Question

Please select the correct answer for each part, 1 through 4. Thank you!

Part 1

What assumptions need to be satisfied in order to perform ANOVA? Select all that
apply.
a) The observations from each group (or treatment or population) should adhere to
approximately normal distributions.
b) The variances (or standard deviations) of the groups (or treatments or
populations) should be the same.
c) The samples must be simple random samples, and independent of each other.
d) The sample sizes for the groups must be exactly the same, and also happy.

Part 2

Which of the following are practical ways to assess the normality of the residuals? Select all
that apply.
a) Normal probability plots (the R command is qqnorm()).
b) Anderson-Darling tests.
c) Shapiro-Wilks tests.
d) Boxplots.
e) Just ask if they are normal, or, guess, because, who really cares?

Part 3

Which of the following are practical ways to assess equal variances of the residuals?
Select all that apply.
a) Hartley’s F-max test (provided data look normal and sample sizes are the same);
b) Bartlett’s test (provided normality seems to hold; sample sizes do not have to be
the same);
c) Levene’s test (normality and equal sample sizes aren’t needed).
d) Boxplots of residuals, or boxplots of standardized residuals, or boxplots of the
original data.
e) Boxplots of cats and dogs.

Part 4

If the normality or equal variance assumptions are violated, what can be done? Select
all that apply.
a) Apply a transformation to the data, say, using square-roots, logs, or Box-Cox.
b) Use a non-parametric alternative to ANOVA, like Kruskal-Wallis.
c) Ask for help from a statistician or scour the web for an answer.
d) Give up.

Answer 1

Solution part1:

a) The observations from each group (or treatment or population) should adhere to
approximately normal distributions.
b) The variances (or standard deviations) of the groups (or treatments or
populations) should be the same.
c) The samples must be simple random samples, and independent of each other.

Solution Part2:

In normal probbaility plotif we get straight line then performs

a) Normal probability plots (the R command is qqnorm()).

b) Anderson-Darling tests.
c) Shapiro-Wilks tests.

Solution Part3:

Boxplot to know distribution and to check whether means are same or not. but not for equality of variance

b) Bartlett’s test (provided normality seems to hold; sample sizes do not have to be
the same);
c) Levene’s test (normality and equal sample sizes aren’t needed).

Solution part4:

a) Apply a transformation to the data, say, using square-roots, logs, or Box-Cox.

b) Use a non-parametric alternative to ANOVA, like Kruskal-Wallis