Lecture 7: One-way and two-way repeated measures ANOVA Flashcards

Question 1

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Diagram of Repeated measures regression model

Question 2

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In regression model for repeated measures ANOVA, we have - (2)

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a model for each participant with the values of u tweaking the model to account for individual differences in the baseline mean and the change in mean associated with the predictor(s)

g denotes the condition and i is the participant

Question 3

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One-way ANOVA between groups can be linked to linear model shown below..

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We have three means and the model accounts for three levels of a categorical variable with dummy variables

Question 4

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Diagram of repreated measure design equation

Question 5

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**

Repeated-measures is a term used when the

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same participants participate in all conditions of an experiment

Question 6

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What is the decision tree for choosing one-way repeated measures ANOVA? - (5)

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Q: What sort of measurement? A: Continuous
Q:How many predictor variables? A: Two or more
Q: What type of predictor variable? A: Categorical
Q: How many levels of the categorical predictor? More than two
Q: Same or Different participants for each predictor level? A: Same

Question 7

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The assumption of sphericity in within-subject design ANOVA can be likened to

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the assumption of homogeneity of variance in
between-group ANOVA

Question 8

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Sphericity is sometimes denoted as

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ε or circularity

Question 9

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Sphericity is
a more general condition of

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compound symmetry

Question 10

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What is compound symmetry?

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true when both the variances across conditions are equal and the covariances between pairs of conditions are equal

Question 11

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Compound symmetry holds
true when both the variances across conditions are equal and the covariances between pairs of conditions are equal

In other words, it means..

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variation within experimental conditions is fairly similar (similar to homogenity of variance in between) and that no two conditions are any more dependent than any other two

Question 12

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Sphereicty is a less restrictive form of

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compound symmetry

Question 13

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What does spherecity refer to?

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equality of variances of the differences between treatment levels.

Question 14

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Spherecity means the equality of variances of the differences between treatment levels

E.g.,if you were to take each pair of treatment levels, and calculate the differences between each pair of
scores, then it is

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necessary that these differences have approximately equal variances.

Question 15

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you need at least … conditions for spherecity to be an issue

Question 16

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How is sphereicty assumed in this dataset?

Question 17

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How is spherecity calculated? - (2)

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Calculating differences between between pairs of scores for all treatment levels e.g., A-B, A-C , B-C
Calculating variances of these differences e.g., variances of A-B, A-C, B-C

Question 18

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What does the data from table show in terms of assumption of spherecity (calculated by hand)? - (3)

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there is some deviation from sphericity because the variance of the differences between conditions A and B (15.7) is greater than the variance of the differences
between A and C (10.3) and between B and C (10.3).

However, these data have local circularity (or local sphericity) because two of the variances of differences are identical.

The deviation from spherecity in the data does not seem too severe (all variances roughly equal) but here assess deviation is serve to warrant an action

Question 19

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How to assess the assumption of sphereicity in SPSS?

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via Mauchly’s test

Question 20

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If Mauchly’s test statistic is significant (p < 0.05) then

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variance of differences between conditions are significnatly different - must be vary of F-ratios produced by computer

Question 21

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If Mauchly’s test statistisc is non significant (p > 0.05) then it is reasonable to conclude that the

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varainces of the differences between conditions are equal and does not significantly differ

Question 22

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Signifiance of Mauchly’s tes is dependent on

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sample size

Question 23

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Example of signifiance of Maulchy’s test dependent on sample size - (2)

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in big samples small deviations from sphericity can be
significant,

small samples large violations can be non-significant

Question 24

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What happens if the data violates the sphereicity assumption? - (2)

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several corrections that can be applied to
produce a valid F-ratio

or

use multivariate test statistics (MANOVA)

Question 25

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What corrections to apply to produce valid F-ratio when data violates sphereicity? - (2)

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Greenhouse-Geisser correction ε

Huynh-Feldt correction

Question 26

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The Greenhouse-Geisser correction varies between

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1/k (k is number of repeated measures conditions) and 1

Question 27

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The closer that Greenhouse Geisser correction is to 1, the

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more homogeneous the variances of differences, and hence the closer the data are to being spherical.

