CHI-SQUARE GOODNESS OF FIT TEST u A nonparametric statistic u Nonparametric: u does not test a hypothesis about a population value (parameter) u requires fewer assumptions and can be used to replace parametrics

Chi-Square Goodness of Fit u Purpose: Test whether an observed frequency distribution differs from a Null Hypothesis frequency distribution u Design: Individuals categorized into two or more groups

u Assumptions: u independent observations u mutually exclusive groups u expected frequencies at least 5 per cell

How it Works u Determine the frequencies you expect if the Ho is true. u Compare the observed frequencies to the Ho expected frequencies. u Large differences between observed and expected give a large value of chi- square, likely to be significant.

Formula for Chi-Square

Chi-Square Goodness of Fit Computation Example: Registered voters took a survey in which they indicated their political party preference. Determine whether there is a significant difference in the popularity of the parties.

Observed frequencies RepublicansDemocratsOthers

STEP 1: Compute expected frequencies. Ho is equal frequencies, so divide total number of people by number of groups. fe = ( )/3 = 75/3 = 25 per group

STEP 2: For each group, compute (fo-fe) 2 and divide by fe.

Republicans Democrats Others

STEP 3: Add up the results across all the groups to get the chi-square.  2 = = 1.04

STEP 4: Look up  2 -critical in table, using df = # of groups-1. df = 3-1= 2  2 crit = 5.99

STEP 5: Compare your x 2 to the critical value.  2 = 1.04  2 crit = 5.99 Not significant.

APA Format Sentence A chi-square goodness of fit test showed no significant difference among the three parties,  2 (2, N = 75) = 1.04, p >.05.