Paired T Test Assumptions Equal Variance

An unpaired t test compares the means of two independent or unrelated groups. Paired two sample t test used to compare means on the same or related subject over time or in differing circumstances.

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As an aside thanks to the central limit theorem you can safely use t tests to analyze nonnormal data when have 20 or more observations per group.

Paired t test assumptions equal variance. In an unpaired t test the variance between groups is assumed to be equal. Paired t tests are typically used to test the means of a population before and after some treatment i e. The result of this tool is a calculated t value.

In a paired sample t test the observations are defined as the differences between two sets of values and each assumption refers to these differences not the original data values. For our two tailed t test the critical value is t 1 α 2 ν 1 9673 where α 0 05 and ν 326. When the sample sizes are equal b true or b false yields the same result.

When running a two sample equal variance t test the basic assumptions are that the distributions of the two populations are normal and that the variances of the two distributions are the same. This test does not assume that the variances of both populations are equal. The first one lehman o rourke hatcher stepanski 2013 indicates explicitly that homogeneity of variance is an assumption for paired samples t test page 45.

In a paired t test the variance is not assumed to be equal. Two samples of math scores from students before and after a lesson. This is equal to the denominator of t in theorem 1 if b true default and equal to the denominator of t in theorem 1 of two sample t test with unequal variances if b false.

A paired t test is designed to compare the means of the same group or item under two separate scenarios. The rejection regions for three posssible alternative hypotheses using our example data are shown below. Each of these functions ignores all empty and non numeric cells.

If we were to perform an upper one tailed test the critical value would be t 1 α ν 1 6495. The dependent variable must be continuous interval ratio. The second one mcdonald 2014.

Another form of the test known as welch s t test does not assume equal variances. Does not assume that the variances of both populations are equal. However the conventional t test also assumes the standard deviations variances for both groups are equal.

The common assumptions made when doing a t test include those regarding the scale of measurement random sampling normality of data distribution adequacy of sample size and equality of variance. The paired sample t test has four main assumptions.

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