Lecture 9

Question 1

What is a Type I Error?

Answer 1

A type I error is rejecting the null hypothesis when it is actually true. Typically, the alpha level is set at .05, which means that there is still a 5% chance of obtaining the data when the null hypothesis is true.

Question 2

What is a Type II Error?

Answer 2

A Type II error is failing to reject the null hypothesis when it is false (and the research hypothesis is actually true). The chance of a Type II error is referred to as beta and corresponds to 1–power of the test.

Question 3

What is power?

Answer 3

Power is the probability of obtaining a test statistic that equals or exceeds the alpha level criterion to reject the null hypothesis if the research hypothesis is true

Question 4

How can we increase the power of a study?

Answer 4

We can increase the power of a study by ensuring a large effect size and/or increasing sample size.

Question 5

What is the purpose of an independent samples t test? What are its assumptions?

Answer 5

An independent samples t test is used to compare the means of TWO independent groups. It has ONE DV and ONE IV.

It assumes normality, homogeneity of variance, independence of samples, and that data is ratio/interval

Question 6

What is the purpose of a dependent samples t test? What are its assumptions?

Answer 6

A dependent samples t test is used to compare the means of TWO related groups (i.e. the SAME participants tested on TWO occasions). It has ONE DV and ONE IV.

It assumes normality, and that data is ratio/interval.

Question 7

What is the purpose of the Mann-Whitney U Test? When should it be used?

Answer 7

The Mann-Whitney U test is a non-parametric alternative to the independent samples t test. It should be used when the data is NOT normally distributed. There is only ONE (ordinal) DV and ONE (categorical) IV.

Question 8

What is the purpose of the Wilcoxin Signed Rank Test? When should it be used?

Answer 8

The Wilcoxin Signed Rank test is a non-parametric alternative to the dependent samples t test. It should be used when the two sets of scores from the SAME participants are NOT normally distributed.

Question 9

What is the basic designed of the between groups one way ANOVA?

Answer 9

3 or more groups of participants are compared on a single DV. E.g. 3 different types of therapy, 3 different age groups etc.

Question 10

What is the null hypothesis of the between groups one way ANOVA?

Answer 10

H0: U1 = U2 = U3

Question 11

What is “within groups variance”

Answer 11

The individuals within a group will vary on the DV because of “error variance”.
Non-systematic
Due to individual differences
Due to sampling error

Question 12

What is “between groups variance”?

Answer 12

Variance between groups will have a component of error variance/individual differences, but also due to the effects of the IV. Therefore, between groups variance = systematic + non-systematic

Question 13

What does hypothesis testing tell us in the one-way between groups ANOVA?

Answer 13

It tells us if the between groups variance is significantly greater than the within groups variance (i.e. variance that we would expect from chance/individual differences alone)

Question 14

What does a significant F ratio tell us?

Answer 14

F = between / within
Therefore, if F is significantly greater than 1 (indicated by p), then we reject the null hypothesis and we can say that the IV is having an effect.

It only tells us that there is a significant difference between at least 2 of the means. It does NOT tell us where this difference lies.

Question 15

What are the assumptions of the one-way between groups ANOVA?

Answer 15

1. Independent groups/observations
2. Normal population distributions
3. Homogeneity of variance
   
   • If this is violated, use Welch’s statistic or make a Bonferroni correction to decrease the alpha level

Question 16

What does eta-squared represent?

Answer 16

This measure of effect size represents the proportion of variance in the DV accounted for by the IV

Question 17

What do post hoc tests tell us? When should they be used? What are some examples? What is an issue with post hoc tests?

Answer 17

They tell us where the differences lie in a significant F test, i.e. between which two means.
E.g. Tukey’s HSD, Bonferroni test
They can be used when there isn’t a planned/predicted difference.

However as the number of post hoc comparisons increases, so too does the likelihood of making a Type I Error

Question 18

What do planned comparisons tell us? How do they work? When should they be used?