Question 28

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How to calculate lower-bound estimate fo spherecity for Greenhouse-Geisser correction when there is 5 conditions? - (2)

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Limit of f ε^ is 1/k (number of repeated-measures conditions)

so… 1/(5-1) = 1/4 = 0.25

Question 29

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Huynh and Feldt (1976) reported that when the

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Greenhouse-Geisser correction is too conservative

Question 30

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Huynh-Feldt correction is less conservative than

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Greenhouse-Geisser correction

Question 31

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when estimates of sphericity are greater than 0.75 (1/k) then the

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Huynh–Feldt
correction should be used,

Question 32

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when sphericity estimates are less than 0.75 (1/k) or nothing is
known about sphericity at all, then

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the Greenhouse–Geisser correction should be used instead

Question 33

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Why is MANOVA used when data that violates spherecity?

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MANOVA is not dependent upon the assumption of sphericity

Question 34

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In repeated measures ANOVA, the effect of our experiment is shown up in within participant variance than

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between group variance

Question 35

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In independent ANOVA, the within-group variance is our…. and it is not contaimed by… - (2)

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residual variance (SSR) = variance produced by individual differences in performance

SSR is not contaimined by experimental effect as study carried out by different people

Question 36

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In repeated-measures ANOVA, the within-participant variability is made up of

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the effect of experimental manipulation and individual differences in performance (random factors outside of our control) - this is error SSR

Question 37

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Similar to independent ANOVA, repeated-measures ANOVA uses F-ratio to - (2)

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compares the size of the variation due to our experimental
manipulations to the size of the variation due to random factors

has same type of variances in independent - total sum of squares (SST), model sum of squares (SSM) and a residual sum of squares (SSR)

Question 38

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What is the differences between independent ANOVA and repeated-measures design ANOVA?

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repeated-measures ANOVA the model and residual sums of squares are both part of the within-participant variance.

Question 39

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In repeated-measures ANOVA

If the variance due to our manipulations is big relative to
the variation due to random factors, we get a .. and conclude - (2)

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big value of F ratio

we can conclude that the observed results are unlikely to have occurred if there was no effect in the population.

Question 40

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To compute F-ratios we first compute the sum of squares which is the following… - (5)

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SST
SSB
SSW
SSM
SSR

Question 41

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How is SST calculated in one-way repeated measures ANOVA?

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SST = grand variance (N-1)

Question 42

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What is the DF’s of SST?

Question 43

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The SSW (within-participant) sum of squares is calculated in one-way repeated ANOVA by…

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square of the standard deviation of each participant’s scores multiplied by the number of conditions minus 1, summed over all participants.

Question 44

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What is the DF of SSW of one-way repeated ANOVA? - (2)

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DF = N(n-1)

number of participants multiplied by the number of conditions minus 1;

Question 45

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How is SSM calculated in one-way repeated ANOVA? - (2)

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square of the differences between the mean of the participant scores for each condition and the grand mean multiplied by the number of participants tested, summed over all conditions.

do this for each condition grp

Question 46

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What is the DF of SSM in one-way repeated ANOVA? - (2)

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DF = n-1
n is number of conditions

Question 47

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How is SSR calculated in one-way repeated ANOVA?

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the difference between the within-participant sum of squares and the sum of squares for the model.

Question 48

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What is the DF for SSR in one-way repeated ANOVA?

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DF of SSW minus DF of SSM

Question 49

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How do we calculated mean squares (MS) and mean residuals (MR) to acalculate F-ratio in one-way repeated ANOVA?

Question 50

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SSM tells us how much variation the

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model (e.g. the experimental manipulation) explains

Question 51

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SSR tells us how much variation

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n is due to extraneous factors

Question 52

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MSM represents the average amount of variation explained by

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the model (e.g. the systematic variation),

Question 53

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MSR is a gauge of the average amount of variation explained by

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extraneous variables (the unsystematic variation).

Question 54

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The F-ratio is a measure of the ratio of the varation

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explained by the model and the variation explained by unsystematic factors.

