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Independent one-way ANOVA Flashcards

1
Q

Used when we have 1 IV with more than 2 levels

A

One-way ANOVA

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2
Q

Used when we have 1 IV with more than 2 levels, between subjects

A

One-way independent ANOVA

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3
Q

Used when we have 1 IV with more than 2 levels, within subjects

A

One-way repeated measures ANOVA

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4
Q

What does one-way ANOVA estimate?

A

Estimates whether the population means under the different levels of the IV are different

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5
Q

Estimates whether the population means under the different levels of the IV are different

This is known as…?

A

One-way ANOVA

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6
Q

One-way ANOVA estimates whether the population means under the different levels of the IV are different

What are the estimates based on?

A

The difference between the
measured sample means

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7
Q

Why use ANOVA and not stick to t-tests for studies with more than 2 IVs?

List 3 points

A
  1. With each IV levels, we’d have to run different t-tests

e.g. With 3 IV levels, we’d have to run 3 t-tests

  1. For each of these t-tests there would be a 5% chance of making a Type 1 error
  2. But the overall Type 1 error rate (across all t-tests) would be higher
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8
Q

Explain the sock drawer analogy in 3 points

A
  1. Sock drawer contents:
    - 19 pairs of black socks
    - 1 pair white socks
  2. If you randomly pick out one pair:
    - 1 in 20 chance of picking out the white socks (5%)
  3. If you repeatedly go back and randomly pick out socks (returning those previously picked to the drawer)
    - Chance of eventually picking out the white socks increases (>5%)
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9
Q

The probability that at least one of a ‘family’ of comparisons, run on the same data, will result in a
Type I error

This is known as…?

A

Familywise Error Rate

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10
Q

Describe Familywise Error Rate

A

The probability that at least one of a ‘family’ of comparisons, run on the same data, will result in a Type I error

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11
Q

The probability that at least one of a ‘family’ of comparisons, run on the same data, will result in a…?

a. Type I error
b. Type II error

A

a. Type I error

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12
Q

What is the formula for familywise error rate?

A

a’ = 1 - (1 - a)^c

or

Error rate for family of comparisons = 1 - (1 - Level of confidence we’re working to for each comparison (.95 if α=.05)^Number of comparisons

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13
Q

This study had 3 IV levels (A, B & C)

a. What is the familywise error rate?

b. What is the chance of Type I error?

A

A - B
A - C
B - C
= 3 comparisons

a.
a = 1 - (1 - 0.05)^3
a = .143

b. 14%

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14
Q

This study had 5 IV levels (A, B, C, D & E)

a. What is the familywise error rate?

b. What is the chance of Type I error?

A

A - B
A - C
A - D
A - E
B - C
B - D
B - E
C - D
C - E
D -E
= 10 comparisons

a.
a = 1 - (1 - 0.05)^10
a = .401

b. 40%

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15
Q

How many d.p. do we report Familywise error rate in?

A

3 d.p.

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16
Q

Do we include a 0 in front of the decimal point when reporting familywise error rate?

A

No

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17
Q

What tests control for the familywise error rate?

A

Omnibus tests (e.g. ANOVA)

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18
Q

Omnibus tests (e.g. ANOVA) control for…?

A

Familywise error rate

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19
Q

What is the formula for the F ratio in one-way ANOVA?

A

F = variance between IV levels / variance within IV levels

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20
Q

Is the variance between IV
levels relative to within IV levels small or large when the F value is close to 0?

A

Small

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21
Q

Is the variance between IV
levels relative to within IV levels small or large when the F value is further from 0?

A

Large

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22
Q

The variance between IV
levels relative to within IV levels is small when the F value is…?

a. Far from 0
b. Close to 0

A

b. Close to 0

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23
Q

The variance between IV
levels relative to within IV levels is large when the F value is…?

a. Far from 0
b. Close to 0

A

a. Far from 0

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24
Q

What contributes to variance between IV levels in independent designs?

