week 11 - Chi-squared Goodness of Fit Test, ANOVA, and ANOVA Related Tests

what does the chi-square test for independence test for?

when we want to know whether the observed counts fit a particular distribution

what are the null and alternative hypotheses for chi-square tests of independence?

• H0 - p1=p2…=pn, ie all probabilities are equal (or conform to a specific dist)

• Ha - at least 2 probabilities are different (ie not all the same)

how do you calculate expected counts for chi-square test of independence?

E = row total x null probability

why are degrees of freedom usually n-1?

to find the probs of all 4, you only need 3 as you can calculate the 4th (1-P of the 3), we only ever have to estimate n-1; the last is fixed

what is one scenario where you reject the null hypothesis even with a small chi-square statistic?

spatial distribution too uniform to be random eg fox example

for ANOVA, how do you calculate the between-group variation? what is this called?

for ANOVA, how do you calculate the within-group variation? what is this called?

treatment sum of squares

what are the null and alternative hypotheses for ANOVA tests?

how do you calculate the test statistic for ANOVA? what is this statistic called?

when do you reject H0 for ANOVA tests?

when the F statistic is greater than the critical value (F crit), p<0.05

is this result statistically significant?

yes, F>F crit, therefore p<0.05

C

what are the 2 assumptions of ANOVA? how do we test for them?

check for normality using q-q plot, check for equal variances using levene’s test

how do we check for variability within groups?

what are the null and alternative hypotheses for Levene’s test for equal variances?

for Levene’s test, what data do you do ANOVA with?

do not do ANOVA on the original data, do it on the absolute value of the residuals - Xbarj - Xbar

what test do you use to determine which groups have different means after rejecting H0 from ANOVA?

tukey’s honest significant differences test (HSD) aka post hoc test

what are the assumptions for HSD test?

how do you calculate qij for tukey’s test? how do you test if p<0.05?

• MSE from within group variation from ANOVA

• if qij is > q crit (with N-a df, same as ANOVA), reject H0

what statistic do you use when the samples have different sizes?

how do you construct a confidence interval for the difference in means between each pair of groups?