Within-Participants ANOVA Learning Objectives Flashcards
(25 cards)
Describe the characteristics of a fully within-participants design
A fully within-participants design has the same people in each condition. They can be experimentally manipulated or naturally occurring.
List the various names used to describe “within-participants” designs/factors
Repeated measure, within-groups
Specify the general and specific notations for a within-participants factorial design
The number of numbers tells you how many factors there are, and the number values tell you how many levels.
Explain how individual differences can be accounted for in within-participants ANOVA
Individual differences are treated as a separate factor, rather than being included in the error term. A main effect for the differences between participants is calculated and removed from the error term.
Explain the difference between fixed factors and random factors
Fixed factors are those where all levels of the factor are included in the analysis - they are deliberately chosen. On the other hand, random factors are those where the population is a random sample - the goal is to generalise the findings to an entire population, by testing the levels of a random sample.
Describe the research question that can be addressed in one-way within-participants ANOVA
Whether there is a significant difference between the means of two or more conditions when there are the same participants in each condition.
Explain the structural model (also known as the linear or conceptual model) of one-way within-participants ANOVA
+ Tri + + e i j
Xij score of participant i in condition j
g. grand mean
individual difference effect for participant i
Tj treatment effect for condition j
inconsistency of the treatment effect of condition j for participant i
In conceptual terms (i.e., in words), explain what is represented by SStreatment, SSparticipants, SSerror, MStreatment, MSparticipants, and MSerror in one-way within-participants ANOVA
SStreatment represents the variability in scores between conditions (due to the treatment effect). SSparticipants represents the variability in scores between participants (due to individual differences). SSerror represents how much more each individual score would vary from the grand mean after accounting for effects of treatment and individual differences. MStreatment represents the variance between the different levels of the independent variable. MSparticipants represents the variability in the data due to individual differences between participants. MSerror represents the average variability within the groups after accounting for the main effect of the independent variable and any interaction effects.
Specify how the F ratio is calculated in one-way within-participants ANOVA
F = MStreatment/MSerror
Explain why error variance can be considered a Treatment x Participant interaction in one-way within-participants ANOVA
Error variance can be considered a treatment x participant interaction because it is residual variance that cannot be explained by mean differences between treatment conditions or participants alone.
Describe the research questions that can be addressed in two-way within-participants ANOVA
If there a main effect of A on the DV? Is there a main effect of B on the DV? Is there a A x B interaction?
Explain how variance is partitioned in two-way within-participants ANOVA and explain which sources of variance are considered “between-participants” and sources of variance are considered “within-participants”
Variance is partitioned into participant variance (considered between-participants variance), and treatment variance (considered within-participants variance) - separated into A, B, AxB interaction - and error variance (considered within-participants variance) - separated into error AxP, error BxP, error AxBxP.
Explain the structural model (also known as the linear or conceptual model) of two-way within-participants ANOVA
i jk = Tri 13k + +
+ ßT1ik + aßT1ijk
x
Xijk score of person i at level j (of Factor A) and level k (of Factor B) - i.e., cell jk
B.. grand mean
individual difference effect for participant i
treatment effect of level j (of Factor A)
13k treatment effect of level k (of Factor B)
aßjk treatment effect of cell jk (based on interaction between Factor A and B)
inconsistency of the treatment effect of level j (of Factor Al for person i
1311* inconsistency of the treatment effect of level k (of Factor B) for person i
inconsistency of the treatment effect of cell jk (based on Ax B interaction)
for person i
Explain what each of the following tell us in two-way within-participants ANOVA:
- A significant F test for the main effect of Factor A
- A significant F test for the main effect of Factor B
- A significant F test for the A x B interaction
- A significant F test for the main effect of Factor A
That there is a significant difference between the means of the levels of factor A on the DV.- A significant F test for the main effect of Factor B
That there is a significant difference between the means of the levels of factor B on the DV. - A significant F test for the A x B interaction
That there is a significant difference where A changes at the levels of B.
- A significant F test for the main effect of Factor B
When the F ratio is calculated for each omnibus test in two-way within-participants ANOVA, identify which MS terms are used in the numerator and denominator in each case
- Explain how this differs compared to terms used in a fully between-participants design
For the main effect of factor A, F = MSa/MSaxp. For the main effect of factor B, F = MSb/MSbxp. For the AxB interaction, F = MSaxb/MSaxbxp.
Identify how many error terms are used for the follow-up tests in two-way participants ANOVA
Explain how this differs compared to terms used in a fully between-participants design
A separate error term must be calculated for each follow-up test. The error term for any effect reflects the interaction between that specific effect and the participant factor. This is different to between-participants ANOVA, as the same omnibus error term is used across all omnibus and follow up tests.
List the main assumptions of within-participants ANOVA
Independence of observations, normality of difference scores, continuous DV, sphericity (variances of the pairwise differences between conditions should be roughly equal - can be directly tested)
Explain what Mauchly’s test of sphericity tests for
Mauchly’s test of sphericity tests for the assumption of sphericity (variances of the pairwise differences between conditions being roughly equal). A chi-square test is often how it is tested.
Explain what a significant result means
- Specify whether Mauchly’s test is robust test or not
A significant result means that sphericity is violated - however, the test often fails to detect violations (it is not robust).
Explain what Epsilon (ε) adjustments are and which specific statistics they adjust
Epsilon is a value by which the degrees of freedom for both the numerator and denominator in the F test are multiplied. By adjusting df in this way, epsilon changes the critical F that the obtained F is compared against. The lower the epsilon (further from 1), the greater the violation of sphericity, the stronger the epsilon adjustment, and the more conservative the F test.
Describe the three types of Epsilon (ε) adjustments and explain the differences between them (e.g., bias/conservativeness):
- Greenhouse-Geisser
- Huynh-Feldt
- Lower-bound
The Greenhouse-Geisser is where the size of the epsilon depends on degree to which sphericity is violated (generally recommended, and sits in-between in regards to its conservative status). The Huynh-Feldt modifies GG’s epsilon upwards towards one, and is less conservative (designed because DD was considered too conservative. The lower-bound epsilon assumes the worst-case violation of sphericity, and is the most conservative correction - almost never used.
Explain the advantages of fully within-participants designs relative to fully between participants designs
More power: allows us to estimate and remove variance due to individual differences, which results in a smaller error term in the F test. This makes within-participants ANOVA more powerful. Also, fewer participants are needed to detect the same sized effect in comparison to a between-participants design.
Explain the disadvantages of fully within-participants designs relative to fully between participants designs
Demand characteristics: participants may guess the aims and hypotheses and consciously or unconsciously alter their behaviour to ‘assist’ or resist what the researcher wants - not relevant in a between-participant design.
