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ANOVA Flashcards

1
Q

What is S^2 within?

A

The within-groups estimate of the population variance

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2
Q

What is S^2 between?

A

Between-groups estimate of the population variance

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3
Q

What is SStotal?

A

Total sum of squares

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4
Q

What is SSbetween?

A

Between-groups sum of squares

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5
Q

What is SSwithin?

A

Within-groups sum of squares

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6
Q

What is dftotal?

A

Total degrees of freedom

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7
Q

what is dfbetween?

A

Between-group degrees of freedom

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8
Q

Is dfbetween always on the numerator or denominator?

A

Numerator

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9
Q

What is dfwithin?

A

Within-groups degrees of freedom

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10
Q

Is dfwithin always on the numerator or denominator?

A

Denominator

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11
Q

How many IV’s are in a one way ANOVA?

A

One
Nominally scaled
Three or more levels

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12
Q

What do you assume about the populations in a one way ANOVA?

A

They’re normal, have equal variances and independent scores

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13
Q

How many dependent variables does a one way ANOVA have?

A

One

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14
Q

What scale of measurement does the DV have in a one way ANOVA?

A

Equal interval

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15
Q

Step one of one way ANOVA

A

Restate the question as a research and null hypothesis

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16
Q

What is the null hypothesis in a one way ANOVA?

A

Mew1 = mew2 = mew3

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17
Q

What is the research hypothesis for a one way ANOVA?

A

The population means differ in some way
- cannot be written in symbols

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18
Q

What is type 1 error in a one way ANOVA?

A

The probability of rejecting the null hypothesis when it is true

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19
Q

S^2 within in a one way ANOVA

A

Looks at variance within each sample to estimate population variance

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20
Q

S^2 between in one way ANOVA

A

Looks at variance between samples to estimate population

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21
Q

What happens in a one way ANOVA if there’s no treatment effect and the null is true?

A

S^2 within = S^2 between

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22
Q

What happens in a one way ANOVA if there’s a treatment effect and the null is false?

A

S^2 between > S^2 within

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23
Q

What is an F ratio in a one way ANOVA?

A

Comparison of the two population variances

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24
Q

What will the F ratio be when there’s no treatment effect and the null is true?

A

Close to 1

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25
What will the F ratio be when the null is false and there’s no treatment effect?
Greater than 1
26
Numerator of the F ratio dfbetween
N groups - 1
27
Denominator of the F ratio dfwithin
Df1 + df2 +df3
28
What is a grand mean
The overall mean of the means
29
How to measure SSbetween
How much does each mean deviate from the grand mean?
30
Calculate SSwithin
How much do individual scores deviate from the mean of each group?
31
Calculate SStotal
SSbetween + SSwithin
32
How to calculate SStotal from cell means in a one way ANOVA
Find the grand mean of all individual scores by finding the mean of the means of each column . (X - GM) = subtract the grand mean from each individual score . (X - GM)^2 = Square that answer . Add up all of them squares to get SStotal
33
Calculate SSbetween
(M - GM)^2
34
Calculate SSwithin
(X - M)^2
35
How to calculate S^2 from SS and df values
SS / df = S^2
36
How to calculate F ratio
S^2 between / S^2 within
37
How to use F table
Numerator F = dfbetween Denominator F = dfwithin If the F ratio is more extreme than cutoff reject the null
38
When do you reject the null in a one way ANOVA?
When the F ratio is more extreme than the F cutoff
39
Effect size symbol
R^2
40
R^2
The proportion of variance in the dependent variable that can be accounted for by the independent variable
41
R^2 conventions
.01 = small .06 = medium .014 = large
42
Using a power table
How many groups do you have? What is the effect size?
43
How many effects are you assessing in a two way ANOVA?
Three
44
What are the three effects you assess in a two way ANOVA?
Main effect of x Main effect of y Interaction effect
45
What is the null hypothesis in a two way ANOVA?
No main effect of x, no main effect of y, no interaction effect
46
How do we determine if there’s a main effect of the row factor?
Assess marginal means for row factor
47
What is a marginal mean?
The mean of the cell means for each row and column
48
How do we determine if there’s a main effect for the column factors?
Assess marginal means for column factors
49
How do we determine if there’s an interaction effect?
Assess the difference between all cell means
50
What is the row factor in a two way ANOVA?
The factor down the side of the table, so the information goes across the rows
51
What is the column factor in a two way ANOVA?
The top factor along the top, so the information goes down the columns
52
Graphing a two way ANOVA
When independent variables are normal use a bar graph
53
SSwithin
(X - GM)^2
54
SSbetween
(M - GM)^2
55
How to calculate the SSbetween value in a two way ANOVA
SScolumn + SSrow + SSinteraction
56
How to calculate SSinteraction
SStotal - (SSwithin + SSrow + SScolumn)
57
Calculate SSrow in two way ANOVA
SSrow = (Mrow - GM)^2 - Mrow is the row mean (mean of means in the row)
58
Calculate SScolumn in a two way ANOVA
SScolumn = (Mcolumn - GM)^2
59
For a one way ANOVA, how is dfbetween calculated?
# groups - 1
60
How to calculate dfcolumns in a two way ANOVA
# columns - 1
61
How to calculate dfrows in a two way ANOVA
# rows -1
62
How to calculate dfinteraction in a two way ANOVA
(# rows - 1) x (# columns - 1)
63
For a one way ANOVA, how is dfwithin calculated?
Df of each group added together
64
For a two way ANOVA, how is dfwithin calculated?
Dfwithin = the sum of the df of each cell Df1 + df2 + df3 + df4
65
For a one way ANOVA, how is dftotal calculated?
Total # of participants - 1
66
For a two way ANOVA, how is df total calculated?
Total # of participants - 1
67
How is F ratio calculated for one way ANOVA?
S^2 between / S^2 within
68
How many F ratios are there in a two way ANOVA?
Three - three effects so three F ratios
69
What is always the denominator of an Fratio for a two way ANOVA?
S^2 within
70
F column equation for a two way ANOVA
S^2 column / S^2 within
71
F row equation for a two way ANOVA
S^2 row / S^2 within
72
F interaction equation for a two way ANOVA
S^2 interaction / S^2 within
73
Determining F cutoff in two way ANOVA
The df in the denominator will always be the same dfwithin - df column / df within - df row / df within - df interaction / df within
74
Determining effect size (R^2) in a one way ANOVA
SS between / SStotal
75
Determining effect size (R^2) for a two way ANOVA
Use R^2 equations on the sheet given

Psych Stats (2 decks)

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