Assumptions Required for t Distribution

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Chapter: Biostatistics for the Health Sciences: Sampling Distributions for Means

For the t distribution to apply strictly we need the following two assumptions:


ASSUMPTIONS REQUIRED FOR t DISTRIBUTION

For the t distribution to apply strictly we need the following two assumptions:

1. The observations are selected at random from the population.

2. The population distribution is normal.

Sometimes these assumptions may not be met (particularly the second one). The t test is robust for departures from the normal distribution. That means that even when assumption 2 is not satisfied because the population differs from the normal distribution, the probabilities calculated from the t table are still approximately correct. This outcome is due to the central limit theorem, which implies that the sample mean will still be approximately normal even if the observations themselves are not.

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