Question 55

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Calculating F-ratio is the same for one-way repeated-measures design and independent design as..

Question 56

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We don’t need to use SSB (between-subject variation )to calculate F-ratio in

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one-way repeated ANOVA

Question 57

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What does SSB represent in one-way ANOVA?

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individual differences between cases

Question 58

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Not only does sphereicity produces problems for F in repeated measures ANOVA but causes complications for

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post-hoc tests

Question 59

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When spereicity is violated in one-way repeated ANOVA , what post-hoc test to use and why - (2)

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Bonferroni method seems to be generally the
most robust of the univariate techniques,

especially in terms of power and control of the Type I error rate.

Question 60

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When sphereicity is not violated in one-way repeated ANOVA, then what post-hoc tests to use?

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Tukey can be used

Question 61

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In either case where sphereicity is violated or not in one-way repeated ANOVA, a post-hoc test called - (2)

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Games–Howell procedure, which uses a pooled error term,

it is more preferable to Tukey’s test.

Question 62

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Due to complications of sphereicity in one-way repeated ANOVA,

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standard post hoc tests used for independent designs not avaliable for repeated measure designs

Question 63

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Why is repeated contrast useful in repeated-measures design especially one-way repeated measures?

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evels of the independent variable have a meaningful order e.g., meausred DV at successive time points or adminstered increasing doses of a drug

Question 64

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When should Sidack correction as post hoc be selected for one-way repeated ANOVA?

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concerned about the loss
of power associated with Bonferroni corrected values.

Answer 58

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Left shows variables represent each level of IV which is animal
Right shows descriptive statistics - higher mean time to retch when celebrity eating stick insect (8.12)

Answer 59

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P-value is 0.047 which is less than 0.05
Thus, reject the assumption of spherecity that variances of the differences between levels are equal

Answer 60

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Since there are 4 conditions, lower limit of ε^ is 1/(4-1) = 0.333 (lower-bound estimate in table)
SPSS Output 13.2 shows that the calculated value of ε
^ is 0.533.
0.533 is closer to the lower limit of 0.33 than it is to the upper limit of 1 and it therefore represents a substantial deviation from sphericity

Answer 61

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The value of F = 3.97 which is compared against a critical value for 3 and 21 DF and p-value is 0.026
conclude there is significant difference between 4 animals in their capacity to induce retching when eaten

Answer 62

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group differences lie

just tells the differences between grps is significant

Answer 63

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The F-ratios are the same across the rows
the D.F is changed as well as critical value the F-statistic is compared with

Answer 64

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Adjustment made by multiplying the DF by the estimate of spherecity.

Answer 65

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Observed F statistic not significant using Greenhouse-Geisser ( p> 0.05)
Greenhouse-Geisser is quite conservative and miss true effects that exist
Thus, Huynh-Feldt showend F-statistic is still significant as p-value of 0.048

Answer 66

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Taking average of two significant values e.g., 0.063+ 0.048/2 = 0.056
Thus, go with Greenhouse-Geisser correction and conclude F ratio is non-significant

Answer 67

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Type 1 error (False positive) or not

Answer 68

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MANOVA multivariate tests is significant , p = 0.002 which is less than 0.05

The results supports a decision to conclude that there are significant differences between the time taken to retch after eating different animal

Answer 69

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Contratss of 0 means grp not included in a contrast
Contrast 1 (labelled Level 1 vs Level 2) ignores the fish eyeball and witchetty grub (as labelled 0 throughout column
Grps with positive wieght is compared with grps with negative weight
E.g., first contrast (Level 1 vs Level 2) compares the stick insect (1)with the kangaroo testicle (-1)
E.g., second contrast (Level 2 vs Level 3) compares kangaroo testicle (1) with fish eye (-1)
E.g., third contrast (Level 3 vs 4) compared fish eyeball (1) with witchetty grub

Answer 70

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celebrities took significantly longer to retch after
eating the stick insect compared to the kangaroo testicle (Level 1 vs. Level 2) - p-value of 0.002
Time taken to retch was not significantly different in Level 2 vs 3 and Level 3 vs 4

