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A chi square analysis is used with nominal data to determine how frequency counts are distributed for different samples. This method compares expected with observed observations. To conduct an analysis of the chi square, one must first collect the expected frequencies. After conducting a study, and gathering the observed nominal data, one must use the chi square formula. Calculate the degrees of freedom and use the chi square table to find the critical value. Next, compare the critical value to the chi square value. If the χ2 cv > χ2 , then p>.05. There would be no statistical significant difference in this case. If χ2 cv < χ2 , then p<.05. There would be statistical significant difference in this case. Lastly, one would calculate the standard residual (R) to determine which factors are the major contributors toward significance. When R>2, then this factor is a major contributor toward the chi square value.


''contributed by Chris Longo''

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In the last sentence above, it should read when the absolute value of R is greater than 2 (|R|>2), then this factor is a major contributor toward the chi square value. If the R is negative, it means there is a decrease in the data that is significant and when R is positive, it means there is an increase that is significant.


''contributed by Margie Aldrich''


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Thank you Margie. I typed that entry a while ago and didn't realize that my wording was off. Also, to add, it is important to remember that when analyzing chi square data, look at the "R" column (or calculate yourself using the formula) to determine which factors are significant. For example, in a study measuring reading achievement scores based on 4th, 5th, 6th and 7th grade teachers, also broken down by gender, you would have to look at each factor (level) individually in order to determine whether or not it is a major contributor toward significance. For example, 4th grade male teachers and 7th grade female teachers are major contributors to chi square value, based on the fact that |R|> 2.


''contributed by Chris Longo''