Answer 18

Planned comparisons are used to test predicted differences. The means are weighted in such a way that they compare the scores of interest. All weights must add to zero. Any mean that is NOT being compared should be assigned a weight of zero. By using weights that compare just two means at a time, you are effectively conducting a t-test

Question 19

What is trend analysis? When should it be used?

Answer 19

A type of orthogonal planned comparison.

It is only applicable when the levels of the IV correspond to an ordered set of conditions, (e.g., age, time in therapy, number of sessions).

For a set of k treatments, there are (k-1) possible trends that could be analysed.

Trend analysis tells us the manner in which the data is changing (i.e. is it linear, cubic, quadratic etc.) The trend with a sum of squares that accounts for the largest proportion of the total between groups sum of squares may be viewed as the dominant trend.

Question 20

What is the Kruskal-Wallis one-way ANOVA?

Answer 20

A non-parametric alternative to the one-way between groups ANOVA used when assumptions are violated.
The follow-up tests are also non-parametric: multiple pairwise comparisons of the medians are carried out using the Mann Whitney U test

Question 21

What is a covariate?

Answer 21

A confounding variable that influences the DV, which can arise from non-equivalent groups, or from the researcher selecting naturally occurring groups.

Question 22

What is the purpose of the ANCOVA?

Answer 22

To compare the means of 2 or more groups, while statistically equating the groups in terms of the covariate. If the groups STILL differ significantly after the effect of the covariate has been removed, THEN we can say that the IV is responsible for that difference

Question 23

What is an example of data that has been examined using the ANCOVA?

Answer 23

Data showing that there is a relationship between age (IV) and the amount of recovery after a stroke (DV). However, it is known that older people generally have more severe strokes, and therefore less recovery. Therefore “severity” is a confounding variable. After equating the groups in terms of severity, it turns out that there is no longer a significant relationship between “age” and “recovery”, but rather there is a relationship between “severity” and recovery”

Question 24

What are the assumptions of the ANCOVA?

Answer 24

• That there is a LINEAR relationship between the covariate and the DV
• Homogeneity of slopes: i.e. the slope of the relationship between the covariate and the DV is the same for all IVs/groups.
• Normality
• Homogeneity of variances

Question 25

What is the difference between the null hypothesis testing in ANOVA and ANCOVA?

Answer 25

Both assume that all the means are equal. However, in the ANCOVA, the researcher first ADJUSTS all the means to remove the effect of the covariate

Question 26

What is the repeated measures ANOVA? What is a clinical example of an ANOVA?

Answer 26

Used to compare 3 or more group means, where the participants are the SAME in each group.

E.g. assessing whether %SS improves after a particular therapy. In this case, “%SS” is the DV, and “time” is the IV (with three levels, e.g. immediately after treatment, 3 months later, and 6 months later).

Question 27

What are the assumptions of the repeated measures ANOVA?

Answer 27

• DV is interval/ratio data
• IV has at least 3 categorical RELATED groups
• No significant outliers
• Normally distributed
• Sphericity: the variances of the differences between all pairs are equal (i.e. two conditions are not more highly correlated than any other two conditions)

Question 28

What is sphericity?

Answer 28

The variances of the differences between all pairs are equal (i.e. two conditions are not more highly correlated than any other two conditions)

Question 29

What are the advantages of using a repeated measures ANOVA?

Answer 29

• Fewer subjects required
• Increased power (Individual differences across conditions are minimised because the same individuals participate 
in each condition.
• Necessary for longitudinal designs/assessing the effectiveness of a treatment

Question 30

What are the disadvantages of using a repeated measures ANOVA?

Answer 30

• Order or carryover effects could confound 
the results. To control for order effects it is possible to counterbalance order across subjects
• The sphericity assumption rarely holds for time series or longitudinal data. Measures taken closer together in time are more likely to be similar compared to measures taken further apart.

Question 31

What is the Friedman two-way ANOVA?

Answer 31

It is a non-parametric rank alternative to the repeated measures ANOVA, when assumptions have been violated.