Topic 6: Hypothesis Testing with 3+ samples, ANOVA

Question 1

Multiple Group designs

Answer 1

• Have one independent variable with three or more levels and a continous DV

*extension of the two-group designs

Question 2

As with the two-group design, multi-group designs…

Answer 2

can be experimental or ex post facto

Question 3

One-way Analysis of Variance (ANOVA)

Answer 3

• A hypothesis-testing technique used to compare means from three or more possible populations

Question 4

ANOVA hypothesis

Answer 4

Ho= All population means are equal (u1=u2u3=…uk)
Ha= At least one of the means is different from the others

Question 5

What is ANOVA? (2)

with the diagram+ overall in words

Answer 5

In ANOVA we compare:
- How much the sample means differ (on average) from the overall mean (of all scores) to how much individual score differ from their own sample means (on average)
- Aka: How much are we as a group differing from overall average?

Question 6

x double bar

Answer 6

Overall mean for all the mean of the score in the study

Question 7

If there is more between than within group variability then…

Answer 7

samples are not all from the same population thus, we reject null that they are from the same population

Question 8

In anova, bigger the green arrow, smaller the red the more sure we are that

Answer 8

This group is diff

Question 9

Explain the F value+formula

+error

Answer 9

• error between and within groups should be similar assuming no confounds

Question 10

If the IV has no effect (does not lead to variability between groups), the variability due to the IV will be

Answer 10

close to 0

Question 11

The higher the F-value,

Answer 11

the greater the likelihood that the IV caused an effect

Question 12

Assumptions of the one-way ANOVA (3)

Answer 12

1. The samples are independent of eachother
2. Each sample comes from a normal (or approximately normal) population. Fairly robust against violations of this assumptions unless n is small
3. Each population has the same variance. Also fairly robust against violations of homogeneity of variances

Question 13

F distrubution is —- skewed and you shouldnt get a —– number

Answer 13

• positively
• negative

Question 14

The degrees of freedo for the F-test are:

Answer 14

dfN=k-1
dfD=N-k

Question 15

k

Answer 15

The number of groups

Question 16

N

Answer 16

Total sample size

Question 17

Answer 17

Average variation of each score (from own sample means. Tells us how much each participant deviate from their own condition.

Question 18

Answer 18

Tells us overall mean from all participants

Question 19

Calculating F for one-way ANOVA

Answer 19

Question 20

SD and variance relationship

Answer 20

Square SD to get variance

Question 21

Performing a one way ANOVA Test

Answer 21

• determine the critical value from the F-distribution table
• Calculate the F value with formula.
• If F is in the rejection region, reject H0. Otherwise, fail to reject H0

Question 22

Denominator is the

Answer 22

bottom number

Question 23

Effect size for ANOVAs

Answer 23

Small = 0.01
Medium = 0.06
Large = 0.14

Question 24

Multiple comparisons

Answer 24

Test suitable for the simultaneous testing of several hypotheses concerning the equality of three or more population means.

Question 25

Significant F only shows that ——. Multiple comparisons tell us —-

Answer 25

• Not all groups are equal
• which group differ

Question 26

Why not just run a series of t-test? Why use multiple comparisons?

Answer 26

We run into issues with the family-wise error rate. The more you run a study, the higher chance of making a type 1 error. Everytime you run, you increase type 1 by 5%.

Question 27

The reason we use multiple comparison procedures is because

Answer 27

They control the familywise error rate

Question 28

Liberal multiple comparison tests (4)

Answer 28

1. More chance of type 1 error
2. More likely to find a significant difference
3. More power
4. Less chance of type 2 error

Question 29

Conservative multiple comparison tests (2)

Answer 29

1. Less chance of type 1 error (every scared of making)
2. More chance of making type 2 error (missing a significant difference)

Question 30

The Tukey procedure

Answer 30

Tells you which population means are significantly different from eachother
Ex: No difference between 1 and 2 but a difference between 3 and the other 2

Question 31

We only used a Tukey procedure after —— if …….

Answer 31

• after we found a significant result woth the ANOVA
• If your F is not significant, you cant do Tukey as you will find no difference

Question 32

Tukey procedure what do we do?

Answer 32

• We find the mean difference between each of the groups being compared.
• If the mean difference is greater than the critical rangel than the two groups are significantly different

Question 33

Critical range degree of freedom calculations

Answer 33

• amount of groups (K)
• N-K