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Pearson Goodness of Fit Test

Pearson's Goodness of Fit Test is used to compare the observed distribution of a categorical variable to some historical reference.

Let \(X_i\) be the response from the \(i^{th}\) observation taking values in \( \{x_1, \dots, x_r \} \). If we let \(p_k = P(X_i = p_k) \) for \( k = 1, \dots, r \), Pearson's goodness of fit test tests the hypothesis:

\[ H_0: p_k = p_{k, 0} \text{ versus } H_a: p_k \ne p_{k,0} \]

where \(p_{k,0}\) is some reference value.

Power Calculation Parameters

To input multiple values, seperate them by a comma.

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Power Calculation Explanation

Solve For
The unknown you are interested in solving for.
The sample size used to test the hypothesis.
The \(\alpha\) (Type I error rate) level of the hypothesis test.
The power (1 - Type II error rate) of the hypothesis test.
A comma seperated list of the reference probabilities.
A comma seperated list of the observed probabilities.

Note: \(p\) and \(p_0\) must have the same number of probabilites.

Calculation Results

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  • Chow, S., Shao, J., & Wang, H. (2003), Sample size calculations in clinical research, New York: Marcel Dekker.