Heiman G. Basic Statistics for the Behavioral Sciences

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compute the mean, median, and/or mode, as well as the standard deviation, variance,

and/or range. For example, say we have these ten test scores:

40 33 36 38 49 39 40 38 36 37

Enter the data: Name the variable and enter the scores into the Data Editor as usual.

Select a frequency table: Repeat the previous steps for a frequency table: On the

Menu Bar, select Analyze, Descriptive Statistics, and Frequencies. Then move each

variable to “Variables(s).”

Select statistics: Click Statistics. The “Frequencies: Statistics” box appears. Under

Central Tendency, click to place a checkmark at each measure that you seek. Disper-

sion means variability, so check these measures that you seek.

Note: The standard (std.) deviation and variance given here are the estimated popu-

lation versions, what we called and , in which the final division involves .

Also, the “S.E. mean” is the standard error of the mean introduced in Chapter 6.

The output: Click Continue and click OK. You’ll see Screen B.6.

Transforming a Sample to z-Scores

Enter the data: Enter the data as above. (Let’s use the previous scores.)

Select Descriptives: On the Menu Bar click Analyze, Descriptive Statistics, and

Descriptives. The “Descriptives” box appears.

Select the variable(s): Move each variable to “Variable(s).”

Select z-scores: Check Save standardized values as variables.

The output: Click OK. The output includes the mean and standard deviation of the

raw scores. But back in your Data Editor, a new variable (a new column) will appear

containing the z-score for each raw score.

For Practice

Using the data in questions 14 and 15 in Chapter 5, determine the mean, median, mode,

estimated standard deviation and variance, and range.

N 2 1s

398 APPENDIX B / Using SPSS

SCREEN B.6

Output for Central

Tendency and Variability

Answer

B.4 Correlation Coefficients and the Linear Regression Equation 399

USING SPSS

B.4 CORRELATION COEFFICIENTS AND THE LINEAR REGRESSION EQUATION

This section describes how to compute the Pearson and the Spearman (as in

Chapter 7) and the linear regression equation (as in Chapter 8).

Computing the Pearson Correlation Coefficient

SPSS computes , as well as the mean and estimated standard deviation of the and

. (You may have more than two variables and correlate all pairs of variables.) As an

example, say that we wonder if a person’s extroversion level is correlated with his or

her aggression level. We obtain these scores:

Participant Extroversion Aggression

11423

21210

31011

41318

51920

62018

7910

849

Enter the data: Name the two variables and enter the scores in the two columns.

(Save the file for use later with regression.)

Select the correlation: On the Menu Bar, select Analyze, Correlate, and Bivariate.

The “Bivariate Correlations” box appears. Be sure Pearson is checked. (Anything refer-

ring to “significant” will make sense after you’ve read Chapter 11.)

Select the variable(s): Move the two variables you want to correlate to “Variables.”

Select Descriptives: Click Options and then check Means and standard deviations.

Click Continue.

The output: Click OK. In the “Descriptive Statistics” table are the and for

each variable. In the “Correlations” table is the “correlation matrix,” shown in

Screen B.7.

Xsr

The matrix contains the correlation coefficients produced when the variable in every

row is correlated with the variable in every column. Thus, in the first row, the (mean-

ingless) between extroversion scores and extroversion scores is . However, the

that we seek between extroversion and aggression is . (If it were negative, a

minus sign would appear.) If we had a third variable, we’d also see the between it

and extroversion and between it and aggression.

Computing the Spearman Correlation Coefficient

Say that we rank-ordered ten participants in terms of their attractiveness and their

apparent honesty and we wish to correlate these ranks.

Participant Attractive Honest

187

268

354

476

533

612

7109

822

941

10 9 5

Enter the data: Enter the scores as we did for . SPSS automatically resolves tied

ranks as discussed in Chapter 15. Also, you may enter interval or ratio scores, and

SPSS will transform them to ranks.

Select the correlation: On the Menu Bar, select Analyze, Correlate, and Bivariate.

The “Bivariate Correlations” box appears.

Select the variable(s): Move the variables you want to correlate to “Variables.”

Select Spearman: Check Spearman; uncheck Pearson.

The output: Click OK. A correlation matrix again appears. Notice that is called

“rho” here. Our between attractiveness and honesty is .1.815r

obt

1.747r

obt

11r

obt

400 APPENDIX B / Using SPSS

SCREEN B.7

Output for the Pearson r

Computing the Linear Regression Equation

SPSS computes the components of the linear regression equation. For example, in the

Pearson above, we correlated extroversion and aggression. To perform linear regres-

sion on these data, retrieve the file (or re-enter the scores).

