Brainscape's Knowledge GenomeTM

Browse over 1 million classes created by top students, professors, publishers, and experts.


See full index

PSYC3010 > Week 2 - ANOVA I > Flashcards

Week 2 - ANOVA I Flashcards

1
Q

What is the difference between treatment variance and error variance ? (x2)

A

Treatment is systematic variance due to our IV levels

Error is unsystematic - random, or due to unmeasured influence

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
2
Q

What are the sources of variance in a one-way ANOVA? (x2, and x2)

A

Between groups variance: systematic variance due to membership in different groups/treatments
o Distribution of group means around the grand mean
Within-groups variance: error variance (random chance, unmeasured influences)
o Distribution of individual DV scores around the group mean

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
3
Q

How are the sources of variance in a 1-way ANOVA related to 
error variance and treatment variance ? (x2)

A

Between-groups is the systematic/IV variance

Within-groups is the error/unmeasured influence variance

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
4
Q

In a 1-way ANOVA, what is SStreatment? (equation x1, words x2)

A

n∑(X bar j – X bar dot)2
People per group x sum of squared differences between group means and grand mean
Estimate of between groups variability

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
5
Q

In a 1-way ANOVA, what is SSerror? (equation x1, words x 2)

A

∑(X ij – X bar j)2
Sum of squared differences between individual scores and group mean
Estimate of within groups variability

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
6
Q

In a 1-way ANOVA, what is MStreatment? (words x1, equation x 2)

A

Index of variability among treatment means

SStreat/dftreat or SSj/dfj

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
7
Q

In a 1-way ANOVA, what is MSerror? (words x4, equation x1)

A

Index of variability among participants within a cell,
i.e. pooled within-cell variance
Average of s2 from each sample,
*Good estimate of σe2 (population error variance)
SSerror/dfError

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
8
Q

How do you calculate the F-ratio in 1-way ANOVA? (equation x1)

A

F = MStreat/MSerror

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
9
Q

Describe the structural (linear) model of 1-way ANOVA (x6)

A

Xij = μ. + τj + eij
o For i cases and j treatments
Xij, any DV/individual’s score at a given level of j is a combination of:
o μ. - the grand mean
o τj - the effect of the j-th treatment (μj - μ.)
o eij - error for i person in j-th treatment

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
10
Q

How is variance partitioned in a 2-way ANOVA? (x6)

A 
Total =
Between-groups (treatment) variance, which =
(Variance due to Factor A, plus
Variance due to Factor B, plus
Variance due to A x B), plus
Within-groups (error) variance
How well did you know this?
1
Not at all
2
3
4
5
Perfectly
11
Q

For a 2-way ANOVA, explain the SS for each main effect (x4)

A

Sum the squares of
(Marginal means for each level of the factor minus the
Grand mean), and times the lot by
[n x levels of other factor (ie, the # of observations behind each factor marginal mean)]

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
12
Q

For a 2-way ANOVA, explain the SS for the interaction (x4, or x2)

A

Sum the squares of
Grand mean minus each cell mean,
(Adjusting for the 2 marginal means),
Times the lot by n (# of observations behind each cell mean)
Simple: Between-groups variance minus Factor A variance minus Factor B variance
*SStreat - SSa - SSb

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
13
Q

For a 2-way ANOVA, explain the SSerror (x4)

A

Same as in 1-way -
∑(X ij – X bar j)2
Sum of squared differences between individual scores and group mean
Estimate of within groups variability

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
14
Q

For 2-way ANOVA, how do you calculate df for: total effects? (x2)

A

df total = N - 1

Where N is the total number of observations

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
15
Q

For 2-way ANOVA, how do you calculate df for: effect of each factor? (x3)

A

df factor = # of levels of the factor – 1
o dfB = b – 1
o dfA = a – 1

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
16
Q

For 2-way ANOVA, how do you calculate df for: effect of the interaction? (x2)

A

df interaction = product of df for factors in the interaction
o dfBA = (b – 1) x (a –1)

17
Q

For 2-way ANOVA, how do you calculate df for: error? (x4)

A

dferror = total # of observations – # of treatments
o = N – ba
• = df for each cell x # of cells
• = (n – 1) ba

18
Q

What does the null hypothesis represent in tests of main effects in 2-way ANOVA? (equation x1, words x1)

A

H0: μ1 = μ2 = μ3

No differences among means across levels of the factor

19
Q

What does the null hypothesis represent in tests of the interaction in 2-way ANOVA? (equation x2, words x3)

A

H0: μ11 - μ21 = μ12 - μ22 = μ13 - μ23
(where μ11 = mean of the following group/1st level of Factor A and 1st level of Factor B)
H0: μ1k - μ.. = μ2k - μ..
So it’s comparing simple effects,
And saying that all those cell-mean differences are the same

20
Q

What are the three omnibus test in a 2-way design?

