SPSS Guide: Tests of Differences

I put this together to give you a step-by-step guide for replicating what we did in the computer lab. It should help you run the tests we covered. The best way to get familiar with these techniques is just to play around with the data and run tests. As you do it, though, think of the research questions from your project and how these tests can answer them.

One-Sample T-Test

In the SPSS menu, select Analyze>Compare Means>One Sample T-test

Select the variable(s) from the list you want to look at and click the button to move it into the Test Variable(s) area. Then enter the test value. In this example, were testing the hypothesis that the median house value is 200,000.

Select the Options button and check that the confidence interval is where you want it (the default is 95%, which is what we normally use.

Select Continue and then OK on the main window. You should get the following output.

One-Sample Statistics

N Mean Std. Deviation Std. Error Mean

D6 House Value ($) 1123 203786.40 184926.607 5518.354

One-Sample Test

Test Value = 200000

t df Sig. (2-tailed) Mean Difference

95% Confidence Interval of the

Difference

Lower Upper

D6 House Value ($) .686 1122 .493 3786.401 -7041.05 14613.85

Note that the mean is $203,786.40, which is pretty close to the hypothesized value. The significance is .493, well above the .05 threshold, so our hypothesis is supported.

How do you know whether the significance should be higher or lower than .05? Recall that this is a test of whether there is a statistical difference between the test value and the sample mean. Since the t-value is not significant, we reject the null hypothesis that there is a difference, and accept our hypothesis.

Independent Samples T-test

This test is similar to the one-sample test, except rather than testing a hypothesized mean, were testing to see if there is a difference between two groups.

For the grouping variable, you can choose a demographic trait (such as gender, age, ethnicity, etc) or any other variable that classifies your groups. (In an experimental design, it is a good way to test the differences between the control group and the manipulation group.) In this example, well use gender.

In the SPSS menu, select Analyze>Compare Means>Independent Samples T-test

Select your Test variable from the list. This is the variable for which you want to compare means. In this example, we will test C18 (I would describe myself as environmentally responsible.)

Now select the grouping variable, which is the trait youre using to divide the groups. For this example, we will select gender. Select it from the list and click the arrow next to Grouping Variable.

Then, click Define Groups and enter the values for the two groups. In this example, 1=Female and 2=Male. Also notice the Cut Point option. What if we wanted to divide the sample into two groups based on home value? The cut point would be the value where you split the sample. For example, if you entered 100,000, it would create two groups one for home value less than 100,000 and another for more than 200,000. For this example, lets stick to gender, though. Select continue, and then click OK. Youll go back to the previous window with the groups fiilled in.

Select OK, and youll get the output on the following page. Youll notice that the means appear to be pretty close and the standard deviations are pretty close, too. So the means and distribution dont appear to be different, but we need to test it statistically. This one is similar to the one-sample test, except first we have to test for equal variance.

Step One: Is there a difference in variance? If the Lavernes Test is

Group Statistics

D1 Gender N Mean Std. Deviation Std. Error Mean

C18 I would describe myself

as environmentally

responsible

1 Male 886 3.32 .963 .032

2 Female782 3.38 .957 .034

Independent Samples Test

Levene's Test

for Equality of

Variances t-test for Equality of Means

F Sig. t df

Sig. (2-

tailed)

Mean

Difference

Std. Error

Difference

95% Confidence

Interval of the

Difference

Lower Upper

C18 I would describe

myself as

environmentally

responsible

Equal

variances

assumed

.021 .886 -1.248 1666 .212 -.059 .047 -.151 .034

Equal

variances not

assumed

-1.249 1642.573 .212 -.059 .047 -.151 .034

The Lavernes test of .886 indicates that we should assume equal variances.

The t-test significance is .212, so there does not appear to be a difference in means. The null hypothesis is supported.

Paired Samples t-test

With the paired samples t-test, were not testing for differences between groups. Instead, were testing for means of different variables within the sample sample.

For example, we want to compare the mean for user-created videos and the mean for company-generated videos.

Go to Analyze>Compare Means>Paired Samples T-test

Select the two variables you want to compare, and click the arrow to move them into the Paired Variables pane.

Under options, make sure that youre using a 95% confidence interval.

Click continue and then OK and youll get the following output.

