AGRI 2400 Lecture 33 - Chi-Square

Nominal (Categorical) Scale Data

• analyses like chi-sqaure assume the nominal (categorical) scale data:

  • can be assigned to 2 or more discrete and mutually exclusive categories

  • these categories make up the entire set of possible outcomes within the sample, and are therefore contingent on one another

Chi-Square Test for Goodness of Fit

• compares the observed frequencies of a nominal scale variable in a sample to the expected frequencies in a population

Caution Small Sample Sizes

• when your expected frequencies are small, there is an increased risk of Type 1 error

  • a general rule to follow is that no more than 20% of your expected frequencies should be 5 or less

  • if you violate this rule, a more appropriate analysis would be a randomization test

Chi-Square Test for Homogeneity

• to test whether two or more independent samples were drawn from the same population

  • unlike the goodness of fit approach with a single sample, there are no predefined expected values based on a population

  • instead, we examine whether the number of obs in each category are homogeneous among the samples being compared

Fisher Exact Test

• a better alternative for datasets with small sample sizes, when it can be used

• typically applied for 2×2 contingency tables

• use when more than 20% of your expected frequencies are 5 or less

• this test is unbiased and directly calculates the probability so risk of type 1 error is unaffected by sample size