## SPSS: Analyze: Inferential Statistics

#### Compare Means : One Sample T-Test

Use to test the claim that a population mean is equal to a specific value.

In this particular example, we will test the claim that the mean height is = 65.

You can only do a two-tail test in SPSS. That may sound limiting, but it's not really. If you have a one-tail test, just divide the p-value SPSS gives you by two to make the decision.

See the output of the T-Test procedure.

#### Compare Means : Independent Samples T-Test

When comparing two means, you have to use a grouping variable.

Once you've decided on your grouping variable, SPSS makes you define your groups. If there are only two groups, as in the case of gender, then specify the two values.

If you have more than two groups, then you can specify a cut point. All values less than the cut point go into one group and all values greater than or equal to the cut point go into the second group.

The output also gives the results of an F-test to see if the variances are equal. You should use the appropriate p-value from the t-test.

See the output from the T-Test procedure.

#### Compare Means : Paired Samples - T-Test

This would be appropriate to use when you have paired data such as a before and after score. I don't have any in my dataset, so I can't show an example with the data.

#### Compare Means : One-Way ANOVA

This is used to test the equality of three or more means. The "Factor" variable is a grouping variable that should have at least three distinct values. The dependent variables are the response variables that you wish to see if the means are equal.

Tests about one, two, or more proportions can be found under Non-Parametric Tests. Remember that for tests about proportions, the expected frequencies of each category have to be at least five to use parametric tests.

#### Non-Parametric Tests : Binomial

Test a claim about a single population proportion.

Specify the variable to test. In this case, we're testing that the probably of being male is 0.50.

See the output from the Binomial procedure.

#### Non-Parametric Tests: Chi-Square

This procedure is used to perform a chi-square goodness of fit test. If your test variable(s) are dichotomous, then you can test the equality of two proportions.

This is the frequencies procedure run with the chi-square option checked.

In this particular example, we're testing that all seasons appear with equal frequency.

See the output from the Frequencies procedure.

Two test the equality of two variances, use the test for two independent means mentioned above. This can also be done under the explore procedure, but explore gives a ton of information that may not be necessary.

### Tests for Normality

Much of our parametric hypothesis testing requires that data be approximately normally distributed. The normal distribution, student's t, chi-square, and F tests all required that. So, other than looking at a Normal Probability Plot (Q-Q Plot), how do you tell?

#### Non-Parametric Tests : 1 Sample K-S

The One Sample Kolmogorov-Smirnov Test can be used to test whether data is normally distributed. It can also test whether the data comes from an uniform, poisson, or exponential distribution.

The null hypothesis is that the data is distributed as claimed, so if the p-value is less than the level of significance, we will reject that claim and say it's not. Otherwise, we will assume that it is distributed as indicated.

See the output of the Kolmogorov-Smirnov test.