L9/10: ONE WAY ANOVA

Question 1

Why might researchers use designs with three or more conditions?

Answer 1

To study more complex effects and relationships that aren’t just linear

Question 2

What did Sluckin et al. (1980) find about liking and familiarity?

Answer 2

The relationship is best described by an inverted-U shape

Question 3

Why can having only two conditions lead to incorrect conclusions?

Answer 3

Because some effects are not linear and need multiple conditions to show the true pattern

Question 4

What’s an example of a study needing three or more conditions?

Answer 4

Comparing household income across the Home Nations: England, Northern Ireland, Scotland, and Wales

Question 5

What happens if you only include two conditions in such studies?

Answer 5

You won’t get the full information or understanding of differences among all groups

Question 6

Why shouldn’t we run multiple t-tests instead of using a design with 3+ conditions

Answer 6

Because running multiple t-tests increases the risk of Type I errors (false positives), making it more likely to find a significant result just by chance

Question 7

What is a false positive in statistics?

Answer 7

It’s when a test wrongly shows a significant effect even though there isn’t one — basically, a “false alarm.”

Question 8

How many t-tests would you need to run if you have 4 conditions?

Answer 8

6 t-tests

Question 9

What’s the chance of having at least one Type I error (false positive) when running multiple t-tests with 4 conditions?

Answer 9

Around 20%

Question 10

What cautionary example is used to show the problem with multiple t-tests?

Answer 10

The dead fish study

Question 11

What is the dead fish study and why is it important in statistics?

Answer 11

It showed that by running many tests on random data (like brain scans of a dead fish), you can get false positives — highlighting the risk of Type I errors with multiple comparisons.

Question 12

What was the Bennett et al. (2009) dead fish study about?

Answer 12

They did an fMRI study with a dead Atlantic Salmon, running many t-tests on brain voxels to see if the fish’s brain “reacted” to emotional photos—highlighting false positives from multiple tests.

Question 13

What surprising result did Bennett et al. (2009) find in the dead fish study?

Answer 13

They found significant brain activation in a dead salmon during an emotion task — showing the problem of false positives from running many t-tests.

Question 14

What lesson does this study teach?

Answer 14

Don’t run multiple t-tests without correction, or you risk false positives (finding effects that aren’t real)

Question 15

What does an ANOVA do?

Answer 15

It tests whether there are differences in means across three or more groups by checking if all group means are equal (the null hypothesis).

It avoids the problem of increased false positives from running multiple t-tests by testing all groups at once

Question 16

When would you use a one-way ANOVA?

Answer 16

To compare blood oxygen levels across smokers, non-smokers, and former smokers.
To compare spelling test scores among children from five different schools

Question 17

When should you use a one-way ANOVA?

Answer 17

When comparing three or more groups (levels of an independent variable)
Data is interval or ratio scale
Study design is between-subjects (different participants in each group)

Question 18

What are levels of an independent variable in a one-way ANOVA?

Answer 18

Levels are the different conditions or values of the independent variable.
Example: Caffeine amounts (0mg, 25mg, 50mg, 75mg, 100mg) are 5 levels in a study on memory performance.

Question 19

When should you use a one-way ANOVA based on data type?

Answer 19

Use it when your data is interval or ratio scale.
Interval: Ordered data with equal gaps, no true zero (e.g., degrees Celsius, IQ).
Ratio: Like interval but with a true zero (e.g., weight, amount of money).

Question 20

When should you use a one-way ANOVA based on study design?

Answer 20

When the study is between subjects — each participant is in only one condition.
Example: Comparing academic achievement among children born in different seasons

Question 21

What are the key assumptions of a one-way ANOVA?

Answer 21

Independence of observations - each participants should be indepdent of others. No participants results should influence others

Homogeneity of variance (equal variances across groups) - spread of scores that should be roughly equal across all groups you’re comparing

Dependent variable is normally distributed in each group - should be approximately normally distributed within each group

Question 22

Whats the basis of anova?

Answer 22

Compares the variance between groups with the variance within groups.

F = variance between groups/ variance within groups

Question 23

Whats effect size?

Answer 23

The strength of the relationship between IV and DV

Question 24

What measure of effect size is commonly reported in ANOVA?

Answer 24

Partial eta squared (η²)

Question 25

What are the general benchmarks for interpreting partial eta squared (η²)?

Answer 25

Small effect = 0.01, Medium effect = 0.06, Large effect = 0.14.

Question 26

What was the effect size for community connectedness in the example study? N2 =1 N² 0.011

Answer 26

It had a small effect size

Question 27

What does a significant ANOVA tell you about group differences?

Answer 27

It tells you that at least one group mean is significantly different from another, but it doesn’t specify which groups differ.

Question 28

How do you find out which groups differ after a significant ANOVA?

Answer 28

By conducting post-hoc tests to identify the specific group differences

Question 29

Why do we correct for multiple tests in post-hoc analyses?

Answer 29

To keep the chance of making a Type 1 error (false positive) at 5%, despite doing multiple comparisons.

Question 30

What happened in Bennett et al. (2009) after correcting for multiple comparisons?

Answer 30

There were no significant differences found, showing the importance of correction.

Question 31

What is the impact of the Bennett et al. (2009) study on current fMRI research?

Answer 31

Almost every fMRI study now uses corrections for multiple comparisons to avoid false positives.

Question 32

What is Tukey’s HSD test?

Answer 32

A common post-hoc test used after ANOVA to compare group means while controlling for multiple comparisons.

Question 33

How does Tukey’s HSD control the Type 1 error rate?

Answer 33

It makes it harder to get p < .05 by adjusting for multiple tests, keeping the false positive rate at 0.05.

Question 34

What is a downside of Tukey’s HSD test?

Answer 34

It increases the Type 2 error rate, meaning it may miss some true differences (false negatives).

Question 35

What do post-hoc tests do?

Answer 35

They compare each group’s mean to every other group’s mean after a significant ANOVA

Question 36

How do we know if the differences between groups are significant in post-hoc tests?

Answer 36

By looking at the p-values—significant p-values indicate real differences.

Question 37

What does it mean if a post-hoc comparison is non-significant?

Answer 37

The difference between those groups is likely due to chance

Question 38

A recent study showed that birds have regional accents, and so birdsong differs between different areas of UK. Dr Harris wants to examine whether cows also have regional accents. She studies three different groups of cows living in different areas of the UK: 1) Devon, 2) Birmingham, and 3) Aberdeen. She measures the length of each cows’ moo in milliseconds, and runs a one-way ANOVA to compare moo length between the three groups. 1) Does the data meet the assumption of homogeneity of variance? a. Yes, because Levene’s test is significant. b. Yes, because Levene’s test is non-significant c. No, because Levene’s test is significant d. No, because Levene’s test is non-significa

Answer 38

B

Question 39

2) Which of the follow is accurate? a) Post-hoc tests revealed that moo length is significantly longer for Aberdeen cows than Devon cows, and longer for Birmingham cows than Aberdeen cows. b) Post-hoc tests revealed that moo length is significantly shorter for Aberdeen cows than Devon cows, and shorter for Birmingham cows than Aberdeen cows. c) Post-hoc test revealed no significant differences between groups of cows d) Post-hoc tests should not have been carried out

Answer 39

A

Question 40

What’s an independent sample t-test?

Answer 40

Parametric test for a between subject design

Question 41

Whats a paired sample t-test?

Answer 41

parametric test for a within subject design