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Quiz #3 Review - QUIZ#3 REVIEW Chi-Square Non-parametrics...

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QUIZ#3 REVIEW Chi-Square Non-parametrics tests o No assumptions about the shape of the population (Binomial, X², Sign Test) o Nominal & Ordinal Data Chi-Square Tests o Hypothesis testing procedure for nominal variables (group people into categories; i.e. hair color, gender, political parties) o Compare how well an observed distribution fits an expected distribution. The expected distribution can be based on theory, prior results, and assumption of equal distribution across categories o When do we use Chi-Square? Data in the form of frequency counts in different categories. Nominal categories (still categories although it is changed to frequencies…no rank or order (nominal data) o Two types of Chi-square tests: Goodness of Fit and Test of Association / Independence 1. Goodness of Fit a. Single nominal variable b. Dichotomous (only two choices: yes/no; male/female; correct/incorrect
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c. Can use either the binomial X²GoF d. Degrees of Freedom = number of categories – 1 i. Example: Hair color is the variable and the categories are red, blonde, black, brown, other. Df = 5-1=4 e. Formula: X² = Σ (O-E) ^2 / E Where O = observed frequencies and E= expected frequencies for each category f. For all chi-square tests the formula is the same, what changes is the formula for getting the expected frequencies and df. g. Obtaining the Expected Frequencies: you figure out the expected frequencies by multiplying the proportion in the population to which you are comparing times the # in your sample. If a population is not known, then in some cases you compare observed to an equal number of people in each category. h. X² Distribution i. Df = # categories – 1 ii. Use table to get critical value according to alpha and df (cut off values) iii. Shape varies as df changes iv. Only positive X² critical values since you square each value v. Compare obtained X² value to critical X² value vi.
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