Chapter 19: Categorical Outcomes, Chi-Square Tests

Question 1

assumptions of chi-square test:

Answer 1

1. independence: residuals are independent
2. expected frequencies: no expected values should be below 5

Question 2

chi square test of association

Answer 2

used to see whether there’s a relationship between two categorical variables in the population

comparing the frequencies you observe in certain categories to the frequencies you might expect to get in those categories by chance

Question 3

Fisher’s exact test

Answer 3

the larger the sample, the better the chi square distribution approximation

expected frequencies in each cell should be greater than 5 , if not, the sampling distribution of the test statistic is too deviant from a chi square distribution to be accurate

fisher’s exact test: way to compute the exactly probability pf the chi square test statistic in small samples
- used on 2x2 contingency tables/small samples

Question 4

p notation

Answer 4

proportion of units in a sample that have a characteristic

mean of a dichotomous variable in the sample and has the same properties of a sample mean

p is an estimator of pi (E(p) = pi)

sampling distribution becomes normal as n increases (higher n = more normal distribution)

variance/SD = pi (1-pi) or square root pi(1-pi)

SE of p: square root of (p(1-p)/n)

Question 5

pi notation

Answer 5

proportion of units in the population that have a characteristic

Question 6

chi square goodness of fit

Answer 6

Use the goodness-of-fit test to decide whether a population with an unknown distribution “fits” a known distribution

can determine whether the shape of a distribution differs from a theoretical distribution

only one observed value exists

Question 7

z test

Answer 7

can be used to test whether a sample proportion differs significantly from the hypothesized value of pi