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Inference for Chi Square Two-way Tables

Inference for Chi Square Two-way Tables. Chapter 11 Section 2. 13.2 Two-Way Tables. There are two types: the Test of Homogeneity, and Test of Independence Also called Contingency Tables allows you to do multiple comparisons of proportions

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Inference for Chi Square Two-way Tables

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  1. Inference forChi Square Two-way Tables Chapter 11 Section 2

  2. 13.2 Two-Way Tables • There are two types: the Test of Homogeneity, and Test of Independence • Also called Contingency Tables • allows you to do multiple comparisons of proportions • This test is conducted when comparing categorical data and responses are counts of yes or no, success or failure, A,B, C, or D. Etc.

  3. Test of Homogeneity Test of Homogeneity – compares distributions of a single categorical variable across 2 or more populations or treatments. For example: The distribution of colors of Plain M&Ms to the distribution of colors of Peanut M&Ms to the distribution of Caramel M&Ms etc. State Ho and Ha as such Ho: There is no difference in the distribution of colors between M&M Plain, Peanut or Caramel. Ha: There is a difference in the distribution of colors of M&M Plain, Peanut and Caramel.

  4. Test of Independence Tests of Independence – compares 2 categorical variables to see if there is an association or relationship between them. For example: Is there a association between the level of education of a person and the type of car they drive? State the null and alternative hypotheses as such: Ho: There is no association between level of education of an Individual and the type of car they drive. Ha: There is an association between the level of education of an Individual and the type of car they drive.

  5. Chi Square Test in Summary Chi Square Goodness of Fit Test: 1 variable,1 population Compares sample proportions to known proportions or percentages Chi Square Test of Homogeneity: 1 variable, 2 or more populations or 1pop with2 or more treatments. Compares distribution of proportions of 1variable in 2 or more pops/or 1pop with 2 or more treatment groups. Chi Square Test of Independence: 2 variables, 1population Looks for a relationship between proportions of 2 different variables

  6. Chi Square distributions are all right skewed and their actual shape depends on their degrees of freedom = (rows-1)(columns -1) Again the larger the sample size, the closer the distribution comes to being normal. FYI: the mean of a chi square distribution is equal to its degrees of freedom and If df > 2 then the mode of the chi square distribution is (df - 2)

  7. Use Chi Square Two-way statistics to evaluate if proportions are equal, similar as for Goodness of Fit test – which compares your observed values to some standard values. • Done almost the same as goodness of fit. • Chi Square values and p values are still interpreted the same way.

  8. To perform Chi square Test of Independence • State the null and alternative hypotheses. • Calculate expected values ((row total x column total)/table total) • Calculate Chi Square value using Check assumptions • Find P-value using table C degrees of freedom = (r-1)(c-1) 5. Interpret as usual

  9. Remember, these observations only show association not causation. • Only a comparative experiment can show probable cause. • Remember your assumptions: same as goodness of fit test • SRSs • All expected counts are at least 5 • n ≤ (1/10)N Homework: page 753-754 probs. 27,29,31 & 35

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