ANOVA test

Question 1

When we want to compare more than 2 variables, looking at the differences between conditions between the variables.

Answer 1

ANOVA test

Question 2

What is ANOVA?

Answer 2

ANOVA is similar to a t-test, the job of an ANOVA is to determine whether the variation of sample means among groups is greater than expected by chance.

Question 3

Why can we not use a t-test for more than two variables?

Answer 3

The more comparisons we make, the greater the possibility we’ll pick up a difference purely by chance and associate it with some biological effect when in reality, there is none.

Question 4

What are the 3 primary assumptions of ANOVA?

Answer 4

1. The responses for each factor level have a normal distribution
2. Homogeneity of variance: These distributions have the same variance
3. The data are independent

Question 5

One way ANOVA

Answer 5

One independent variable
One p value

Question 6

two way ANOVA

Answer 6

Two independent variables
Three p values
Factorial design

Question 7

Why can we not answer these questions with repeated t-tests?

Answer 7

1. Large number of pairwise comparisons are difficult to comprehend
2. As the number of tests increases, the Type I error increases
3. Does not permit us to recognize the structure of the data, e.g.a natural ordering within the groups
4. Does not permit us to improve our estimate of the variance in each group by using information from all groups.

Question 8

When do we use a one way ANOVA?

Answer 8

• An ANOVA for comparing 3 or more groups defined by one independent variable is called a one-way ANOVA.
• For example, the 3 groups defined by the variable “schizophrenia diagnosis” can be compared using a one-way ANOVA.
  *More complex models would allow comparisons across groups defined by more than one variable, e.g.a two-way ANOVA could be used to compare groups defined by “schizophrenia diagnosis” and “family history”.

Question 9

ANOVA in R

Answer 9

Degrees of freedowm (df)
F value
P value
The variable defining the groups must be identified as a factor (or a categorical variable). Otherwise it will be treated as a continuous variable.
The relevant functions are the ‘aov’ and ‘summary’ functions as illustrated below (Note some numbers may differ slightly from those on the preceding slides due to rounding).
It needs to be set as a factor or else the variable will just be treated as a character.

Question 10

What is an F-test?

Answer 10

Basically the critical value equivalent of the ANOVA.
As with the other hypothesis tests we studied earlier, we need to calculate the test statistic and determine the rejection region
MS denotes the mean squared error.
The rejection region is determined using an F distribution with degrees of freedom equal to the degrees of freedom between groups and the degrees of freedom within groups.