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ANOVA Flashcards

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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
Q

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

A

Greater than 1

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26
Q

Numerator of the F ratio dfbetween

A

N groups - 1

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27
Q

Denominator of the F ratio dfwithin

A

Df1 + df2 +df3

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28
Q

What is a grand mean

A

The overall mean of the means

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29
Q

How to measure SSbetween

A

How much does each mean deviate from the grand mean?

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30
Q

Calculate SSwithin

A

How much do individual scores deviate from the mean of each group?

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31
Q

Calculate SStotal

A

SSbetween + SSwithin

32
Q

How to calculate SStotal from cell means in a one way ANOVA

A

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
Q

Calculate SSbetween

A

(M - GM)^2

34
Q

Calculate SSwithin

A

(X - M)^2

35
Q

How to calculate S^2 from SS and df values

A

SS / df = S^2

36
Q

How to calculate F ratio

A

S^2 between / S^2 within

37
Q

How to use F table

A

Numerator F = dfbetween
Denominator F = dfwithin
If the F ratio is more extreme than cutoff reject the null

38
Q

When do you reject the null in a one way ANOVA?

A

When the F ratio is more extreme than the F cutoff

39
Q

Effect size symbol

A

R^2

40
Q

R^2

A

The proportion of variance in the dependent variable that can be accounted for by the independent variable

41
Q

R^2 conventions

A

.01 = small
.06 = medium
.014 = large

42
Q

Using a power table

A

How many groups do you have?
What is the effect size?

43
Q

How many effects are you assessing in a two way ANOVA?

A

Three

44
Q

What are the three effects you assess in a two way ANOVA?

A

Main effect of x
Main effect of y
Interaction effect

45
Q

What is the null hypothesis in a two way ANOVA?

A

No main effect of x, no main effect of y, no interaction effect

46
Q

How do we determine if there’s a main effect of the row factor?

A

Assess marginal means for row factor

47
Q

What is a marginal mean?

A

The mean of the cell means for each row and column

48
Q

How do we determine if there’s a main effect for the column factors?

A

Assess marginal means for column factors

49
Q

How do we determine if there’s an interaction effect?

A

Assess the difference between all cell means

50
Q

What is the row factor in a two way ANOVA?

A

The factor down the side of the table, so the information goes across the rows

51
Q

What is the column factor in a two way ANOVA?

A

The top factor along the top, so the information goes down the columns

52
Q

Graphing a two way ANOVA

A

When independent variables are normal use a bar graph

53
Q

SSwithin

A

(X - GM)^2

54
Q

SSbetween

A

(M - GM)^2

55
Q

How to calculate the SSbetween value in a two way ANOVA

A

SScolumn + SSrow + SSinteraction

56
Q

How to calculate SSinteraction

A

SStotal - (SSwithin + SSrow + SScolumn)

57
Q

Calculate SSrow in two way ANOVA

A

SSrow = (Mrow - GM)^2
- Mrow is the row mean (mean of means in the row)

58
Q

Calculate SScolumn in a two way ANOVA

A

SScolumn = (Mcolumn - GM)^2

59
Q

For a one way ANOVA, how is dfbetween calculated?

A

groups - 1

60
Q

How to calculate dfcolumns in a two way ANOVA

A

columns - 1

61
Q

How to calculate dfrows in a two way ANOVA

A

rows -1

62
Q

How to calculate dfinteraction in a two way ANOVA

A

(# rows - 1) x (# columns - 1)

63
Q

For a one way ANOVA, how is dfwithin calculated?

A

Df of each group added together

64
Q

For a two way ANOVA, how is dfwithin calculated?

A

Dfwithin = the sum of the df of each cell
Df1 + df2 + df3 + df4

65
Q

For a one way ANOVA, how is dftotal calculated?

A

Total # of participants - 1

66
Q

For a two way ANOVA, how is df total calculated?

A

Total # of participants - 1

67
Q

How is F ratio calculated for one way ANOVA?

A

S^2 between / S^2 within

68
Q

How many F ratios are there in a two way ANOVA?

A

Three
- three effects so three F ratios

69
Q

What is always the denominator of an Fratio for a two way ANOVA?

A

S^2 within

70
Q

F column equation for a two way ANOVA

A

S^2 column / S^2 within

71
Q

F row equation for a two way ANOVA

A

S^2 row / S^2 within

72
Q

F interaction equation for a two way ANOVA

A

S^2 interaction / S^2 within

73
Q

Determining F cutoff in two way ANOVA

A

The df in the denominator will always be the same dfwithin
- df column / df within
- df row / df within
- df interaction / df within

74
Q

Determining effect size (R^2) in a one way ANOVA

A

SS between / SStotal

75
Q

Determining effect size (R^2) for a two way ANOVA

A

Use R^2 equations on the sheet given

Psych Stats (2 decks)

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