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Stats 4 > 7. Independent groups One Way ANOVA > Flashcards

7. Independent groups One Way ANOVA Flashcards

1
Q

Why use an ANOVA?

A

To show whether there are differences among groups (IVS) on a variable of interest (DV) … do the means VARY?

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2
Q

What does an ANOVA compare a ratio of?

A

Systematic variance to Unsystematic variance (error)

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3
Q

In ANOVA speak what is Systematic variance and unsystematic variance written as?

A

Variance Between Groups

Variance Within Groups

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4
Q

What is the total mean of means called in an ANOVA?

A

The Grand Mean (the simplest model)

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5
Q

Why is the grand mean important in ANOVA?

A

The regression ANOVA model must be a sig. better fit than the grand mean

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6
Q

What does b0 represent in the regression line equation?

A

the coefficient of the intercept

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7
Q

What does b1 represent in the regression line equation?

A

the slop of the line

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8
Q

What happens as the coefficient of the regression line (b1) gets bigger?

A

The difference between the model and the mean gets bigger

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9
Q

When would we expect that the regression model is a better fit than the mean?

A

When the group means are sig. different

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10
Q

What is the grand mean represented as in the regression output?

A

The Total Sum of Squares
SST
(The Total Variance)

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11
Q

What is the variance from the model represented as in the regression output?

A

The Model Sum of Squares
SSM/B
(Variance Between Groups)

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12
Q

What is the residual variance represented as in the regression output?

A

Residual Sum of Squares
SSW
(Variance Within Groups)

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13
Q

What do we need to do in an ANOVA if we have more then 2 levels in a categorical IV?

A

Dummy code the levels to create new dummy variables

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14
Q

How many Dummy variables do you need?

A

1 less than the number of levels with a baseline variable of 0
(e.g. with 4 levels you would have 0, 1, 2, 3)

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15
Q

To create the dummy variables, how many times do you need to code them if you have four levels?

A

3 times… e.g. baseline (0) and dummy variable 1, then baseline (0) and DV2, then baseline (0) and DV3

CODED as 0 AND 1 each time (with the other non-used variables as 0 as well)

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16
Q

What does OLS stand for?

A

Ordinary Linear Squared (regression)

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17
Q

What are the degrees of freedom for SSB/M?

A

k - 1

k = number of groups

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18
Q

What are the degrees of freedom for SSW (error)?

A

N - k
(N = total sample size
k = number of groups)

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19
Q

What are the degrees of freedom for SST or Grand Mean?

A

N - 1

N = total sample size

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20
Q

How do you calculate the effect size for an ANOVA?

A

Take the square root of
Rsq = SSM / SST

= r (Cohen’s conventions)

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21
Q

What is the effect size normally reported as?

A 
Eta squared 
(based on the SS sample not SS population = issue)
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22
Q

What should we used instead of Eta Squared?

A

Omega Squared

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23
Q

What is Omega Squared?

A

A less biased measurement of effect size

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24
Q

How is Omega Squared calculated?

A

ωSq (omega squared)
= SSB - (k - 1)*MeanSqSSW /
SST+MeanSqSSW

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25
Q

How is Omega Sq interpreted?

A

Using Cohen’s RSq conventions: 1%, 9%, 25%

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26
Q

What are the 2 ways you can test for group differences?

A

Planned comparisons (planned contrasts)
or
Post-hoc tests

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27
Q

What is the difference between using contrasts and post-hoc tests?

A 
Contrasts = one-tailed for specific priori hypotheses 
Post-hoc = two-tailed for non directional hypotheses
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28
Q

What are the 5 rules for planned contrasts?

A

number of contrasts = k - 1
(e.g. 0 v. 1,2&3; 1 v. 2&3; 2 v. 3)

Orthogonal

if group not in contrast = 0

two chunks of variance contrasted

sum of weights = 0
(coefficients balance out e.g. if using 0 v.1,2,3 then 0 has a coefficient of 3 because it is being compared to 3 other variables with coefficients of 1: 1+1+1=3)

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29
Q

What does orthogonal mean?

A

Unrelated

30
Q

Why do contrasts need to be orthogonal?

A

To compare two unique chunks of variance (t-tests)

31
Q

What are the 5 options for testing planned contrasts and are they orthogonal or not?

A

Deviation (non-orthogonal). Simple (non-orthogonal).
Repeated (non-orthogonal).

Helmert (orthogonal).
Difference (orthogonal).

32
Q

What does the deviation planned contrasts do?

A

Compares the effect of each group (except the first) to the overall experimental effect

2 v. (1, 2, 3, 4)
3 v. (1, 2, 3, 4)
4 v. (1,2, 3, 4)

33
Q

What does the simple planned contrasts do?

A

Compares each category to the first category.

1 v. 2
1 v. 3
1 v. 4

34
Q

What does the repeated planned contrasts do?

A

Compares each category (except the first) to the previous category

1 v. 2
2 v. 3
3 v. 4

35
Q

What does the Helmert planned contrasts do?

