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Stats 100a ANOVA > ANOVA > Flashcards

ANOVA Flashcards

1
Q

Simple Hypothesis

A

µ1=µ2=µ3

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2
Q

Complex null hypotheses

A

(µ2+µ3)/2=µ1, (µ1+µ3)/2=µ2, (µ1+µ2)/2=µ3

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3
Q

Omnibus test

A

Evaluates all of the simple and complex null hypotheses at the same time

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4
Q

Post-hoc tests

A

If we reject the null hypothesis with the omnibus test, this determines which of the null hypotheses are responsible.

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5
Q

Tukey Test

A

Most widely used Post-Hoc test. It identifies which of the pairwise mean comparisons might be responsible for the rejection of the null hypotheses in the Omnibus test.

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6
Q

What if the tukey test fails?

A

If Omnibus=reject null,& if tukey fails, then one or more of complex hypotheses is responsible. Tukey only compares μ1 = μ2 = μ3, not complex.

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7
Q

What does ‘=’ notation mean?

A

the means are ‘about the same’ or that we do not have enough evidence to reject them as being the same.

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8
Q

What happens to the graph when two groups are averaged together in a complex hypothesis?

A

The width of the average distribution goes down and it is easier to reject a value as coming from the average distribution than from either individual distribution.

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9
Q

Apriori Hypothesis

A

Tests of a specific complex null hypotheses

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10
Q

Apriori v. Omnibus

A

Apriori has an advantage over the Omnibus test in that they are easier to reject due to less variance. Similar to a one-tailed test.

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11
Q

Anova

A

Uses variances estimates to test the null hypotheses of the Omnibus test

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12
Q

How to get the Estimate of Population Score Variance

A
  1. by looking at the scores within each group. If we have 3 sample estimates, we can combine these estimates to get out best estimate of the population variance.
  2. means of each of the groups: mean distribution variance is N times smaller than score distribution variance.
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13
Q

MSWithin

A

The variance estimate coming from scores within the groups.

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14
Q

MSBetween

A

The variance estimate coming from means between the groups

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15
Q

F Ratio

A

Compares the two variance estimates through a ratio by dividing MS Between/ MS Within

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16
Q

When do you use a simple ANOVA and why is it valuable?

A

It is used when the number of scores in each group is equal. It is valuable because it is both easier to understand and easier to calculate than the structural ANOVA

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17
Q

When do you use a structural ANOVA?

A

It can be used in all cases, when the scores in each group are equal or if they are not equal.

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18
Q

If the null hypothesis is true, what happens to the variance of means?

A

It should be relatively small. It should be about the same as the variance of the scores. F ratio is about 1 because MSB and MSW are about the same.

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19
Q

If the null hypothesis is false, what happens to the variance of the means?

A

The variance of the means will rise dramatically because now the means are much further away from each other because they are coming from different distributions. F ratio is greater than 1 because MSB increases while MSW stays about the same.

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20
Q

If the null hypothesis is false, what happens to the F ratio?

A

The ratio of MSB / MSW will also rise because the numerator (MSB) will increase while the denominator (MSW) will stay the same.

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21
Q

When do we use the One-way between subjects ANOVA?

A

The ratio variables are not related and there are 3 or more groups.

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22
Q

1-way between subjects simple ANOVA - Score variance

A

Sj2=Σ(Xi-X)2/(n-1)

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23
Q

1-way between subjects simple ANOVA - MSwithin

A

MSWithin=ΣSj2 / K

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24
Q

1-way between subjects simple ANOVA - MSbetween

A

MSBetween= n * Σ(Xj - XG)2/(k-1)

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25
Q

1-way between subjects simple ANOVA-F obs

A

MS Between/ MS Within

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26
Q

1-way between subjects simple ANOVA-DFTotal

A

dftotal = Ng-1

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27
Q

1-way between subjects simple ANOVA- DFBetween

A

df between= k-1

  • remember that n is the number of scores per group
  • k is the number of groups
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28
Q

1-way between subjects simple ANOVA- DFWithin

A

df Within=(n-1)k

  • remember that n is the number of scores per group
  • k is the number of groups
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29
Q

1-way between subjects structural ANOVA

A

Must be used when the sample sizes are unequal, but also can be used if the sample sizes are equal. Comparing an estimate from the mean variance and an estimate of score variance. for EVERY score in all groups, there is a total amount of variability associated with that score.

