z-score. The minimum for this z to be significant is at “Asymp. Sig. (2-tailed).”

The Kruskal–Wallis H Test

Enter the data: Create the Data Editor as we did for the one-way, between-subjects

ANOVA (B.7).

Select the nonparametric test: On the Menu Bar, select Analyze, Nonparametric

Tests, and Independent Samples. The “Test for Several Independent Samples” box

appears. Under “Test Type” check Kruskal-Wallis .

Select the variables: Move your dependent variable to “Test Variable List.” Move

your independent variable to “Grouping Variable.”

Define the groups: Click Define Range. Enter the lowest score that you used

to identify a condition at “Minimum.” Enter the highest score at “Maximum.” Click

Continue.

The output: Click OK. In the “Ranks” table are the mean of the ranks in each con-

dition. In the “Test Statistics” table, the is at “Chi-Square,” under which is the .

The minimum for to be significant is at “Asymp. Sig. (2-tailed).”

The Friedman Test

Enter the data: Create the Data Editor as in the Wilcoxon above, but name a vari-

able for each level. For example, if you have three conditions then name three vari-

ables. Then in each row, put the three scores from the same participant in the

appropriate columns.

Select the nonparametric test: On the Menu Bar, select Analyze, Nonparametric

Tests, and Related Samples. The “Test for Several Related Samples” box appears.

Under “Test Type” check Friedman.

Select the variables: Move all variables to “Test Variables.”

The output: Click OK. In the “Ranks” table is the mean rank for each condition. In

the “Test Statistics” table, is the number of participants, and at “Chi-Square” is the

. At “Asymp. Sig. (2-tailed)” is the minimum a needed for to be significant.

For Practice

Perform each of the above procedures using the data from the example study that we

discussed when that statistic was introduced in Chapter 15. Compare the answers in

your output to those we obtained using the formulas.

␹

obt

␹

obt

␣

dfH

obt

␣

crit

obt

B.10 Nonparametric Tests for Ranked Scores 415

USING SPSS

B.11 THE ONE-WAY, WITHIN-SUBJECTS ANOVA

This section describes the one-way, within-subjects ANOVA that is discussed in

Appendix A.3, including descriptive statistics and graphs. The student version of SPSS

will not perform the Tukey HSD test here, so follow the instructions in Appendix A.3.

As an example, in Appendix A.3 we discussed a repeated-measures design that

measured participants’ comfort level when wearing either casual, semiformal, or for-

mal clothes. The data are shown again in Table B.2.

Enter the data: As in Appendix A.3, we treat this as a two-way design, so create the

Data Editor as we did in the two-way ANOVA: Name three variables. Name the first

Participants, the next for factor A (Dress), and the third for the dependent variable

(Comfort). Assign a number to identify each level in factor A and label the output!

Then enter the participants’ number (1, 2, or 3, . . .) under “Participants,” the level of A

under “Dress,” and the dependent score under “Comfort.” In this study, three rows in

the Data Editor will belong to the same participant, each containing the score from a

level of A. Thus, for participant 1: In the first row, enter 1, 1, and 4; in the next row,

enter 1, 2, and 9; in the third row, enter 1, 3, and 1, and so on. The completed Data Edi-

tor is in Screen B.21.

Select the ANOVA: On the Menu Bar, select Analyze, General Linear Model, and

Univariate. The “Univariate” box appears.

Select the variables: Move your dependent variable (Comfort) to “Dependent Vari-

able.” Move your independent variable (Dress) to “Fixed Factors.” Move “participants”

to “Random Factor(s).”

Select Plots: Click Plots but, to simplify matters, move only the factor (Dress) to

“Horizontal Axis.” Click Add and Continue.

Select Descriptive: Click Options and checkmark “Descriptive Statistics.” Click

Continue.

The output: Click OK. The ANOVA summary table is in Screen B.22.

We are interested in only the following: In the row labeled “Dress Hypothesis” is the

for factor A (here, 3.486). In the column labeled “Sig.” is , so this is not

significant. In the row labeled “Dress * Participant Hypothesis,” under Mean Square is

our . Use this and its when computing the HSD. When computing , add the

in the above two rows to that in the “Subject Hypothesis” row to obtain ; use

the at “Dress Hypothesis” as .SS

tot

␩

dfMS

obt

.082F

obt

416 APPENDIX B / Using SPSS

Factor A: Type of Dress

Level A

: Level A

Participants Casual Semiformal Formal

1 491

2 612 3

3 844

4 285

5 10 7 2

TABLE B.2

Data from One-Way,

Within-Subjects Study

Also in your output is the “Descriptive Statistics” box: In the rows under “Casual,”

look at the row at “Total.” This contains the and for the casual level. Likewise, find

the and for the other levels.

In your line graph, ignore that it says “estimated marginal means. . . .” They are our

real means.

For Practice

Perform the one-way, within-subjects ANOVA in Application Question 3 in Appendix

A.3. Confirm that your answers match those in Appendix D.

B.11 The One-Way, Within-Subjects ANOVA 417

USING SPSS

SCREEN B.21

Data Editor for the

Within-Subjects ANOVA

SCREEN B.22

Within-Subjects ANOVA Summary Table