Paired Samples Statistics

Mean N Std. DeviationStd. Error

MeanPair 1 C4 I like YouTube

videos created by the sponsor company of the product or brand

2.90 1274 1.191 .033

C5 I like YouTube videos created by customers/fans of the product or brand

3.05 1274 1.183 .033

Paired Samples Correlations

N Correlation Sig.Pair 1 C4 I like YouTube videos

created by the sponsor company of the product or brand & C5 I like YouTube videos created by customers/fans of the product or brand

1274 .689 .000

Paired Samples Test

Paired Differences

t

dfSig. (2-tailed)

MeanStd.

Deviation

Std. Error Mean

95% Confidence Interval of the

Difference

Std. Deviation

Std. Error MeanUpper Lower

Pair 1

C4 I like YouTube videos created by the sponsor company of the product or brand -C5 I like YouTube videos created by customers/fans of the product or brand

-.146 .936 .026 -.197 -.095 -5.568 1273 .000

Remember that the null hypothesis is that there is no difference between the means. Note that the absolute value of the t-value is greater than the critical value (1.96). Since the significance is .000, which is less than .05 we can reject the null hypothesis and conclude that there is a difference between the two means. If you look at the descriptive statistics for the paired sample, you can see which mean is greater.

One-Way ANOVA

What if we want to test for differences between more than two groups. ANOVA (which stands for Analysis of Variance) is the way to go.

Analysis>Compare Means>One-Way ANOVA

Select the variable(s) you want to test and move into the Dependent List pane.

Now, move the variable that you are using to separate them into groups into the Factor pane. For example, in our data set, there are three age groups (1,2 and 3) for the 15-18, 19-24, and 25+ groups, respectively, in the AgeGroup variable.

Click OK and you get the following output.

ANOVA

CON1

Sum of Squares df Mean Square F Sig.

Between Groups 2.707 2 1.353 1.604 .202

Within Groups 1081.801 1282 .844

Total 1084.508 1284

The F-test is less than the critical F-value (1.604Compare Means>One Way ANOVA but this time, click Post-Hoc

Then, select Tukey and Duncan

You will get the following output for the Tukey test.

Post Hoc Tests

Multiple Comparisons

Dependent Variable:CON2

(I) AgeGroup

AgeGroup

(J) AgeGroup

AgeGroup

Mean Difference (I-

J)

Std.

Error Sig.

95% Confidence Interval

Lower

Bound

Upper

Bound

Tukey

HSD

1 15-18 year olds 2 19-24 year olds .00831 .05820 .989 -.1282 .1449

3 25 years old + .27527* .05816 .000 .1388 .4117

2 19-24 year olds 1 15-18 year olds -.00831 .05820 .989 -.1449 .1282

3 25 years old + .26696* .05789 .000 .1311 .4028

3 25 years old + 1 15-18 year olds -.27527* .05816 .000 -.4117 -.1388

2 19-24 year olds -.26696* .05789 .000 -.4028 -.1311

*. The mean difference is significant at the 0.05 level.

Notice that the output compares the group in the left column with the other two groups in the right column and gives you the significance level and the difference in means. The 25 year old + group is significantly different (p=.000) than the other two groups, but there is no significant difference between the 15-18 year olds and 19-24 year olds. The mean difference column indicates that I-J = .27527); that is, the mean for 15-18 year-olds mean for 25yo + = .27527. In other words, the mean for 15-18 year olds is .27527 higher (on a 1-5 scale) than the 25+ yo.

Also, the Duncan and Tukey tests both create homogenous groups (segments, in strategy terms) based on their means.

CON2

AgeGroup

AgeGroup N

Subset for alpha = 0.05

1 2

Tukey HSDa 3 25 years old + 433 3.3409

2 19-24 year olds 432 3.6079

1 15-18 year olds 424 3.6162

Sig. 1.000 .989

Duncana 3 25 years old + 433 3.3409

2 19-24 year olds 432 3.6079

1 15-18 year olds 424 3.6162

Sig. 1.000 .886

Means for groups in homogeneous subsets are displayed.

a. Uses Harmonic Mean Sample Size = 429.629.

As you would expect from the previous test, the 25+ group forms one segment and the other two age groups form a second segment. The values (3.3409, etc.) are the means for each group.