T Tests

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This is the statistical test used to compare means.

When you know the standard deviation of your population, you use a z ratio. However, most times we are not this lucky. When we don't know the standard deviation of the population, we use a t test. So the t test helps us approximate the populations. The distribution of the t test starts to look more like the normal curve as your sample size increases. So larger samples are better!

To use a t test, your independent variable must be dichotomous (nominal with only 2 catergories)  and  your dependent variable must be interval or ratio.

One Sample or One Group
This allows you to compare the mean of a sample to the mean of a population.

If this test is significant, the sample mean is significantly different from the population mean. This means the sample is not likely from that population.

If this test is not significant, your sample mean is not significantly different from the population mean. This means the sample is most likely from that population.


 * For example, since we know IQ in the United States has a mean of 100 and a standard deviation of 15, we can use this information for our population. Then we can compare a sample of people to determine if they are likely to have come from that population.

One Sample in SPSS

 * 1) Click 'Analyze'
 * 2) Highlight 'Compare Means' à 'One Sample T-test'
 * 3) Move the IV from the left column to the right column (Test Variable(s))
 * 4) Enter the Test value (i.e., the population mean)
 * 5) Click 'Options' if you wish to change your confidence interval
 * 6) Click 'OK'
 * 7) Your output should appear1_group_t_test_spss_output.jpg

Independent Measures
This allows you to compare the means of two different samples.


 * For example, imagine a study was done to determine whether studying more resulted in better test grades. One group studied for 1 hour per day and another group studied for 6 hours per day. Then the test scores of the two different groups can be compared with an independent measures t test to find out which did better!

This type of t test has a few assumptions.


 * (1) The scores in each sample must be independent (so like in the example above, the students in one study group could not influence the students in the other study group).


 * (2) The two populations from which the samples are selected are normally distributed.


 * (3) The two populations from which the samples are selected have equal variance (Homogeneity of Variance).

Homogeneity of Variance
This is when the variances of populations are equal or the variances of samples are not significantly different.

If population variances are equal, sample variances should be similar. When sample variances are siimilar, we can be fairly confident Homogeneity of Variance has not been violated.

If this assumption is not met, it means our samples came from different populations. This makes it so that we cannot accurately compare our samples. Meaning, we cannot use the t test if Homogeneity of Variance is violated!

You must test for Homogeneity of Variance before you conduct your independent measures t test. A common test is the Hartley's FMax Test. If this test is significant, then the variance of your samples are significantly different. In this case, you cannot use the independent measures t test because your samples are most likely to have come from different populaitons. If this test is not significant, then the variance of your samples are not significantly different. In this case, you can use the independent measures t test because your samples are most likely to have come from the same population.

Independent Measures in SPSS

 * 1) Click on 'Analyze'
 * 2) Highlight 'Compare Means' -> 'Independent Samples T-Test'
 * 3) Move the DV into the column labeled 'Test Variable(s)'
 * 4) Move the IV into the column labeled 'Grouping Variable'
 * 5) Click 'Define Groups' and specify the value that defines group 1 and group 2
 * 6) Click 'Continue'
 * 7) Click 'OK'
 * 8) Your output should appear

Repeated Measures
This allows you to compare two different means from the same sample.


 * For example, pretend a study was done to determine if playing video games improves spatial abilities. First, participants were tested for spatial ability. Then participants played video games for 20 hours. After playing the video games, the participants were tested again for spatial ability. Finally, the spatial ability scores before the video games were compared to the spatial ability scores after playing video games to see if there was an improvement.

For repested measures t tests, we don't have to worry about Homogeneity of Variancebecause we use the same sample twice (so it has to come from the same population).

Repeated Measures in SPSS

 * 1) Click on 'Analyze'


 * 1) Highlight 'Compare Means' -> 'Paired-Samples T-Test'


 * 1) Click the first IV and click the arrow so it moves from the left column to the right column (under 'Variable 1')


 * 1) Click on the second IV and click on the arrow so it moves from the left column to the right column (under 'Variable 2')


 * 1) Click 'OK'


 * 1) Your output should appear

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