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The smaller the standard error of the mean, the larger the magnitude of the t-value. Therefore, the smaller the p-value. The t-value takes into account of this fact. It is the probability of observing a greater absolute value of t under the null hypothesis.
For a one-tailed test, halve this probability. If p-value is less than the pre-specified alpha level usually. For example, the p-value for write is smaller than 0. So we conclude that the mean for write is significantly different from A dependent group t-test is used when the observations are not independent of one another.
In the example below, the same students took both the writing and the reading test. Hence, you would expect there to be a relationship between the scores provided by each student. The dependent group t-test accounts for this. In the example below, the t-value for the difference between the variables write and read is 0. This is greater than our pre-specified alpha level, 0. We conclude that the difference between the variables write and read is not statistically significantly different from 0.
In other words, the means for write and read are not statistically significantly different from one another. Difference — The t-test for dependent groups is to form a single random sample of the paired difference. Therefore, essentially it is a simple random sample test.
The interpretation for t-value and p-value is the same as for the case of simple random sample. DF — The degrees of freedom for the paired observations is simply the number of observations minus 1. This is because the test is conducted on the one sample of the paired differences. It is the ratio of the mean of the difference in means to the standard error of the difference. If p-value is less than our pre-specified alpha level, usually 0.
For example, the p-value for the difference between write and read is greater than 0. This t-test is designed to compare means of same variable between two groups. In our example, we compare the mean writing score between the group of female students and the group of male students.
Ideally, these subjects are randomly selected from a larger population of subjects. Depending on if we assume that the variances for both populations are the same or not, the standard error of the mean of the difference between the groups and the degree of freedom are computed differently. That yields two possible different t-statistic and two different p-values.
When using the t-test for comparing independent groups, we need to test the hypothesis on equal variance and this is a part of the output that proc ttest produces.
The interpretation for p-value is the same as in other type of t-tests. Variable — This column lists the dependent variable s. In our example, the dependent variable is write. This variable is necessary for doing the independent group t-test and is specified by class statement.
Mean — This is the mean of the dependent variable for each level of the independent variable. On the last line the difference between the means is given.
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