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30
Q

1-way between subjects structural ANOVA- Sum of Squares Within

A

Σ(X - Xj)2

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31
Q

1-way between subjects structural ANOVA- Sum of Squares Between

A

Σ(Xj - XG)2

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32
Q

1-way between subjects structural ANOVA- Sum of Squares Total

A

Σ(X - XG)2

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33
Q

1-way between subjects structural ANOVA- DF Between

A

K - 1

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34
Q

1-way between subjects structural ANOVA- DF Within

A

NG-K

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35
Q

1-way between subjects structural ANOVA- DF Total

36
Q

1-way between subjects structural ANOVA- MS Between

37
Q

1-way between subjects structural ANOVA- MS Within

38
Q

1-way between subjects structural ANOVA- F-Ratio

39
Q

When to use an ANOVA One-Way Within Subjects?

A

When the scores in the groups are related. When each participant has a score in each of the groups.

40
Q

Example of an ANOVA One-Way Within Subject

A

Using the same participants in all three groups – such as examining memory scores with 3 different encoding instructions or matching participants based on IQ.

41
Q

When do use a Between-subject ANOVA?

A

When there are 3 groups or more and they are NOT related. Three experimental conditions where participating in one condition would influence performance in the other condition

42
Q

Advantages of ANOVA One-Way Within Subject?

A

Easier to reject the null because there is less variation between subjects (since we’re using the same or matched participants).

43
Q

Advantages of ANOVA One-Way Between Subject?

A

Can be used with any three or more experimental groups.

44
Q

Disadvantages of ANOVA One-Way Within Subject?

A

Requires matching of groups or using the same person, which is sometimes not possible

45
Q

Disadvantages ANOVA One-Way Between Subject?

A

Subject variability is included making it harder to reject the null hypothesis. (since we’re using different independent people)

46
Q

What is Counterbalancing?

A

Counterbalancing confounding variables by adjusting your design.

47
Q

What are the sources of variability for Anova One-Way Within Subject?

A

Between-group variance, between-subject variance, and residual variability.

48
Q

What is ANOVA One-Way Within Subject Between-Occasions? SSBO

A

Differences between the mean of the score’s group and the grand mean.

49
Q

What is ANOVA One-Way Within Subject: Between-Subject Variance SSBS?

A

This variability will not be part of the F-ratio that we calculate to use for hypothesis testing. This subject variability will be removed from the analysis and will allow us to reject the null hypothesis more easily.

50
Q

What is theA NOVA One-Way Within Subject: residual variability?

A

The within-subject variability. The ‘left over’’ variability after between-group and between-subject variability have been accounted for.

51
Q

What is ANOVA One-Way Within Subject: How to calculate SSBO?

A

Σ(Xj - XG)2

52
Q

What is ANOVA One-Way Within Subject: How to calculate SSBS?

A

Σ(Xi - XG)2

53
Q

What is ANOVA One-Way Within Subject: How to calculate SSResidual?

A

SSTot - SSBO - SSBS

54
Q

What is ANOVA One-Way Within Subject: How to calculate SStotal?

A

Σ(X- XJ)2

55
Q

What is ANOVA One-Way Within Subject: How to calculate DFBetween Occasions?

56
Q

What is ANOVA One-Way Within Subject: How to calculate DFBetween Subjects?

57
Q

What is ANOVA One-Way Within Subject: How to calculate DFResidual?

A

(k-1)(n-1)

58
Q

What is ANOVA One-Way Within Subject: How to calculate DFTotal?

59
Q

What is ANOVA One-Way Within Subject: How to calculate MS Between Occasions?

