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midterm 2 Flashcards

1
Q

compare independent samples t test, one way anova, and two way anova

A

t test:
- two means, one factor

one way anova:
- more than two means, one factor

two way anova:
- more than two means, two factors

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2
Q

what are the three null hypotheses for a two way anova?

A

main effect of factor A
main effect of factor B
interaction between factor A and B

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3
Q

what do we call the two independent variables in two way anova?

A

factors

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4
Q

what are the assumptions of two way anova

A
  • homogeneity of variance- variance of popln distributions is equal for each group’
  • subjects serve in only one of the treatment conditions (independent samples or between subjects design)
  • independence of observations
  • populationa distributions is normal within each group
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5
Q

what is a main effect

A

effect of one factor when the other factor is ignored - difference among marginal means (the mean of all the scores in a column or a row) for a factor

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6
Q

what is the interaction effect

A

the extent to which the effect of one factor depends on the level of the other factor - interaction occurs when the effects of one factor on the DV change at different levels of the other factor (indicates that main effects along do not fully describe the outcome

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7
Q

how to identify interaction effects and main effects on a graph

A
  • lines cross
  • difference in marginal means
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8
Q

within subjects design

A
  • experimental design in which the DV is measured several times within the same subject
  • also called a repeated measures design

simplest example is a before and after treatment design - measure subjects before a treatment and after

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9
Q

one way repeated measures design

A

subjects go through multiple levels of a factor

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10
Q

what are the two possible research questions for one way repeated measures designs

A

within subject effect:
- are there differences in the mean scores of the DV across groups/conditions? each subject measured at each time point
H0: µ1=µ2 etc

between subject effect
- are there differences across subjects
- the variability of subjects
H0: Vs (variance between subjects)=0

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11
Q

what are we more interested in in one way repeated measures ANOVA, the within subjects effect or the between subject effect

A

we are more interested in the within subjects effect

the between subjects effect is irrelevent because it has nothing to do with our treatment (IV) - all it tells us is that differences exist naturally between subjects

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12
Q

how do we partition variation in one way repeated measures anova?

A

SST (total sums of squares) is broken into:
SS(S): variation between row means (subject means) - Xr
SS(A): variation between group means (IV) - Xc
SS (AxS): variation between cell means - SS(AxS)= SS(T)-SS(A)-SS(S)

SS(A) and SS(AxS) come from SS(W)

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13
Q

what are the assumptions in one way repeated measures ANOVA?

A

Normality
- the distributions of observations on the dependent variable is normal within each level of the factor

compound symmetry:
- homogeneity of variance: population variance observations is equal at each level of the factor - gets replaced with sphericity
- homogeneity of covariance: the population covariance between any pair of repeated measurements is equal (homogenous covariance)

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14
Q

variance vs covariance

A

variance is the spread of a data set around its mean value, while a covariance refers to the measure of the directional relationship between two random variables - higher covariance means a stronger relationship

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15
Q

compound symmetry

A

all variances are equal and all covariances are equal

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16
Q

compound symmetry in one way repeated measures ANOVA

A

gets replaced by the assumption of sphericity

sphericity means that the variance of differences of a pair of observations is the same across all pairs
- we assume that the relationship between pairs of experimental conditions is similar

sphericty is a necessary condition for validity of F test in repeated measures ANOVA

17
Q

Mauchly’s W or Mauchly’s test

A

test for violations of sphericity
H0 is that variances of differences between conditions are equal/assumption of sphericity is met

rejecting null indicates that the assumption of sphericity is violated

18
Q

when is the assumption of sphericity and CS violated under Mauchly’s test?

A

if p<.05

19
Q

what happens when CS (compound similarity - also sphericity) is violated in one way repeated measures ANOVA

A

the omnibus Ftests tend to be inflated, leading to more false rejections of H0 - higher type 1 error rate

violations of CS require adjustments to the F test

20
Q

what are some ways to deal with violations of sphericity

A

conservative F test:
- using a conservative critical value based on the possible violation of sphericity
- can achieve a more conservative crit val by increasing it through reducing the degrees of freedom

DF(B)=e(k-1) and DF(BS)= e(k-1)(n-1)

e = epsilon = extent to which sphericity was violated

21
Q

what is epsilon when sphericity holds

A

1

22
Q

what is epsilon when sphericity is violated in one way repeated measures ANOVA

A

<1

23
Q

what are we calculating for one way repeated measures ANOVA

A

SS(T), SS(A(, SS(s), SS(AxS), MS(A), MS(S), MS(AxS)

24
Q

what is partial omega squared

A

a form of omega squared used in one way repeated measures anova that excludes the variability due to differences between subjects

25
Q

SSW - one way repeated measures ANOVA

A

within participant variation
- partitioned into SS(A) and SS(AxS)

26
Q

one way repeated measures ANOVA H0 and F

A

between group/or effect of treatment
H0: µ1=µ2=µ3
H1 not all µg are the same

F = MSa/MSaxs

27
Q

p value <= .05 (or whatever you use for a)

A

reject null

28
Q

APA summary of one way repeated measures ANOVA

A
  • description, independent variable, levels, MAuchly;s test, overall test results - F, p , partial omega squared
29
Q

what are two necessary follow up analyses for each significant effect in two way ANOVA?

A
  • simple main effect effect is interaction is significant
  • post hoc test for significant main effect
30
Q

repeated measures ANOVA F

A

only one:
Fa = MSA/MSAxS

31
Q

if epsilon is greater than 1 in the test for sphericity in one way repeated measures ANOVA what needs to change?

A

df and MS

32
Q

terms in two way ANOVA

A

SSa= variation between sums for Factor A
SSb=variation between sums for Factor B
SSaxb=variation between cell sums

33
Q

effects in three way ANOVA

A

3 main effects
3 simple (two way interactions)
1 three way interaction

SSA, SSB. SSc, SSaxb, SSaxc, SSbxc, SSaxbxc
plus SS residual and SS total

34
Q

effects in three way ANOVA

A

3 main effects
3 simple (two way interactions)
1 three way interaction

SSA, SSB. SSc, SSaxb, SSaxc, SSbxc, SSaxbxc
plus SS residual and SS total

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