List 3 things

A
  1. Manipulation of IV (treatment effects)
  2. Individual differences
  3. Experimental error (Random error, Constant error)
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25
Q

What contributes to variance within IV levels in independent designs?

List 2 things

A
  1. Individual differences
  2. Experimental error (Random error)
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26
Q

Variance between IV levels includes…?

A
  1. The variance caused by the manipulation of the IV
  2. Error variance
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27
Q

Variance within IV levels includes…?

A
  1. Only error variance
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28
Q

Total variance is the sum of…?

A

Variance between IV levels
(incl. variance explained by our model and error variance, aka ‘model’ variance) and Variance within IV levels (only error variance, aka ‘residual’ variance)

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29
Q

Residual variance is known as…?

A

Variance within IV levels

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30
Q

Model variance is known as…?

A

Variance between IV levels

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31
Q

Variance between IV levels is also known as…?

A

Model variance

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32
Q

Variance within IV levels is also known as…?

A

Residual variance

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33
Q

How do we partition the variance?

List 4 points

A
  1. Calculates the means for each IV level
  2. Calculates the grand mean
  • Sum of IV level means, divided by the number of IV levels
  1. Calculates the within IV levels variance
  • Sum of squared differences between individual values and the corresponding IV level mean
  1. Calculates the between IV levels variance
  • Sum of squared differences between each IV level
    mean and the grand mean
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34
Q

An investigator wants to determine whether participants recall more items in a verbal short term memory task if they have been instructed to use a mnemonic strategy.

He recruits 60 participants and randomly assigns them to one of 3 groups: no mnemonic, mnemonic 1 or mnemonic 2. He records how many items they can recall for a list of 20 words

What are the:

a. IVs
b. IV levels
c. DV
d. Subjects design
e. Type of test

A

a. Mnemonic strategy
b. 3 (No mnemonic, mnemonic 1, mnemonic 2)
c. Items/words recalled
d. Between subjects
e. One-way independent ANOVA

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35
Q

What are the 4 assumptions for independent one-way ANOVA?

A
  1. Normality
  2. Homogeneity of variance
  3. Equivalent sample size
  4. Independence of observations
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36
Q

What is the normality assumption for independent one-way ANOVA?

A

The DV should be normally distributed, under each level of the IV

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37
Q

What is the homogeneity of variance assumption for independent one-way ANOVA?

A

The variance in the DV, under
each level of the IV, should be (reasonably) equivalent

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38
Q

How do we check homogeneity of variance on SPSS?

A

Levene’s test

If p < 0.05, we reject the null, data is not homogenous

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39
Q

What can correct for homogeneity of variance for independent one-way ANOVA?

A

Welch F statistic

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40
Q

Welch F statistic can correct for…?

A

Homogeneity of variance

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41
Q

Levene’s test checks for…?

A

Homogeneity of variance

42
Q

What is the equivalent sample size assumption for independent one-way ANOVA?

A

Sample size under each level of the IV should be roughly equal

43
Q

What is the independence of observations assumption for independent one-way ANOVA?

A

Scores under each level
of the IV should be independent

44
Q

What is the non parametric equivalent for the independent one-way ANOVA?

A

Kruskal WallisTest

45
Q

Kruskal WallisTest is a non parametric equivalent for…?

A

Independent one-way ANOVA

46
Q

What is the H0 for Levene’s hypothesis?

A

There is no difference between the variance under each level of the IV (i.e. homogeneity)

47
Q

If p < .05 on the Levene’s test, we reject null hypothesis which means…?

A

The data is heterogenous

48
Q

Where do we find Levene’s statistic on SPSS?

A

The ‘Based on Mean’ row on the ‘Test of Homogeneity of Variances’ table

49
Q

How do you present the SPSS output of independent one-way ANOVA?

A

F(dfm,dfr) = F-value, p = p-value

or

F(Between Groups Sum of Squares, Within Groups Sum of Squares) = F, Sig.

