Week 8: T-tests And ANOVA

Question 1

To determine wether the differences between two groups occurred because if the different therapies, rather than chance we use a T-test.
What are the three pieces of information required for a T-test?

Answer 1

1. The difference between the means: large differences are less likely to occur by chance
2. The standard deviation for each group: groups with smaller standard deviations are more likely to report a significant difference than groups with larger standard deviations
3. The number of subjects in each group: the more subjects that are involved in the study the more confident we can be that the differences we find between groups didn’t occur by chance

Question 2

There are 3 types of T tests and each is calculated differently.
What are they and explain the different circumstances you would use them in.

Answer 2

1. A paired T test:
   -concerned with differences between average scores of a single sample of individuals who are assessed at 2 different times. Before and after treatment.
2. An independent T test is used to compare the averages of two samples that are selected independently of each other (the subjects in the two groups are not the same people) there are two types of of independent T tests
   A) equal variance- used when the subjects in the two groups are the same or the variance of the 2 groups are similar
   B) unequal variance- used when the number of subjects in the 2 groups is different AND the variance if the 2 groups is different.

Question 3

How do we determine which test to use?

Answer 3

Are the scores for the 2 means from the same subject (or related subjects)? If yes-> paired t-test. If no, are there the same number of people in the 2 groups? If yes-> equal variance test. If no are the variances of the 2 groups different? If no-> equal variance t-test if yes -> unequal variance t-test!

Question 4

When do we use the analysis of variance (ANOVA) test instead of a T-test?

Answer 4

When we have more than two samples we should use ANOVA.

Question 5

ANOVA

What is one-way analysis of variance used for?

Answer 5

It’s a technique used to compare the means of two or more samples. This technique can only be used for numerical data.
The ANOVA produces an F statistic, which is?

Question 6

The ANOVA produces an F statistic, which is?

Answer 6

The ratio of the variance calculated among the means to the variance within the samples. From this we can decide a difference of not

Question 7

Two-way ANOVA?

Answer 7

We may be interested in studding 2 interventions at one time. Or we could be studying 3 interventions at one time, which would be classed as the 3-way ANOVA