A

SSBO / dfBO

60
Q

What is ANOVA One-Way Within Subject: How to calculate MS Between Subjects?

A

SSBS / dfBS

61
Q

What is ANOVA One-Way Within Subject: How to calculate MS Residual?

62
Q

What is ANOVA One-Way Within Subject: How to calculate F-Ratio?

A

MSBO / MSR

63
Q

What is ANOVA One-Way Within Subject: HOW TO FIND F-CRITICAL?

A

Use DFBO and DFR

64
Q

ANOVA TWO WAY BETWEEN-SUBJECTS: When to use it?

A

When the effects of two variables are tested at the same time.

65
Q

What are the null hypothesis of an ANOVA TWO WAY BETWEEN-SUBJECTS?

A

H0: μRow 1=μRow 2 (for more groups add more row means)
H0: μColumn 1=μColumn 2 (for more groups add more column means
H0: All Interactions = 0
Therefore, the Two-Way Anova has three separate null hypotheses, Any combination of these three hypothesis test may be rejected.

66
Q

ANOVA TWO WAY BETWEEN-SUBJECTS: What is a Qualified Main Effect?

A

One which we are cautious about interpreting because some or all of the effect may be driven by an interaction null hypothesis that was rejected in the analysis. At least one main effect & interaction are seen.

67
Q

ANOVA TWO WAY BETWEEN-SUBJECTS: SS ROW FORMULA

A

Σ(XR - XG)2

68
Q

ANOVA TWO WAY BETWEEN-SUBJECTS: SS COLUMN FORMULA

A

Σ(XC - XG)2

69
Q

ANOVA TWO WAY BETWEEN-SUBJECTS: SS INTERACTION FORMULA

A

SSTot - SSR - SSC - SSW

70
Q

ANOVA TWO WAY BETWEEN-SUBJECTS: SS Within Formula

A

Σ(X- XJ)2

71
Q

ANOVA TWO WAY BETWEEN-SUBJECTS: SS Total Formula

A

Σ(X - XG)2

72
Q

ANOVA TWO WAY BETWEEN-SUBJECTS: DF Row Formula

A

R - 1 (# of rows-1)

73
Q

ANOVA TWO WAY BETWEEN-SUBJECTS: DF Column Formula

A

C-1 (# of columns -1 )

74
Q

ANOVA TWO WAY BETWEEN-SUBJECTS: DF Interaction Formula

A

(R-1)(C-1)

75
Q

ANOVA TWO WAY BETWEEN-SUBJECTS: DF Within Formula

A

NG - (R*C)

76
Q

ANOVA TWO WAY BETWEEN-SUBJECTS: DF Total Formula

77
Q

ANOVA TWO WAY BETWEEN-SUBJECTS: MS Row

78
Q

ANOVA TWO WAY BETWEEN-SUBJECTS: MS Column

79
Q

ANOVA TWO WAY BETWEEN-SUBJECTS: MS Interaction

A

SSInt / dfInt

80
Q

ANOVA TWO WAY BETWEEN-SUBJECTS: MS Within

81
Q

ANOVA TWO WAY BETWEEN-SUBJECTS: Row F-Ratio

82
Q

ANOVA TWO WAY BETWEEN-SUBJECTS: Column F-Ratio

83
Q

ANOVA TWO WAY BETWEEN-SUBJECTS: Interaction F-Ratio

A

MSInt / MSW

84
Q

Null hypotheses that compare the average of more than one mean with another mean are called __________________ hypotheses

85
Q

In an ANOVA with 3 groups and 7 subjects per group, what is the critical F value for alpha =.05.

A

dfB = 2, dfW = (7*3)-3=18.

So critical value is 3.555 where column =2 and row = 18.

86
Q

If we run the same analysis as both a between-subject ANOVA and a within-subject ANOVA, then how will dfR compare to dfW?

A

dfR is lower than dfW by dfBS because dfR does not include dfBS (degrees of freedom between subjects)

Stats 100a ANOVA (2 decks)

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