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relation between t and f distributions

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The factor 2 disappearing since the total probability in the range (-∞, ∞) is unity. This is the probability function of student’s t – distribution with v degrees of freedom. Hence we have the following relation between t and F distributions.

If a statistic t follows student’s t distribution with n degrees of freedom then t2 follows Snedecor’s F – distribution with (1. N) degrees of freedom. Symbolically,

If t ~t(n) then t2 ~ F( 1, n)

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