Question

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.

When I look for the answers, I found:1. a, b, c 2. a, b, c 3. b, c    4. a, b

However, I think #2: a, b, c, d(Boxplot) Because, when I do my assignment the question was check the normality with boxplot, qqnorm, ad.test, shapiro.test

Also, #3, the answer was b, c

However, I think a, b, c : a Hartley's F-max test.

Would you please check the answer #1, #2, #3, #4?

Answer 1

For Question 1, options a, b and c are correct.

For Question 2, options a, b and c are correct. You can use a boxplot to check whether the distribution is symmetric, left skewed or right skewed by checking the placement of the middle (median) line in the box, but you won't able to decide surely whether the distribution follows a normal distribution or not.

For Question 3, options b and c are correct. We generally use the Hartley's F-max test to check whether the variances of two groups are same or not. We do not use it to check whether the residuals have equal variances.

For Question 4, options a and b are correct.