STATS 250 Lecture Notes - Lecture 39: Count Data, Test Statistic, Null Hypothesis
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I. Chi-Square Analysis
A. Inference for Categorical Variables
1. Goodness of Fit Test = Assessing if a particular discrete model is a good
fitting model for a discrete characteristic, based on a random sample from
the population
a) One-sample test for count data
2. Test of Homogeneity = Assessing if two or more populations are
homogenous (alike) with respect to the distribution of some discrete
(categorical) variable
3. Test of Independence = Assess if two discrete (categorical) variables are
independent for a population, or if there is an association between the two
variables
a) Same test as homogeneity but with differently stated hypotheses
and underlying assumptions
4. All three test are based on 𝜒2test statistic, following a chi-square
distribution
B. Chi-Square Distribution
𝜒2(2) 𝑑𝑖𝑠𝑡𝑟𝑖𝑏𝑢𝑡𝑖𝑜𝑛 𝜒2(5) 𝑑𝑖𝑠𝑡𝑟𝑖𝑏𝑢𝑡𝑖𝑜𝑛
0
20
0
Chi-square distributions are skewed to the right and take on only positive
values
If we have a chi-square distribution with df = degrees of freedom, then the
a) Mean is equal to df
b) Variance is equal to 2df thus Standard Deviation is equal to √2𝑑𝑓
C. Chi-Square Table
1. Big Idea
a) Data consists of observed counts
