Chapter 2 Probability Topics SPSS T tests

Data file used: gss.sav

In the lecture about chapter 2, only the One-Sample T test has been explained. In this handout, we also give the SPSS methods to perform Independent Samples T tests and Paired Samples T tests, for the sake of completeness. You might need these later in the course.

How to get there: Analyze Compare Means

One-Sample T test To test the null hypothesis that a sample comes from a population with a particular mean.

Independent Samples T test To test the null hypothesis that two population means are equal, based on the results of two independent samples.

Paired Samples T test To test the null hypothesis that two population means are equal, based on the results of two samples that are NOT independent; the means are related to each other.

One-Sample T test In a one-sample T test you must select in the source variable list the variable you want to test and move it into the Test Variable(s) List.

You can move more than one variable into the list to test all of them against the specified Test Value. For each selected variable, SPSS calculates the t statistic and its observed significance level.

Button Options The confidence interval level can be changed here. See following figure.

Output of running One-Sample T test Performing a One-Sample T test on the variable age, with a test value of 40, the results are the following: T-Test

One-Sample Statistics

1495 46,23 17,418 ,450Age of RespondentN Mean Std. Deviation

Std. ErrorMean

One-Sample Test

13,822 1494 ,000 6,23 5,34 7,11Age of Respondentt df Sig. (2-tailed)

MeanDifference Lower Upper

95% ConfidenceInterval of the

Difference

Test Value = 40

In the table One-Sample Statistics you can find the number of valid cases (N), the mean age of the respondents (Mean), the standard deviation (Std. Deviation) and the standard error (Std. Error Mean).

In the table One-Sample Test you can see the test value (40) which is tested against the age distribution. The t value is quite high (13,822) and reveals a significant (Sig. = ,000) difference. This indicates that the mean (46,23) is not equal to the test value (40). The Mean Difference (46,23 40) is also given.

Independent Samples T test

In an independent samples T test you must indicate the variable whose mean you want to test, and move it to the Test Variable(s) list. You can move more than one variable into the Test Variable list to test all of them.

Then, you must select the variable whose values define the two groups and move it into the Grouping Variable box. To define how this variable has to be split into groups 1 and 2 use Button Define groups. You can choose between the options use specified values and cut point, see following figure.

In this example, the values correspond to codes used in variable satjob2: 1 = very satisfied; 2 = not very satisfied.

The cut point can be used to separate continuous numerical variables. If one group corresponds to small values of the grouping variable and the other group to large values, select this option and enter a value that separates the groups.

Output of running Independent Samples T test When you perform an Independent Samples T test on the variable age, grouped by the variable satjob2 (Very satisfied versus Not very satisfied), the results are the following:

T-Test Group Statistics

489 43,09 13,824 ,625651 39,51 12,736 ,499

Job SatisfactionVery satisfiedNot very satisfied

Age of RespondentN Mean Std. Deviation

Std. ErrorMean

Independent Samples Test

2,943 ,087 4,522 1138 ,000 3,58 ,791 2,024 5,127

4,469 1002,625 ,000 3,58 ,800 2,006 5,145

Equal variancesassumedEqual variancesnot assumed

Age of RespondentF Sig.

Levene's Test forEquality of Variances

t df Sig. (2-tailed)Mean

DifferenceStd. ErrorDifference Lower Upper

95% ConfidenceInterval of the

Difference

t-test for Equality of Means

In the table Group Statistics you can find, for each group (Very satisfied and Not very satisfied) the number of valid cases (N), the mean age of the respondent (Mean), the standard deviation (Std. Deviation) and the standard error (Std. Error Mean).

In the table Independent Samples Test you first find the result of Levenes Test for Equality of Variances. As the name suggest, it tests the condition that the variances of both samples are equal, indicated by the value of F. A high number of F results normally in a significant difference and you should look at the row behind Equal variances not assumed. A low number of F results normally in a non-significant difference and you should look at the row behind Equal variances assumed.

In this example, the variances of the ages of Very Satisfied and Not very satisfied are compared, and the quite low value of F (2,943) reveals a not significant (Sig. = 0,087) difference. Thus, you should look at the row behind Equal variances assumed, and you should NOT use the values in the row behind Equal variances not assumed. You see that the t value is 4,522 and the 2-tailed significance of 0,000. Thus, there is a significant difference in age between the groups Very Satisfied and Not very satisfied.

Paired Samples T test

In a paired samples T test you must select each of the two variables whose means you want to compare. Make sure that their names occur in the Current Selections group, and then move them to the Paired Variables list. See following figure.

Output of running Paired Samples T test We performed a Paired Samples T test on the variables maeduc and paeduc, which are matched pairs of variables.

T-Test Paired Samples Statistics

11,10 1044 3,397 ,105

11,02 1044 4,274 ,132

Highest Year of SchoolCompleted, MotherHighest Year of SchoolCompleted, Father

Pair1

Mean N Std. DeviationStd. Error

Mean

Paired Samples Correlations

1044 ,649 ,000

Highest Year of SchoolCompleted, Mother &Highest Year of SchoolCompleted, Father

Pair1

N Correlation Sig.

Paired Samples Test

,08 3,310 ,102 -,12 ,28 ,785 1043 ,432

Highest Year of SchoolCompleted, Mother -Highest Year of SchoolCompleted, Father

Pair1

Mean Std. DeviationStd. Error

Mean Lower Upper

95% ConfidenceInterval of the

Difference

Paired Differences

t df Sig. (2-tailed)

In the table Paired Samples Statistics, separate summary statistics (mean, N, standard deviation and standard error) are given for the two matched variables.

The Correlation value in table Paired Samples Correlations indicates how strong the variables are related.

The table Paired Samples Test is most important now. A one-sample T test is performed on the differences between the two variables. The null hypothesis is that the average difference between the two measurements is 0, in the population. The test value of the one-sample T test is therefore 0. The mean (0.08) is the difference between the two means standing in the table Paired Samples Statistics (11.10 11.02 = 0.08) and the standard deviations of the difference is 3.310. The 95% Confidence Interval for the average difference is from 0.12 to 0.28. This confidence interval includes the value of 0, so the null hypotheses is true. There is no average difference between the two variables. The Sig. of the T value also indicates this, as 0.432 < 0.05.