A

Compares each category (except the last) to the mean effect of all subsequent categories

1 v. (2, 3, 4)
2 v. (3, 4)
3 v. 4

36
Q

What does the difference planned contrasts do?

A

Compares each category (except the first) to the mean effect of all previous categories

4 v. (3, 2, 1)
3 v. (2, 1)
2 v. 1

37
Q

How do you calculate t?

A

Mean Diff/ SE

38
Q

What is the post-hoc process that looks for differences that might exist between groups called?

A

Data Mining
or
Data Snooping

39
Q

What are the two types of error rates that are important in post-hoc tests?

A

Error rate per comparison (PC)

Family wise error rate (FW) … probability of containing Type I Error

40
Q

What is Type I Error?

A

The incorrect rejection of the null hypothesis (a “false positive”: finding something that’s not there)

41
Q

What is Type II Error?

A

The failure to reject a null hypothesis (a “false negative”: not finding something that’s there)

42
Q

What is the most popular way to control the error rate in post-hoc tests?

A

Bonferroni Correction

43
Q

What determines which post-hoc procedure you should use?

A

If groups have equal numbers
or
If groups have equal variance

44
Q

What are the 6 types of post-hoc tests you can do?

A 
Tukey HSD
Bonferroni 
Levene's
Gabriel 
Hochberg's GT2
Games-Howell
Brown-Forsythe F
45
Q

When should you use Tukey?

A

To compare differences among group means when:
Equal variances
Equal sample sizes

46
Q

When should you use Levene’s test?

A

When testing the equality of group variances on the DV in an ANOVA

47
Q

When should you use Brown-Forsythe F?

A

To compare differences among group means when: Unequal variances

48
Q

When should you use Bonferroni?

A

To adjust for the error rate when multiple post-hoc tests are performed

49
Q

When should you use Gabriel test?

A

Post-hoc test when comparing groups with:
Equal variances
Slightly different sizes

50
Q

When should you use Hochberg’s GT2?

A

To compare differences among group means when:
Equal variances
Markedly different sizes

51
Q

When should you use Games-Howell?

A

To compare differences among group means when: Unequal variances

52
Q

What is the difference between post-hoc tests and contrasts?

A 
Post-hoc = compare each group mean again each other group mean on DV
Contrasts = comparing different pairs
53
Q

What df do you use when reporting the t-tests for post-hoc tests?

A

Within Subjects: N - k
(N = total sample size
k = number of groups)

54
Q

How many df do you need to report when reporting on t-tests?

A

1

55
Q

How many degrees of freedom do you need to report when reporting F?

A

2

56
Q

What can you use other than Bonferroni to correct for error rate?

A

Fisher’s LSD

57
Q

What is the formula for the effect size of contrasts and comparisons?

A

sqrt (tsq / tsq +df)

(Using cohen’s r conventions)

Only computed for sig. contrasts/ comparisons

58
Q

What are the 3 assumptions for an independent group ANOVA?

A 
Normal distributions (6 sub checks)
Homogeneity of variances (Non sig. Levene's)
Independence
59
Q

What are the 6 sub checks for normality?

A 
Symmetry (Mean= medium = mode) 
Modality 
Skew
Kurtosis 
Outliers 95%, 5%, 3% 
Non sig. S-W
60
Q

How often does normality need to be checked in an independent groups ANOVA?

A

Once for each group/ level

61
Q

Violations of normality are only problematic in an independent groups ANOVA if?

A

The populations are dramatically skewed

The populations are skewed in opposite directions from each other

62
Q

Which Levene’s test do you read from?

A

“Based on Mean”

63
Q

When is an independent groups ANOVA okay even when Levene’s is sig.?

A

When the largest variance isn’t more than 4x the smallest
AND
Sames sizes approach equal

64
Q

What should you use if normality is violated in an independent groups ANOVA?

A

Kruskal-Wallis

Non-parametric test

65
Q

What should you use if homogeneity of variance is violated in an independent groups ANOVA?

A

Brown-Forsythe
or
Welch F

66
Q

What should you use if BOTH normality AND homogeneity of variance is violated in an independent groups ANOVA?

A

Kruskal-Wallis

Non-parametric test

67
Q

What should you use if your design is oneIVwith3ormore

unrelated groups and one DV?

A

An Independent groups one-way ANOVA

68
Q

What should you do if after running an Independent groups one-way ANOVA, you DON’T get a sig. F?

A

STOP

69
Q

What should you do if after running an Independent groups one-way ANOVA, you GET a sig. F?

A 
Planned contrasts (directional hypothesis) 
Post-hoc tests (non-directional hypothesis)
70
Q

What post-hoc test should you use if you have equal groups and equal variance?

A

Tukey HSD

71
Q

What post-hoc test should you use if you have unequal group sizes?

A

Gabriel
or
Hochberg’s

72
Q

What post-hoc test should you use if you have unequal variances?

A

Games Howell

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