W9 Ch. 28 - Measures of Association for the Categorical Variables - Chi-Square

nominal, ordinal

What levels of data are typically used with questions of proportions or frequencies?

chi-square

family of tests used to analyze data by determining if there is a difference between proportions observed within a set of categories and the proportions that would be expected

chi-square statistic

assumptions: (1) frequencies represent individual counts, (2) categories are exhaustive and mutually exclusive

increases

As difference between observed and expected frequencies increase, the chi-square statistic INCREASES/DECREASES. (think about equation)

zero

If the observed and expected frequencies are the same, the chi-square statistic is ___> (think about equation)

goodness of fit

use of chi-square; determine if a set of observed frequencies differs from a given set of theoretical frequencies that define a specific distribution; testing to see if sample is actually split 50:50 (or other ratio) on some attribute; comparing frequency counts with a known or theoretical distribution

uniform distribution, known distribution

List the two common models of goodness of fit tests.

uniform distribution

model of goodness of fit test; assumes all categories have equal probabilities; used to test if outcomes are equally likely (ex: rolling fair die)

known distribution

model of goodness of fit test; compares observed data to a specific, pre-defined distribution; used when probabilities are based on prior knowledge or theory (ex: expected frequencies in a population with a know proportion of subgroups)

less

Sample sizes should be large enough that no expected frequencies are MORE/LESS than 1.

test of independence

use of chi-square; examines the degree of associated between two independent categorical variables; example - DPT student classified as sex and module preference ... is there a relation?

McNemar's test

used if the categorical variables are dependent/paired/repeated; examines the potential association between two categorical variables in a repeated measures design commonly used in pre- and post- studies where the same subjects are exposed to two conditions; ex - clinic patients experiencing joint paint before or after tx

Fisher's Exact test

alternative to chi-square test for analyzing small sample sizes or when expected frequencies in a contingency table are low (<5)