chi-square goodness of fit and multinomial test

chi square

nominal/ categorial data, non-para test, frequency level (why we cant find out the mean cuz the data doesn’t really have meaning)

chi square

used to compare diff lvls of one category

compares the sample propors to the pop propors as specified by the null hyp

how to calc the chi square

subtract the no of cases expected from the no. of cases observed and the square it.

after that divide the results by the no of cases expected and add all the values from all the categories

chi square assumption-expected frequencies

must be greater that 5 in each cell of the contingency table or have a total sample higher than 20to avoid type 1 error

observed freqs

the numbers of participants measured in individual categories

These frequencies are then compared to the Expected Frequencies predicted by the Null Hypothesis (that occur if the null H0 is true).

working out expected freqs

**The Multinomial test**

No difference between the specified categories ie the number of men and women are equal and not ratio-ed out

**The Chi2 goodness of fit test**

No difference between the frequency distribution for the observed categories and an existing population.

eg the number of men and women in the computing department reflects the gender balance in the whole university

calc expected freq

–For the no preference Null Hypothesis, the number of people would be predicted to be equal for each of the two categories eg

The number of observed cases in each category would make up 50% of the 50 participants recorded.  e.g. 25 participants

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–For the **comparison population** the number of people would be predicted by the distribution of the frequencies for the whole university. E.g. 45:55 eg Men = 0.45(50) = 22.5 participants

Women = 0.55(50) = 27.5 participants

**x² computation: with comparison population**

determining significance

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**Critical Value**

depends on a (alpha – usually .05), and the *df*  (degrees of freedom). 

**P-value**

the probability of rejecting the null hypothesis when it is true.

**A Test Value > Critical Value**

a *p* value less than alpha of .05 (a) means a significant effect