# Thread: Percent From The Critical Value

1. ## Percent From The Critical Value

Afternoon,

Here is one I haven't experienced before and haven't seen discussed:

I have a series of goodness-of-fit tests using chi-square a few of which are below,

DF Chi-Square Reject Null Hypothesis
49 1744.68 Yes
81 742.33 Yes
19 228.12 Yes
13 38.05 Yes

I would like to rank the samples by how far they depart from the expected distribution. Am I able to rank these based on the percentage that the test statistic deviates from the critical value? I feel like doing such is acceptable and can be accurately interpreted, but am I missing something?

For example, in "Test A" the critical value (0.05) at 49 degrees of freedom is 66.339. The test statistic is 1744.68, which is about 185% greater than the critical value. For "Test B," at 81 degrees of freedom the critical value (0.05) is 103.010 and the test statistic is 742.33. In the case of "Test B" the test statistic is about 151% greater than the critical value. Can I interpret this to mean that the observed distribution of "Test A" is worse/less desirable/etc. than that of the observed distribution of "Test B?"

Thank you,

CAS

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