Chapter 11 Flashcards
Goodness-of-Fit Tests
Conducted on a single categorical variable within multiple categories. Used to determine if observations fall into the categories at certain rates according to certain distributions.
Test for Independence
Conducted on two categorical variables. Used to determine if the two variables are related.
Chi Squared much like t-distributions use _____
degrees of freedom.
How do degrees of freedom differ between chi-squared and t tests?
The chi squared distribution is always positive and right skewed.
As degrees of freedom increase, the ___ lessens and the ______ distribution becomes more ____ shaped
skew, chi-squared, bell
When is it appropriate to use goodness of fit test.
That is a single categorical variable with two or more categories of interest.
What question does the goodness of fit test attempt to answer?
How good is the fit of the model to the data? Are the observed counts in each category far enough away from what we would expect to conclude that the purported model is incorrect?
Null Hypothesis for Goodness of Fit Test
p1 = [value], p2 = [value], … , pk = [value], where k = # of categories. Represents the value of the proposed model.
Alternative Hypothesis for Goodness of Fit Test
Ha: At least one of the proportions in the null hypothesis is incorrect.
Null Hypothesis for Goodness of Fit for Multiple Categories
H0: p1 = 1/k, p2 = 1/k, … , pk = 1/k
Assumptions for Chi-Squared Goodness of Fit Test
a) Randomization
b) Expected cell frequency condition- the expected count for each category must be at least 5.
Goodness of Fit Test Statistic
Chi-squred= E(observed count-expected count)^2/ expected count.
Contribution to chi-squared
observed count-expected count)^2/ expected count.
Conclusions for chi-squared goodness of fit tests.
1) If p-value is less than alpha, reject null hypothesis. There is evidence to conclude that the hypothesized distribution if incorrect. The data indicate the population does not follow the indicated model.
2) If p-value is greater than alpha. we do not reject null hypothesis. There is insufficient evidence to conlude that the model is inaccurate.
Residuals
(Obs-Exp)/sqrt(exp). Each c ategory will produce its own standardized residual.
