Article: Functional anatomy of the null hypothesis and of tests of it.(a discussion of research design, including the null hypothesis)

TOPIC HEADINGS IN STATISTICS TEXTS for the t test usually include the phrase "... for the difference between means." The phrase is commonly used because it describes the typical application of the test, which is to determine the probability that two sample means could have come from distributions that have the same mean. Two other forms of the t test are statistically equivalent--one for the difference between a sample mean and an arbitrary (usually hypothetical or theoretical) value, and the other for the magnitude of a linear function (contrast) of means. I examine the former form of the t test in the present study.

To evaluate the probability of a sample ...

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