50
Q

Where the assumption of homogeneity of variance has been violated (i.e. a significant Levene’s result), we should report the result of …?

A

Welch’s F test

51
Q

How do we report the results on SPSS of Welch’s F test?

A

F(df1,df2) = Statistic, Sig.

52
Q

Sum of squared differences between IV level means and grand mean (i.e. between IV level variance)

This is known as…?

A

Model Sum of Squares (SSM)

53
Q

What is Model Sum of Squares (SSM)?

A

Sum of squared differences between IV level means and grand mean (i.e. between IV level variance)

54
Q

Sum of squared differences between individual values and corresponding IV level mean (i.e. within IV level
variance)

This is known as…?

A

Residual Sum of Squares (SSR)

55
Q

What is Residual Sum of Squares (SSR)?

A

Sum of squared differences between individual values and corresponding IV level mean (i.e. within IV level
variance)

56
Q

What is the formula for Mean Square Between Groups (MSM)?

A

Sum of Squares Between Groups (SSM) / df Between Groups (dfM)

57
Q

What is the formula for Mean Square Within Groups (MSR)?

A

Sum of Squares Within Groups (SSR) / df Within Groups (dfR)

58
Q

What is the F value formula on SPSS?

A

F = Mean Square Between Groups (MSM) / Mean Square Within Groups (MSR)

59
Q

How many df values does independent one-way ANOVA have?

A

2

  • df model (between IV levels)
  • df residual (within IV levels
60
Q

How do you calculate the df model (between IV levels) for independent one-way ANOVA?

A

df model = k (number of IV levels) - 1

61
Q

How do you calculate the df residual (within IV levels) for independent one-way ANOVA?

A

df residual = N (sample size) - k (number of IV levels)

62
Q

Between IV level variance is known as…?

A

Model variance

63
Q

Within IV level variance is known as…?

A

Error/Residual variance

64
Q

N (sample size) - k (number of IV levels)

This is the formula to calculate the df for…?

A

Within IV levels or df residual

65
Q

This is the formula to calculate the df for…?

k (number of IV levels) - 1

A

Between IV levels or df model

66
Q

What are Post-hoc tests?

A

Secondary analyses used to assess which IV level mean
pairs differ

67
Q

Secondary analyses used to assess which IV level mean
pairs differ

This is known as…?

A

Post-hoc tests

68
Q

When are Post-hoc tests used?

A

When F-value is significant

69
Q

Post-hoc tests are run as t-test but include…?

A

Correction for multiple
comparisons

70
Q

What are the 3 types of Post-hoc tests?

A
  1. Bonferroni
  2. Least Significant Difference (LSD)
  3. Tukey Honestly Significant Difference (HSD)
71
Q

What is the Type I Error risk for Bonferroni?

a. Very high
b. High
c. Low
d. Very low

A

d. Very low

72
Q

What is the Type I Error risk for Least Significant Difference (LSD)?

a. Very high
b. High
c. Low
d. Very low

73
Q

What is the Type I Error risk for Tukey Honestly Significant Difference (HSD)?

a. Very high
b. High
c. Low
d. Very low

74
Q

What is the Type II Error risk for Bonferroni?

a. Very high
b. High
c. Low
d. Very low

A

a. Very high

75
Q

What is the Type II Error risk for Least Significant Difference (LSD)?

a. Very high
b. High
c. Low
d. Very low

76
Q

What is the Type II Error risk for Tukey Honestly
Significant Difference (HSD)?

a. Very high
b. High
c. Low
d. Very low

77
Q

What is the classification for Bonferroni?

A

“very conservative”

78
Q

What is the classification for Least Significant Difference (LSD)?

A

“liberal”

79
Q

What is the classification for Tukey Honestly Significant Difference (HSD)?

