Possible alternatives if your data violate goodness of fit (chi-square) test assumptions

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If the populations from which data for a goodness of fit (chi-square) test were sampled violate one or more of the chi-square test assumptions, the results of the analysis may be incorrect or misleading. If there are factors unaccounted for in the analysis, then the chi-square test may not give useful results. In such cases, stratification may provide a better analysis. Alternatively, you can use a test specifically tailored to the family of your hypothesized distribution, such as tests for normality.

Data from a continuous distribution might better match a specific hypothesized distribution after transformation.

All of these alternatives require that you have access to the original individual data values.

Alternative procedures:

For p = -0.5 (reciprocal square root), 0, or 0.5 (square root), the data values must all be positive. To use these transformations when there are negative and positive values, a constant can be added to all the data values such that the smallest is greater than 0 (say, such that the smallest value is 1). (If all the data values are negative, the data can instead be multiplied by -1, but note that in this situation, data suggesting skewness to the right would now become data suggesting skewness to the left.) To preserve the order of the original data in the transformed data, if the value of p is negative, the transformed data are multiplied by -1.0; e.g., for p = -1, the data are transformed as x --> -1.0/x. Taking logs or square roots tends to "pull in" values greater than 1 relative to values less than 1, which is useful in correcting skewness to the right. Transformation involves changing the metric in which the data are analyzed, which may make interpretation of the results difficult if the transformation is complicated. If you are unfamiliar with transformations, you may wish to consult a statistician before proceeding.

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