Social Stats Unit 3 Week 2

chi-square ($\chi^2$)

conditional proportion test for bivariate tables; evalates relationship between 2 categorical variables

joint frequencies

cells with data that are not totals

marginal frequencies

cells that are totals

joint relative frequency

cell value divided by size of full sample

marginal relative frequency

each marginal frequency cell divided by total sample size

conditional relative frequency

joint frequency of each value of the independent variable divided by the marginal frequency of each value of the independent variable

what would it look like if there was no relationship between the 2 variables

the percentages would be the same for each

expected table calculation

(column total $\cdot$ row total) / overall total

chi-square calculation

$$\chi^2=\sum\frac{\left(O-E\right)^2}{E}$$

steps for using chi-square to assess relationships between variables

1. calculate expected values

2. calculate chi-square

3. calculate degrees of freedom

4. find critical value on the chi-square table

5. interpret results of the test

degrees of freedom

the number of independent categories that are free to vary

degrees of freedom calculation

df= (row-1) $\cdot$ (column-1)