Identify X and Y: First decide which variable is the predictor variable (your ) and

which is the criterion variable (your ). Say that we want to use extroversion scores to

predict aggression scores.

Select Regression: On the Menu Bar, select Analyze, Regression, and Linear. The

“Linear Regression” box appears.

Select the variable(s): Move your predictor or variable (here “Extroversion”)

under “Independent(s).” Move your criterion or variable (here “Aggression”) under

“Dependent(s).”

Select Descriptives: Click Statistics and, in the box check Descriptives to compute

the and for each variable and the between them. Click Continue.

The output: Click OK. Considerable information is provided, but the basic material

is shown in Screen B.8.

In the “Model Summary” table is (called R), (called R Square), and the

standard error of the estimate. (This is computed differently than our , because ours

describes the standard error for our sample, but in SPSS it is an estimate of the stan-

dard error that would be found in the population. You’ll get the same answer if, in

our defining formula for you divide by instead of .) The components of the

regression equation are in the “Coefficients” table. Locate the column under B. In the

row at “Constant” is the intercept (our a). Here, a is 5.030. In the row at our predictor

variable’s name (here, “Extroversion”) is the slope (our b). Here, b is . Thus, the

linear equation here is

For Practice

1. Compute the Pearson in Application Question 19 in Chapter 7. Compare your

output to the answers in Appendix D.

2. As in Application Question 21 in Chapter 8, compute the linear regression equa-

tion when using Burnout to predict Absences. Compare your output to the

answers in Appendix D.

3. Compute the Spearman Application Question 21 in Chapter 7. Compare your

output to the answers in Appendix D.

5 .780X 1 5.030.

.780

NN 2 2S

obt

B.4 Correlation Coefficients and the Linear Regression Equation 401

USING SPSS

SCREEN B.8

Output for Linear

Regression

B.5 THE ONE-SAMPLE t-TEST AND SIGNIFICANCE TESTING

OF CORRELATION COEFFICIENTS

As discussed in Chapter 11, this section describes how to (1) perform the one-sample

t-test and compute the confidence interval for , and (2) perform significance testing

of the Pearson and Spearman coefficients.

The One-Sample t-Test

SPSS simultaneously computes and for the sample, performs the t-test, and com-

putes the confidence interval. For example, we want to test if poor readers score differ-

ently on a grammar test than the national population of readers (where so

). Our dependent (grammar) scores are

72 67 59 76 93 90 75 81 71 93

Enter the data: Name the variable and enter the scores as usual.

Select the t-Test: On the Menu Bar, select Analyze, Compare Means, and One-sample

T Test. The “One-Sample T Test” box appears.

Select the variable: Move your dependent variable to “Test Variable(s).”

Enter : Click the space at Test Value and enter your value of . (For the example,

enter 89.)

The output: Click OK. The “One-Sample Statistics” table shows the and

for our data. The “Std. Error Mean” is . The t-test results are in Screen B.9.

Deciding if a Result Is Significant

In Screen B.9, the is with . For a two-tailed test you do not need to look

up . Under “Sig. (2-tailed)” is the smallest possible value of that is needed for the

results to be significant. This must be less than or equal to your for the results to be sig-

nificant. In the example is , indicating that is significant if the region of rejection

is the extreme of the sampling distribution. Thus, is in a region that is smaller than

our usual of the curve. Therefore, this would be beyond our , so it is significant.

If the “Sig. (2-tailed)” value is .000, it means that —and —is less than .

On the other hand, if “Sig. (2-tailed)” had been, say, , then this is beyond

only when the region of rejection is of the curve. This is larger than our region,

so is not beyond our , and is not significant.t

crit

obt

.05.06

crit

obt

.06

.001p␣

crit

obt

.05

obt

.012

obt

.012

␣

␣t

crit

df 5 923.424t

obt

111.4612

X 177.702

␮␮

: ␮ 5 89

␮ 5 89;

␮

402 APPENDIX B / Using SPSS

SCREEN B.9

Output for the One Sample t-Test

The Confidence Interval for

Also in Screen B.9 is a slightly different version of a confidence interval. It indicates

the minimum and maximum difference that is likely between the in and the rep-

resented by our sample. To convert this to our confidence interval, add the values

shown under “Lower” and “Upper” to the in your . Here we happen to be adding

negative numbers, so adding to 89 gives 69.5016; adding to 89

gives 85.8984. Thus, after rounding, the 95% confidence interval for the of poor

readers is .

