Factorial ANOVA (repeated measures & mixed) Flashcards by D E

Test for differences when we have more than one IV/factor

This is known as…?

Factorial ANOVA/ Two-way ANOVA

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Test for differences when we have more than one
IV/factor, within subjects

Two-way repeated measures ANOVA

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Test for differences when we have more than one IV/factor, a mix of between and within subjects

Two-way mixed ANOVA

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Television executives are interested to learn how best to provoke fear in celebrity
contestants during jungle-based trials. They want to know how the presence of jungle critters impacts fear, and whether any influence of jungle critters is dependent on the nature of the task.

They recruit a sample of celebrities and monitor their heart rate during a series of trials.

Each celebrity takes part in six trials: two trials completed under water (one with no critters and one with critters); two trials involving confinement (one with no
critters and one with critters); two trials completed at height (one with no critters and one
with critters).

What are the:

a. IVs
b. IV levels
c. DV
d. Subjects design
e. Type of test

a. Presence of jungle critters, Nature of the trials

b. 2 (critters, no critters), 3 (under water, confinement, height)

c. Heart rate (fear)

d. Within subjects

e. Two-way repeated measures ANOVA

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What type of effects are based on marginal means?

a. Main effects
b. Interaction effects

a. Main effects

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What type of effects are based on cell means?

a. Main effects
b. Interaction effects

b. Interaction effects

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The effect of factor 1 depends on the level of factor 2

This is known as…?

Interaction

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In repeated measures designs, the variance between IV levels does not
include variance due to _____?

Individual differences

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In repeated measures designs, the variance between IV levels does not include variance due to individual differences

Why?

Because each participant acts as his/her own control

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In repeated measures designs, the variance within IV levels does not include variance due to ____?

Individual differences

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Because the same participants take part in each IV level, we can calculate the degree of error associated with each factor separately

What does this help us do?

Test each main effect and interaction against its own error term

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What makes up variance between IV levels in a two-way repeated measures ANOVA?

IV 1 variance
IV 2 variance
Interaction variance

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What makes up variance within IV levels in a two-way repeated measures ANOVA?

Error IV 1
Error IV 2
Error interaction

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What is the formula for the F ratio for a two-way repeated measures ANOVA?

F = variance between IV levels / variance within IV levels

F = MSM / MSR

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Mean scores for each condition is known as…?

Cell means

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What are cell means?

Mean scores for each condition

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e.g. mean heart rate during a water-based trial with critters = 98.88

This is an example of…?

a. Cell means
b. Marginal means

a. Cell means

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What are marginal means?

Mean scores for single IV levels (ignoring the other IV)

This is known as…?

Marginal means

e.g. mean heart rate during trials involving heights = 105.35

This is an example of…?

a. Cell means
b. Marginal means

b. Marginal means

What are the 3 assumptions for a two-way repeated measures ANOVA?

Normality
Sphericity (homogeneity of covariance)
Equivalent sample size

What is the normality assumption for a two-way repeated measures ANOVA?

The distribution of difference scores under each IV level pair should be normally distributed

Does this apply to…?

a. Repeated measures ANOVA
b. Independent ANOVA

a. Repeated measures ANOVA

What is the sphericity (homogeneity of covariance) assumption for a two-way repeated measures ANOVA?

The variance in difference scores under each IV level pair should be reasonably
equivalent

What is the equivalent sample size assumption for a two-way repeated measures ANOVA?

Sample size within each condition should be roughly equal

What is the non parametric equivalent for factorial ANOVA?

There are none Instead, we can attempt a fix or simplify the design

What is the null hypothesis for Mauchly's test?

There is no difference between the covariances under each IV level pair (i.e. homogeneity)

Mauchly's result is not relevant for...? a. IVs with more than 2 levels b. IVs with only 2 levels

b. IVs with only 2 levels

Mauchly's is for the homogeneity of...? a. Variances b. Covariances c. Effect size d. Mean

b. Covariances

Levene's is for the homogeneity of...? a. Variances b. Covariances c. Effect size d. Mean

a. Variances

If Mauchly's is not assumed, what do we refer to on SPSS?

Greenhouse-Geisser

What do we report after finding a significant interaction between IVs?

Report simple effects

How do we investigate simple effects? List 2 points

1. Compare across the levels of the main IV, separately for each level of the secondary IV 2. If IV is a within-subjects IV, we use paired t-tests to compare across the IV levels

Tests of simple effects should only be conducted IF ...?

You obtain a significant interaction

Simple effects results Trial involving water No critter vs. critter: t(9) = 4.93, p = .001 Trial involving confinement No critter vs. critter: t(9) = 8.62, p < .001 Trial involving heights No critter vs. critter: t(9) = 2.67, p = .026 Which are significant after following a Bonferroni correction?

Comparisons are significant if: p = .05 / 3 p < 0.017 Trial involving water No critter vs. critter: t(9) = 4.93, p = .001 Trial involving confinement No critter vs. critter: t(9) = 8.62, p < .001

A Psychologist interested in how attraction operates in online dating apps wants to investigate whether intelligence plays a role. She asks participants to review an app user’s profile and rate their attractiveness on a 20 point scale; 10 participants are shown the profile of an app user with high intelligence (IQ > 110) and 10 participants are shown the profile of an app user with low intelligence (IQ < 90). The researcher is also keen to determine whether any influence of intelligence is dependent on social interaction. Having given their initial attractiveness rating, participants spend 5 minutes chatting with the user via the app before rating their attractiveness for a second time. What are the: a. IVs b. IV levels c. DV d. Subjects design e. Type of test

a. Intelligence, Social interaction b. 2 (high intelligence, low intelligence), 2 (before chat, after chat) c. Attractiveness rating d. Intelligence = Between subjects Social interaction = Within subjects e. Two-way mixed ANOVA

Intelligence is a between-subjects IV with 2 levels Do we use Mauchly's or Levene's test?

Levene's test

Intelligence is a between-subjects IV with 2 levels Do we need to report for post hoc test if Levene's test is significant?

No because it only has 2 IV levels

Social interaction is a within-subjects IV with 2 levels Do we use Mauchly's or Levene's test?

None Usually for within subjects, we use Mauchly's but this IV only has 2 levels

How do we run simple effects if the main IV had been within-subjects and the secondary IV had been between-subjects? List 2 points

1. We use paired t-tests to compare DV across the levels of the main IV 2. We run separate paired t-tests; one for each level of the secondary IV

How do we run simple effects if the main IV had been between-subjects and the secondary IV had been within-subjects? List 2 points

1. We use independent t-tests to compare DV across the levels of the main IV 2. We run separate independent t-tests; one for each level of the secondary IV

Simply effects result: Before chat High vs. low: t(18) = 1.06, p=.302 After chat High vs. low: t(18) = 3.93, p=.001 Which are significant after following the Bonferroni correction?

Comparisons are significant if: p = .05 / 2 p < .025 After chat High vs. low: t(18) = 3.93, p=.001

Before collecting ANY data, we need to ask 5 questions What are they?

1. Do I have a clear research question? 2. Do I know what analyses I will need to conduct to answer this? 3. Will I be able to carry out and interpret the results of these analyses? 4. Have I considered and controlled for potential confounds? 5. Will I understand the answer I get?