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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Pearson's Goodness of Fit Test is used to compare the observed distribution of a categorical variable to some historical reference.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.
N
The sample size used to test the hypothesis.
Alpha
The $$\alpha$$ (Type I error rate) level of the hypothesis test.
Power
The power (1 - Type II error rate) of the hypothesis test.
$$p_0$$
A comma seperated list of the reference probabilities.
p
A comma seperated list of the observed probabilities.

Note: $$p$$ and $$p_0$$ must have the same number of probabilites.

## Calculation Results

No calculation has been generated yet.

N Alpha Power
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