Significance Testing of the Pearson Correlation Coefficient

SPSS performs significance testing when it calculates . For example, previously in

Section B.4, we correlated extroversion and aggression. Retrieve that file and on the

Menu Bar again select Analyze, Correlate, and Bivariate. In the “Bivariate Correla-

tions” box, be sure Flag significant correlations is checked. Also check whether you

want a one-tailed or a two-tailed test. Click OK. The relevant output is the “Correla-

tions” table in Screen B.10.

The . The second row shows “Sig. (2-tailed)” and to its right is .

This is interpreted as discussed previously in the one-sample t-test: is less than

so the is significant in a two-tailed test. In fact, notice the * at and the

footnote under the table. For a one-tailed test, we interpret “Sig. (1-tailed)” as above.

Significance Testing of the Spearman

Correlation Coefficient

Interpret the output for a Spearman like the Pearson r. For example, in Section B.4,

we correlated rankings that reflected attractiveness and honesty, producing Screen B.11.

The . The “Sig. (2-tailed)” is . Because is less than , this

is significant.

For Practice

1. Perform the t-test in Application Question 11 in Chapter 11.

2. For these SPSS results, determine whether each is significant .

(a) , Sig. (2-tailed) ; (b) ,

Sig. (2-tailed) ; (c) , Sig. (2-tailed)

Answers

1. Compare your output to the answers in Appendix D.

2. (a) Significant; (b) significant; (c) not significant.

5 .20t

obt

522.21, N 5 85 .000

obt

52.531, N 5 1805 .041N 5 28r

51.42,

1␣ 5 .052

.05.004.004r

51.815

.747r

obt

.05,

.033

.033r

obt

5 .747

69.50 # ␮ # 85.90

␮

23.1016219.4984

␮

␮H

␮

B.5 The One-Sample t-Test and Significance Testing of Correlation Coefficients 403

USING SPSS

SCREEN B.10

Significance Test of r

B.6 TWO-SAMPLE t-TESTS

This section describes how to compute the independent-samples and related-samples

t-test (as in Chapter 12) along with the corresponding confidence intervals and descrip-

tive statistics.

Identifying the Conditions of the Independent Variable

First, we must tell SPSS the condition in which each participants’ dependent score

belongs. For example, say that we test the influence of the independent variable of the

color of a product’s label (Blue or Green) on the dependent variable of how desirable it

is, obtaining these scores:

Independent Variable: Color

Condition 1: Condition 2:

Blue Green

10 20

12 24

14 28

17 19

16 21

Name the variables: In the Data Editor, name one variable using the independent

variable (Color) and one using the dependent variable (Desire.)

Label the output: We will use a number to tell SPSS in which condition each score

belongs. So first, arbitrarily choose a number to identify each condition. Lets use “1”

for Blue and “2” for Green. However, it is very helpful to have output in which the con-

ditions are labeled with words and not 1s and 2s. Therefore, while in variable view in

the Data Editor, in the row for the independent variable, click on the rectangle under

“Values” and then in it click the gray square with the three dots. In the “Values Label”

box, at “Value,” enter the number for one condition (e.g., 1). At “Value Label,” enter

the name of the condition for the output (e.g., Blue). Click Add. Likewise, in the same

“Values Label” box, enter “2” and “Green,” and click Add. Click OK.

404 APPENDIX B / Using SPSS

SCREEN B.11

Significance Test of r

Enter the data: Return to data view. To enter each dependent score, first identify the

condition by entering the condition’s number under “color.” Then, while in the same

row, enter the score under “desire.” Thus, for the first participant in Blue who scored 10,

in the first row of the Data Editor, enter a 1 under “color” and a 10 under “desire.” Next

enter 1 and 12 and so on. In the sixth row, enter 2 (for Green) under “color,” with 20

under “desire,” and so on. The completed Data Editor is in Screen B.12.

B.6 Two-Sample t-Tests 405

USING SPSS

SCREEN B.12

Data Editor for the

Independent-Samples

t-Test

The Independent-Samples t-Test

Enter the data: Input the data as described above. Save this file. (The following

assumes that you have equal ns.)

