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Research Skills > Week 11 (ANOVA) > Flashcards

Week 11 (ANOVA) Flashcards

1
Q

What is ANOVA used for?

A

Testing hypotheses involving multiple means in a single test

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2
Q

What is the simplest ANOVA

A

One way ANOVA

One IV with two or more levels

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3
Q

What is the null hypothesis of ANOVA?

A

All means are equal
H0= u1 = u2 = u3

Rejecting this means some means differ

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4
Q

One way ANOVA partitions variance how?

A 
Into several types 
Total variance: variance of all scores around grand mean 
Between-groups: variance due to the independent variable (MS between) 
Within groups (error): variance that is unaccounted for
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5
Q

What is the ANOVA statistic?

A

F

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6
Q

What are the assumptions of one way ANOVA?

A

Independence: each participant only contributes one score

Normality: data within groups should be normally distributed

Homogeneity of variance: variance of scores within groups should be equal for all groups

Absence of outliers

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7
Q

How is homogeneity of variance assessed in one way ANOVA?

A

Levene’s test
Based on p values
If p is not statistically significant do not reject the null
Concluding homogeneity of variance is still intact

And augment with Harley’s f Max test

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8
Q

What is Hartley’s f max test?

A

Tests homogeneity of variance assumption

Find group with either the largest and smallest SD or variance (SD^2)

Assume equal variance if:
SD^2 ratio = <4.0
SD critical ratio = 2

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9
Q

ANOVA involves calculating the sum of squares (SS). What does this mean?

A

It is a measure of variation or deviation from the mean. A summation of the squares of the differences from the mean. Considers both factors and error

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10
Q

What is the one way ANOVA SS equation?

A

SS total = SS between + SS within

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11
Q

What does SS total mean?

A

SS of squares of all scores from the grand mean

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12
Q

What does SS between mean?

A

SS of group means from grand mean

Reflects variance due to IV

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13
Q

What does SS within mean?

A

SS of individual scores about their group mean

Reflects variance due to error

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14
Q

What can be considered accountable for variability in one way ANOVA?

A

Differences among subjects (within group) - random variance

Effects of conditions (between groups) - variance due to condition

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15
Q

How do we calculate the F statistic?

A

F= MS between/MS within

If variance associated with IV is greater than random variance, F will exceed 1.0

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16
Q

How to write up a one way ANOVA?

A

Refer to statistical significance
Stats F(df,df) = x, p = .001
Means, SD and CI for each condition
Summarise results and suggestions

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17
Q

What is the issue with performing multiple t-tests?

A

Family-wise error rate
Increases the risk of type 1 error

Are procedures to control

18
Q

Why shouldn’t you do ANOVA for 3 or more means?

A

It’s too ambiguous

19
Q

What are conservative tests?

A

Multiple comparison tests that maximally control type 1 error (false positives) - only occurs 5% of the time

However increases the risk of type 2 errors

20
Q

What are liberal tests?

A

Multiple comparison test
They reduce the risk of type 1 errors but not as much as conservative tests to

They have a greater statistical power to detect true effect

21
Q

What is a bonferroni test?

A

Most conservative of all multiple comparison tests
Is simple and effective

Adjusts p value required for statistical significance by dividing desired alpha level by the number of tests performed
Only p values that are less than the adjusted p are considered significant
Adjustment is severe when many comparisons are required so best used when number of comparisons is small

22
Q

What is Tukey’s honestly significant difference (HSD) test?

A

It is moderately conservative
Very popular
Required p value calculated using the studentised range stat
The test is performed by determining difference between means required for significance

Good when lots of comparisons to be made!

23
Q

What is Fishers protected least significant difference test

A

Most liberal test
No adjustment to the p value
Controls type 1 error rate by requiring statistically significant ANOVA before interpreting- others do not require this.

Series of t tests but SE is calculated using all available groups

Use when ANOVA is significant and there are only 3 means

24
Q

What is a repeated measures ANOVA?

A

Used when IV is a within-subjects factor (a repeated measure)

It’s an extension of paired samples t test for 3 or more conditions

25
Q

What are the assumptions for a repeated measures ANOVA

A

Independence: scores for different participants must be independent

Normality: data within groups should be normally distributed

Sphericity: variance of scores within groups should be equal for all groups. Tested through levene’s test and/of F max <4.0

Absence of outliers

26
Q

What is SSwithin-groups divided into in repeated measures ANOVA?

A

SS within subjects

SS between subjects

27
Q

What is sphericity?

A

Sphericity is assumed in repeated measures ANOVA not homogeneity of variance

Requires equal variance for sets of difference scores

28
Q

What are some critiques of repeated measures ANOVA?

A

Practice effects and sequence effects

29
Q

What study design calls for a one way ANOVA?

A

DV is interval or ratio

IV is categorical with 3 or more levels

Hypotheses regard difference among means

30
Q

What claims can be made with a statistically significant ANOVA?

A

There is a difference somewhere among the means. You don’t know which pairs differ significantly

31
Q

How do we determine which pairs of means differ significantly in a one way ANOVA?

A

Multiple comparison tests can be performed

32
Q

Do we make explicit statements about the null hypothesis when reporting ANOVA?

A

Not usually. Instead, frame statements and discussion of the results in terms of the alternative hypothesis that we are altering to support

33
Q

What effect sizes are used for ANOVA?

A

ETA squared

Cohen’s d

34
Q

What is eta square?

A

Eta squared is the proportion of variance associated with one or more main effects, errors or interactions in ANOVA.

35
Q

How is cohens d calculated for ANOVA and what does it suggest?

A

It quantifies how large the difference is between a pair of means. Therefore important for comparisons among means.

Calculated using the effect size excel worksheet

36
Q

What do we report in a one-way ANOVA if the homogeneity of variance assumption is violated?

A

Select Welch’s test and report this F-test instead of the standard f test

37
Q

Does Jamovi provide confidence intervals for one-way ANOVA?

A

No it does not. Need to use the effect size worksheet

38
Q

How do we calculate degrees of freedom for a between groups one way ANOVA?

A

Number of groups - 1

39
Q

How do we calculate the degrees of freedom for a within groups one way ANOVA?

A

If group has 10 participants, 9 df (N-1)

If 5 groups, 45 df (9x5)

40
Q

What does a larger F value mean for a one way ANOVA?

A

Greater probability that differences between the groups will be significant

41
Q

How should we report the p value in a one way ANOVA?

A

A one-way between groups ANOVA revealed a significant effect of group…

42
Q

What are the strengths of eta squared?

A

Weak/small: 0.01
Moderate: 0.06
Strong/large: 0.14

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