Lecture 3: T-test, one way ANCOVA and mixed ANOVA

Question 1

When is a t-test used vs an ANOVA?

Answer 1

Both need a continuous dependent variable, but ANOVA needs more than 2 groups while t-test has a max of 2 groups.

Question 2

What is null and alternative hypothesis for a t-test?

Answer 2

H0= 2 means are equal
H1= 2 means are not equal

Question 3

What is null and alternative hypothesis for an ANOVA?

Answer 3

H0= 2 or more means are equal
H1= 2 or more means are not equal

Question 4

What are the characteristics of non-specific hypotheses?

Answer 4

• post hot tests used-> all possible comparisons
• correct for familywise error rate
• but has less power than planned contrasts

Question 5

What are the characteristics of specific hypotheses?

Answer 5

• planned contrasts used
• simple effects analyses can be used as a follow-up analysis
• not all possible comparisons and looks at just the ones you have a hypothesis about
• more power

Question 6

How is elimination of confounds a reason for carrying out an ANCOVA?

Answer 6

Can correct for initial differences despite random assignment resulting in a more accurate comparison. It can thus filter out explained variance, so the unexplained variance in wellbeing is smaller. The uniquely explained variance is also smaller. The ratio of uniquely explained variance to unexplained variance changes, so the F value can be smaller or greater depending on the data

Question 7

What are the steps of an ANCOVA?

Answer 7

1. check assumption so whether the regression lines are parallel (no significant interaction effect between covariate and intervention)
2. If the assumption is met then do the actual ANCOVA without the interaction term-> just report the F values for the intervention

Question 8

When do we correct for initial group differences on the covariate?

Answer 8

Only in randomized groups that come from the same population

Question 9

What is the other reason for carrying out an ANCOVA?

Answer 9

To reduce variance within groups which allows for a more sensitive comparison. The unexplained variance in wellbeing is smaller, so the effect of the intervention is determined more sensitively, So the intervention explains relatively more variance in the outcome. F value is greater and more easily significant then.

Question 10

Why would you do a mixed ANOVA?

Answer 10

If you want to use several assessments, as one-way ANOVA tests for differences at one-time. So then you can compare changes over time between groups

Question 11

What are the assumptions of a mixed ANOVA?

Answer 11

• Dependent variable continuous (assumption 1)
• (Co)variances in all groups equal (assumption 2)
• Data of subjects are independent (assumption 3)
• Dependent variable is normally distributed in each group
  (assumption 4)
• Sphericity (more than 2 repeated measurements)
  (assumption 5)

Question 12

What is reported for a mixed ANOVA?

Answer 12

Any significant main effects, interaction effect all found between within-subject effects

Question 13

What is the homogeneity of regression slopes?

Answer 13

The relationship between covariate and dependent variable should be similar in all groups. If the assumption is not met, then the F-distribution is actually a different distribution, the type I error is inflated, and the power is suboptimal

Question 14

How can covariate results be reported?

Answer 14

• “The covariate, love of puppies, was significantly related to the participant’s happiness, F(1, 26) = 4.96, p = 0.035, r = 0.40. There was also a significant effect of puppy therapy on levels of happiness after controlling for the effect of love of puppies, F(2, 26) = 4.14, p = 0.027”
• For contrasts: “Planned contrasts revealed that having 30 minutes of puppy therapy significantly increased happiness compared to having a control, t(26) = -2.77, p = 0.01, r = 0.48, but not compared to having 15 minutes, t(26) = -0.54, p = 0.59, r = 0.11.”

Question 15

How to check whether the covariate is the same across groups?

Answer 15

using a one-way ANOVA which should not be significant

Question 16

Why should the covariate be independent of the treatment effect?

Answer 16

→ dependence occurs most often if no random assignment used
→ shared variance of treatment and covariate cannot be separated, one cannot control for a covariate
→ random assignment and matching based on covariate could both eliminate the problem
→ if there is temporal additivity (different treatment groups would have changed to the same degree without intervention), then treatment groups may be biased if they are not equal on the covariate

Question 17

How to report all results for a covariate?

Answer 17

There was a significant main effect of group, F(1, 57) = 26.71, p < .001. Insomnia symptoms were, across both measurements, on average lower for online CBT-I than
for WLC. There was also a significant main effect for measurement, F(1, 57) = 208.00, p < .001. Insomnia symptoms were, across both groups, on average lower at
posttest than at pretest. Finally, there was a significant interaction effect between measurement and group, F(1, 57) = 71.22, p < .001. The effect of measurement differed between groups, with the decrease in insomnia symptoms from pre- to posttest being greater for the online CBT-I group than for the WLC group.

Question 18

Why could it be important to include depressive symptoms at pre-test as a covariate in the analysis of the effect of group on insomnia symptoms at post-test?

Answer 18

Because you want to rule out that differences found between groups in insomnia symptoms (ISI) at posttest are due to initial (pretest) group differences in depressive
symptoms (CES-D). You are interested if there is an effect of online CBT-I compared to WLC on insomnia symptoms at
posttest in subjects who are comparable in terms of depressive symptoms (CES-D) at pretest.