SPSS will execute any test you choose to run on your data. It is up to you to determine the validity of a test to execute.
One needs to verify the assumptions of the tests are fulfilled. Often graphing the data will show this.

Each of the tests listed below have an EXAMPLE data set associated with it. Clicking on the link will download the data set which can then be open in SPSS. i.e. You can download the data file and run the test.

Comparing Mean Tests

• T-Test ( Parametric test of differences between means a PDF)
  For t-tests, the assumptions are normal distribution and equal variance between groups. Both of these can be determined with a scatter plot and a side-by-side box plot, although histogram might be the most useful tool to determine a normal distribution. (SPSS can actually fit a "true" normal distribution over the distribution of your data. This is in the dialog box for histogram under the Variable input.)
  • One-Sample T-Test
  • Independent Samples T-Test
  • Paired (Dependent) T-Test
• ANOVA
  Assumptions listed below.
  • One-Way ANalysis Of VAriance (ANOVA)
  • Factorial ANalysis Of VAriance (ANOVA)

Correlation
For correlation, all you would need to assume is a normal distribution, which can be seen in a scatter plot. If the data look skewed or exponential, one should use a Spearman's Rho correlation, which is in the dialog box for correlation. Rho accounts for the curvature.

Regression
Assumptions listed below.

Kappa's Test for Inter-rater Reliability

For Regression and ANOVA, the assumptions are

(1) A linear relationship between the explanatory and response variables.
	A linear relationship can be determined with scatter plot. If the data is not linear, a log transformation needs to be done or one would need to use a non-parametric test.
(2) The observations are independent of one another.
	The independent observation assumption must be known before the data is run. (There is no test to determine whether the sampling was done correctly!)
(3) The data are normally distributed.
	A normal distribution can be seen with a histogram.
(4) The groups have equal or nearly equal variance.
	Variance can be examined with a scatterplot or a residuals versus fitted line plot.

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