A

“reasonably
conservative”

80
Q

This post-hoc test is classified as “reasonably
conservative”

a. Bonferroni

b. Least Significant Difference (LSD)

c. Tukey Honestly Significant Difference (HSD)

A

c. Tukey Honestly Significant Difference (HSD)

81
Q

This post-hoc test is classified as “liberal”

a. Bonferroni

b. Least Significant Difference (LSD)

c. Tukey Honestly Significant Difference (HSD)

A

b. Least Significant Difference (LSD)

82
Q

This post-hoc test is classified as “very conservative”

a. Bonferroni

b. Least Significant Difference (LSD)

c. Tukey Honestly Significant Difference (HSD)

A

a. Bonferroni

83
Q

This post-hoc test has a very low Type I Error risk

a. Bonferroni

b. Least Significant Difference (LSD)

c. Tukey Honestly Significant Difference (HSD)

A

a. Bonferroni

84
Q

This post-hoc test has a high Type I Error risk

a. Bonferroni

b. Least Significant Difference (LSD)

c. Tukey Honestly Significant Difference (HSD)

A

b. Least Significant Difference (LSD)

85
Q

This post-hoc test has a low Type I Error risk

a. Bonferroni

b. Least Significant Difference (LSD)

c. Tukey Honestly Significant Difference (HSD)

A

c. Tukey Honestly Significant Difference (HSD)

86
Q

This post-hoc test has a low Type II Error risk

a. Bonferroni

b. Least Significant Difference (LSD)

c. Tukey Honestly Significant Difference (HSD)

A

b. Least Significant Difference (LSD)

87
Q

This post-hoc test has a high Type II Error risk

a. Bonferroni

b. Least Significant Difference (LSD)

c. Tukey Honestly Significant Difference (HSD)

A

c. Tukey Honestly Significant Difference (HSD)

88
Q

This post-hoc test has a very high Type II Error risk

a. Bonferroni

b. Least Significant Difference (LSD)

c. Tukey Honestly Significant Difference (HSD)

A

a. Bonferroni

89
Q

What are the 2 different effect sizes calculated for ANOVA?

A
  1. Partial n2
  2. Cohen’s d
90
Q

How much variance in the DV is explained by the manipulation of the IV overall

What effect size is this?

A

Partial n2

91
Q

The magnitude of the difference between pairs of IV level means, expressed in SD units

What effect size is this?

A

Cohen’s d

92
Q

What does partial n2 tell us?

A

How much variance in the DV is explained by the manipulation of the IV overall

93
Q

What does Cohen’s d tell us?

A

The magnitude of the difference between pairs of IV level means, expressed in SD units

94
Q

What is considered a small effect size of partial n2?

95
Q

What is considered a medium effect size of partial n2?

96
Q

What is considered a large effect size of partial n2?

97
Q

What proportion of the variance in the DV is accounted for by the manipulation of the IV?

This is known as…?

A

Partial eta^2

98
Q

What does partial eta^2 tell us?

A

What proportion of the variance in the DV is accounted for by the manipulation of the IV?

99
Q

What is the formula for partial eta^2?

A

Partial eta^2 = SSM / (SSM + SSR)

or

Partial eta^2 = Sum of Squares Between Groups / (Sum of Squares Between Groups + Sum of Squares Within Groups)

100
Q

How many d.p. do you report partial n^2 or partial eta^2?

101
Q

Do you put a 0 in front of the decimal point when reporting partial n^2 or partial eta^2?

102
Q

Calculate the Cohen’s d for each pair of the IV level means

Data:

No Mnemonic
Mean = 8.40
SD = 1.82

Mnemonic 1
Mean = 9.85
SD = 1.53

Mnemonic 2
Mean = 10.40
SD = 1.76

A

NM & M1
d = 8.40 - 9.85 / (1.82 + 1.53 / 2)

d = (-) 0.87 (large effect size)

NM & M2
d = 8.40 - 10.40 / (1.82 + 1.76 / 2)

d = (-) 1.12 (large effect size)

M1 & M2
d = 9.85 - 10.40 / (1.53 + 1.76 / 2)

d = (-) 0.33 (small effect size)

YEAR 2 Stats (10 decks)

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