Select the t-test: On the Menu Bar, select Analyze, Compare Means, and Independent-

Samples T-test. The “Independent-Samples T-test” box appears.

Select the variables: Move your dependent variable (Desire) to “Test variable(s).”

Move your independent variable to “Grouping Variable.”

Identify the conditions: Click Define groups. In the “Define Groups” box, enter the

number used to identify each condition. (We used 1 and 2.) Click Continue.

The output: Click OK. In the “Group Statistics” box is the and for each condi-

tion. The t-test is in the “Independent Samples Test” box, as in Screen B.13.

Read the row for “Equal variances assumed”: The is , with . The

“Sig. (2-tailed)” is , so is significant. The “Mean Difference” is the difference

between the means of the two conditions. The “Std. Error Difference” is our .

The confidence interval is for the difference between the , so with rounding,

. You must compute the effect size using our formula

for .r

213.38 # ␮

2 ␮

#23.82

␮s

obt

.003

df 5 824.147t

obt

The Related-Samples t-Test

For a related-samples t-test, we enter the data differently than above. For example, say

that we study the total errors made in estimating distance by the same people when

using one or both eyes. We obtain these data:

One Eye Two Eyes

10 2

12 4

Enter the data: In the Data Editor, create two variables, each the name of a condi-

tion of the independent variable (for example, One and Two). Then in each row of the

Data Editor, enter the two dependent scores from the same participant; for example, in

row 1, enter 10 under One and 2 under Two. (In a matched-samples design, each row

contains the two scores from a matched pair.)

Select the t-test: On the Menu Bar, select Analyze, Compare Means, and Paired-

Samples T-test. The “Paired-Samples T-test” box appears.

Select the variables: In the area under “Paired Variables,” drag and drop each of

your variables into the highlighted row labeled “1.” Drop one variable under “Variable

1” and the other under “Variable 2.”

The output: Click OK. The output for the t-test is in the “Paired Samples Test” table

as in Screen B.14.

The “Mean” (6.6) and “Std. Deviation” (1.52) are our and . The “Std.

Error Mean” is our . The confidence interval is for , so with rounding,

. The is , with . The “Sig. (2-tailed)” is , so

the results are significant .

The output also includes the “Paired Samples Statistics” table, containing the and

in each condition. In the “Paired Samples Correlations” table is the Pearson

between the scores in the two conditions. This is not effect size! For that, you must use

our formula for .

For Practice

1. Perform the independent-samples t-test in Application Question 21 in Chapter 12.

Your answers should match those in Appendix D.

1p 5 .0012

.001df 5 419.731t

obt

4.72 # ␮

# 8.48

␮

406 APPENDIX B / Using SPSS

SCREEN B.13

Output for the Independent-Samples t-Test

2. Perform the related-samples t-test in Application Question 15 in Chapter 12.

Compare your answers to those in Appendix D.

B.7 THE ONE-WAY, BETWEEN-SUBJECTS ANOVA

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

described in Chapter 13. This includes Tukey’s HSD comparisons, descriptive statistics

for each level, and graphs. (These instructions assume equal ns.)

Say that we expand the study discussed with the independent-samples t-test, testing

the influence of three colors on a product’s desirability. We have these data:

Condition 1: Condition 2: Condition 3:

Blue Green Yellow

10 20 24

12 24 25

14 28 26

17 19 21

16 21 23

Enter the data: Enter the data as we did in the independent-samples t-test: Name

one variable for the independent variable (for example, Color) and one for the depend-

ent variable (Desire). Again identify a participant’s condition by entering the condi-

tion’s number in the Color column (either a 1, 2, or 3). In the same row, enter that

participant’s dependent score in the Desire column.

Label the output: Use words to label each level, as we did in the independent-

samples t-test.

Select the ANOVA: On the Menu Bar, select Analyze, Compare Means, and One-

way ANOVA. The “One-Way ANOVA” box appears.

Select the Variables: Move your dependent variable (Desire) to “Dependent list.”

Move your independent variable (Color) to “Factor.”

Select the post hoc test: Click Post Hoc and, in the box that appears, checkmark the

box with only the word Tukey. Click Continue.

Select Descriptive: Click Options and, in the “Options” box, checkmark Descrip-

tive to get the and of each level.s

B.7 The One-Way, Between-Subjects ANOVA 407

USING SPSS

SCREEN B.14

Output for the Related-Samples t-Test