CHI SQUARE GOODNESS OF FIT TESTS

what is the chi square for goodness of fit (x²)

• non parametric test

• used on unrelated data

• used to compare different levels on one variable.

• compares the sample proportions to population proportions as specified by the null hypothesis

what is the formula for the (x²) statistic?

• Subtract the number of cases expected from the number of cases observed.

• Square this difference

• Divide the results by the number of cases expected.

• Add all the values from all the categories.

what are the chi square assumptions?

• Data for Chi-square must fall into only one category → you can’t use it on a repeated measures (within subjects) design.

• Expected frequencies must be greater than 5 in each cell of the contingency table.

what are observed and expected frequencies?

• number of pp’s measured in individual categories.

• frequencies are then compared to the Expected Frequencies predicted by the null hypothesis.

how do you work out the expected frequency in the multinomial test?

no difference between the specified categories (eg – number of men and women are equal)

how do you work out the expected frequency in the chi square goodness of fit test?

no difference the frequency distribution for the observed categories and an existing population (e.g., the number of men and women in the computing department reflects the gender balance in the whole university)

what number should not be less than in the expected frequencies?

5

what is the critical value and p value?

• Critical value – a - alpha (.05) and the df (degrees of freedom) → if critical value is larger than the observed value it’s not significant.

• P value – probability of rejecting the null hypothesis when its true

• A test value > critical value with a p value less than alpha of .05 means a significant effect