Stat Methods Ch.13

chi-square test

used variables of interest are nominal variables

chi-square test for goodness of fit

examines how well an observed frequency distribution of a nominal variable fits some expected pattern of frequencies

chi-square test for independence

examines whether the distribution of frequencies over the categories of one nominal variable is unrelated to the distribution of frequencies over the categories of a second nominal variable

observed frequency

in a chi-square test, number of individuals actually found in the stduy to be in a category or cell

expected frequency

in a chi-square test, number of people in a category or cell expected if the null hypothesis were true

chi-square statistic

reflects the overall lack of fit between the expected and observed frequencies

chi-square distribution

mathematically defined curve used as the comparison distribution in chi-square tests; distribution of the chi-square statistic

chi-square table

table of cutoff sccores on the chi-square distribution for various degrees of freedom and significance levels

contingency table

two-dimensional chart showing frequencies in each combination of categories of two nominal variables

• possible to have larger ones such as 4×7

• may have relatively few degrees of freedom

independence

situation of no relationship between two variables; term usually used regarding two nominal variables in a chi-square test for independence

cell

in chi-square, the particular combination of categories for two variables in a contingency table

• key idea to keep in mind when figuring expected frequencies in a contingency table is that “expected” is based on the two variables being independent

• if they’re independent, then the proportions up and down the cells of each column should be the same

phi coefficient

effect-side measure for a chi-square test for independence with a 2×2 contingency table

cramer’s phi

measure of effect size for a chi-square test for independence with a contingency table that is larger than 2×2. AKA cramer’s V.

what are the assumptions for chi-square tests?

• the chi-square tests of goodness of fit and for indepenndence do not require the usual assumptions of normal population variances and such

• each score must not have any special relation to any scores. this means you can’t use these chi-square tests if the scores are based on the same people being tested more than once.

what is the controversy on chi-square tests?

• lewis and burke considered the most common weakness in the use of chi-square to be that expected frequencies are too low. now, that’s not really much of a problem

• lewis and burke held that every cell should have a reasonable sized expected frequencies such as a minimum of 10, with 5 as the bottom limit

  • others recommended figures from 1 to 20

what is the most important principle among the controvery of chi-square tests?

there should be at least five times as many individuals as there are cells

what do chi-square tests in research articles look like?

includes the degrees of freedom, N, the chi-square, and significance level

• X² (df, N = _ _) = (chi-square), p < .05 (or n.s. if not significant)