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Modern Robust Data Analysis Methods: Measures of Central
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... discrepancy between the actual distribution of T versus the distribution under normality, and this results in very poor control over the probability of a Type I error when n ⳱ 20. Westfall and Young (p. 40) noted that problems with controlling the probability of a Type I error persist even when n ⳱ ...
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Student's t-test

A t-test is any statistical hypothesis test in which the test statistic follows a Student's t-distribution if the null hypothesis is supported. It can be used to determine if two sets of data are significantly different from each other, and is most commonly applied when the test statistic would follow a normal distribution if the value of a scaling term in the test statistic were known. When the scaling term is unknown and is replaced by an estimate based on the data, the test statistic (under certain conditions) follows a Student's t distribution.
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