Comparing Multiple means & ANOVA

Question 1

Problem with t tests

Answer 1

focus on comparisons of one or two groups - limits the range of questions you could ask
-What if we wanted to see the differences between more than one condition?

Question 2

Multiple comparisons

Answer 2

p-value thresholds use 0.05 allowing 1 in 20 possibility data could be observed if null is true

If we run many comparisons these possibilities combine and inflate chance of observing a false positive

3 groups = 3 tests having been ran

Number of comparisons rises very quickly as number of groups increase

Question 3

p-value corrections

Answer 3

Adjusting p-value threshold makes it difficult to find anything

Bonferroni correction = threshold/number of comparisons

Question 4

Intro to ANOVA

Answer 4

intuitive method to test for any possible difference between multiple groups - without pre-specifying what those differences are.

If ANOVA detects an overall difference, we can use multiple t-tests to find where that difference is post hoc

Question 5

Analysis of variance

Answer 5

ANOVA is about partitioning variance into different factors
e.g. what is the total variance? how much variance occurs between groups?

If there is lots of variability between groups, relative to amount of variability within groups - real difference

Question 6

Hypotheses for ANOVA

Answer 6

make hypotheses about existence of any difference in means of a set of groups (null statesall groups can be defined by a single mean)

we can put forward follow up hypotheses about the location of the difference.

Question 7

Terminology

Answer 7

Factor = categorical (nominal) variable containing the labels of a set of groups
e.g. 1 factor = sport

Levels = different groups within a factor
e.g. 3 levels = running, swimming, cycling

Question 8

Ss total (The total variance in the data) equation

Answer 8

difference in within groups + difference in between groups

Question 9

Sum Square between equation

Answer 9

SS total - Ss within

Question 10

Mean square error within equation

Answer 10

Ss within/ number of participants (N) - number of groups (G)

Question 11

Mean square error between equation

Answer 11

Ss between/ G - 1

Question 12

ANOVA Results

Answer 12

F = MSE between/ MSE within

Large F = MSE between groups is larger than the variability within groups

-This means there is a benefit from modelling the data with the individual group means whilst a small F would indicate sticking to the overall mean

Question 13

ANOVA assumptions

Answer 13

Between-subjects ANOVA

• independence
• normal distributions
• Equality of variance
• categorical factors - predicting factors must be divided into separate groups
• data type of interval or ratio

Question 14

What do we do if data set doesnt pass the test for normality

Answer 14

We use the Kruskall Wallace test