Which we test by…? (x2)

A

Main effect of A
Main effect of B
Interaction AB
Calculating F = MStreat / MSerror for each
(for interactions, MStreat is the effect of factor AB)

21
Q

Describe the structural model of 2-way factorial ANOVA 
(x8)

A

Xijk = μ. + αj + βk + αβjk + eijk
For i cases, factor A with j treatments, factor B with k treatments, and the AxB interaction with jk treatments:
Xijk, any DV/individual’s score is combo of:
μ. - the grand mean
α j - alpha-j, the effect of the j-th treatment of factor A (μAj - μ.)
βk - beta-k, the effect of the k-th treatment of factor B (μBk - μ.)
αβjk - the effect of the interaction/differences in factor A treatments at different levels of factor B treatments (μ. - μAj - μBk + μjk)
eijk - error for i person in j-th and k-th treatments

22
Q

What are the main assumptions of ANOVA? (x7)

A

That treatment populations are normally distributed, and
Have the same variance (homogenous)
That samples are independent,
Randomly selected (no systematic allocation),
Have equal n, and
At least 2 observations
That DV data is measured on a continuous scale

23
Q

What are the numerator/denominator MS terms for each F-ratio in the omnibus tests in 2-way ANOVA? (x3, x2)

A

Factor A or B main effect:
MStreat for effect the factor, over MSerror (the remainder once factor and interaction SS subtracted from total)
For interaction:
MS of effect of the interaction, over MSerror

24
Q

In a 2-way factorial ANOVA, what does a significant F test for Factor A tell us? (X1)

A

That there is a meaningful difference in DV scores for the factor across its different levels

25
Q

In a 2-way factorial ANOVA, was does a significant F test of the AxB interaction tell us? (X1)

A

That there is a meaningful difference among the simple effects -
The (cell mean) differences are different

26
Q

Conceptually, what is an ANOVA test doing? (x2)

A

Looking for an effect as the difference among means

Which means used is dependent on which effect we’re looking at (main/interaction)

27
Q

What does mu-j represent in ANOVA? (x2)

A

Population mean of group j

The mean of any particular level of j

28
Q

What does mu. represent in ANOVA? (x1)

A

Grand mean

29
Q

What is the null hypothesis in a 1-way ANOVA? (equation and words)

A

H0: μj = μ.

No differences between any treatment means

30
Q

What is the alternative hypothesis in a 1-way ANOVA? (equation and words)

A

H1: μj ≠ μ.

There is a difference between treatment means

31
Q

What are three general indicators for interpreting F-values? (x2, x2, x1)

A

If MStreat is a good estimate of error variance,
o F = MStreat/MSerror = 1
If MStreat is more than just error variance,
o F = MStreat/MSerror > 1
Larger values of F indicate that H0 is probably wrong

32
Q

What are the 4 conceptual steps to calculating ANOVA?

A

Estimate of between-groups variability
Estimate of within-groups variability
Weight each variability estimate by # of observations used to generate the estimate (“degrees of freedom”)
Compare ratio: between over within

33
Q

What is meant by ‘expected mean squares error’? (ANOVA) (x3)

A

Expected value of a statistic is defined as the ‘long-range average’ of a sampling statistic
So:
E(MSerror) - σe2
• i.e., long term average of variances within each sample (s2) would be the population variance σe2

34
Q

What is meant by ‘expected mean squares treatment’ (ANOVA)? (x5)

A

Expected value of a statistic is defined as the ‘long-range average’ of a sampling statistic
So:
(Sigma tells us we’re talking about population variance, tau = treatment effect variance)
E(MStreat) - σe2 + n (στ)2
• Where (στ)2 is long term average of variance between sample means, and n is number of observations in each group
• i.e., long term average of variances within each sample PLUS any variance between each sample

35
Q

If group means don’t vary then what would our expected mean squares be (ANOVA) (x3)

A

(n σ τ)2 = 0, and so then
E(MStreat) = σe2 + 0 = σe2
= E(MSerror) = σe2

36
Q

How can you double-check that you have calculated the df correctly in a 2-way ANOVA? (x2)

A

Total equals between plus within

Between equals total of A, B and AxB

37
Q

What is the alternative hypothesis for testing interactions in 2-way ANOVA? (equation x1, words x1)

A

H1: μ1k - μ.. ≠ μ2k - μ..

That at least one of the simple effects of B within A1 is different from that same comparison for A2

38
Q

What is meant by an ‘additive effect’ in factorial ANOVA outcomes? (x1)
As distinct from? (x1)

A

To take one group, and add a constant to get the pattern for the other group
Interactive effect - non-parallel lines

PSYC3010 (11 decks)

Brainscape helps you reach your goals faster, through stronger study habits.
© 2024 Bold Learning Solutions. Terms and Conditions