Answer 71

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ignored

inclined to conclude main effects of animal was significant and proceed with further tetss like contrasts

Answer 72

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Repeated measures design
One IV (Incentive) , four conditions (week 1, week 2, week 3, week 4)
One DV (Sales Generated)
One-way repeated ANOVA

Answer 73

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does not actually make any adjustments to p-value in terms of critical value as what post-hoc test should do

Answer 74

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sales are increasing across the weeks
Week 1 start at 427.93 and gradually rise by week 4 to 642,28 pounds
looks like incentives are having an effect and seem to generate higher sales

Answer 75

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P-value is not significant ( p = 0.080)
Assumption of spherecity is satisfied so we got equal variances between differences across conditions

Answer 76

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DF for week is 3 and 5
Week: F(3,57) = 26.30, p < 0.001 (p = 0.000), eta-squared is 0.58 - large effect

Answer 77

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No sig difference betwen W1 and W2
Sig difference between W1 and W3 = ihigher sales in W3 (538.570) compared to W1 (427.933)
Sig difference between W1 and W4 = ihigher sales in W3 (642.284) compared to W1 (427.933)
*Not sig diff with W2 and W3
Sig difference between W2 and W4 , higher sales in W4 (642.284) than W2 (481.388)
Sig difference between W3 and W4 , higher sales in W4 (642.284) than W3 (538.570)

Answer 78

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- Did sales increase from W1 to W2? = p = 0.010 significant
Did sales increase from W2 to W3? = p = 0.030
Did sales increase from W3 to W4? = p = 0.008

Answer 79

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Post hoc has lack of power due to many multiple comparisons
By limiting comparisons in contradt we get around problem

Answer 80

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Omega squared
R
Partial-eta squared

Answer 81

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η2 = 0.01 indicates a small effect.
η2 = 0.06 indicates a medium effect.
η2 = 0.14 indicates a large effect.

Answer 82

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Values of omega squared range from 0 to 1.0 and can be interpreted semantically as the percentage of variation in the dependent variable attributable to the independent variable.

If calculation yields a negative number, it is interpreted as 0.

Answer 83

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more than one IV

Answer 84

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4 different IV

Answer 85

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IV with 3 levels
IV with 2 levels

Answer 86

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Repeated measures design
Two IVs: alcohol (3 conditions) and sleep (2 conditions)
DV: Reaction Times
Two-way repeated measures ANOVA

Answer 87

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large number for RT means slower RT
Alcohol seem to have an effect on RT but particularly for 2 pints + no sleep

Answer 88

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Two p-values: alcohol ( p = 0.00) and alcohol * sleep [ interaction effect] (p = 0.00) – > sig so assumption of spherecity is violated so report Grenhouse-Geisser values from main ANOVA table
No p-value for sleep as only 2 conditions and test of sphericity need more than 2

Answer 89

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Main sig effect of alcohol: F(1.16,22.06) = 51.38, p < 0.001, partial eta-squared = 0.73
Main sig effect of sleep: F(1,19) = 88.61, p < 0.001, partial-eta-squared = 0.82
Interaction effect: F(1.15,21.91) = 23.36, p < 0.001, partial-eta squared = 0.55

Answer 90

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condition 1 and condition 2 which was significant
Condition 1 vs 3 which was significant
Condition 2 with Condition 3 was significant
So all groups differing significantly from each other so interpret from that higher does of alcohol has more impact on RT

Answer 91

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Interaction effect is there = as line continue they cross
Most pronouned effect was in alcohol grp 3 (2 pints)
When alcohol grp 3 had full nights sleep (2), impairs their RT very slightly
When alcohol grp 3 had sleep deprivation (1) in combination with 2 pints, it impairs RT by a lot –> use simple effect analysis as well as two-way independent ANVOA to see if difference in grp 3 of blue and green line is sig

Answer 92

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R
Partial-eta-squared

Answer 93

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Can do non-parametric test called Friedman’s ANOVA if only one IV

There is no non-parametric counterpart for more than one IV in repeated design

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Lecture 7: One-way and two-way repeated measures ANOVA Flashcards

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