Independent one-way ANOVA Flashcards by D E

Used when we have 1 IV with more than 2 levels

One-way ANOVA

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

One-way independent ANOVA

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

One-way repeated measures ANOVA

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What does one-way ANOVA estimate?

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

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

This is known as…?

One-way ANOVA

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

What are the estimates based on?

The difference between the
measured sample means

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

List 3 points

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

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

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Explain the sock drawer analogy in 3 points

Sock drawer contents:
- 19 pairs of black socks
- 1 pair white socks
If you randomly pick out one pair:
- 1 in 20 chance of picking out the white socks (5%)
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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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…?

Familywise Error Rate

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Describe Familywise Error Rate

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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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. Type I error

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What is the formula for familywise error rate?

a’ = 1 - (1 - a)^c

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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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 - B
A - C
B - C
= 3 comparisons

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

b. 14%

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

3 d.p.

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

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What tests control for the familywise error rate?

Omnibus tests (e.g. ANOVA)

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

Familywise error rate

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

F = variance between IV levels / variance within IV levels

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

Small

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

Large

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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

b. Close to 0

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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. Far from 0

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What contributes to variance between IV levels in independent designs?

List 3 things

Manipulation of IV (treatment effects)
Individual differences
Experimental error (Random error, Constant error)

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What contributes to variance within IV levels in independent designs? List 2 things

1. Individual differences 2. Experimental error (Random error)

Variance between IV levels includes...?

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

Variance within IV levels includes...?

1. Only error variance

Total variance is the sum of...?

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)

Residual variance is known as...?

Variance within IV levels

Model variance is known as...?

Variance between IV levels

Variance between IV levels is also known as...?

Model variance

Variance within IV levels is also known as...?

Residual variance

How do we partition the variance? List 4 points

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 3. Calculates the within IV levels variance - Sum of squared differences between individual values and the corresponding IV level mean 4. Calculates the between IV levels variance - Sum of squared differences between each IV level mean and the grand mean

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

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

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

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

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

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

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

How do we check homogeneity of variance on SPSS?

Levene's test If p < 0.05, we reject the null, data is not homogenous

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

Welch F statistic

Welch F statistic can correct for...?

Homogeneity of variance

Levene’s test checks for...?

Homogeneity of variance

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

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

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

Scores under each level of the IV should be independent

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

Kruskal WallisTest

Kruskal WallisTest is a non parametric equivalent for...?

Independent one-way ANOVA

What is the H0 for Levene's hypothesis?

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

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

The data is heterogenous

Where do we find Levene's statistic on SPSS?

The 'Based on Mean' row on the 'Test of Homogeneity of Variances' table

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

F(dfm,dfr) = F-value, p = p-value or F(Between Groups Sum of Squares, Within Groups Sum of Squares) = F, Sig.

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

Welch’s F test

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

F(df1,df2) = Statistic, Sig.

Sum of squared differences between IV level means and grand mean (i.e. between IV level variance) This is known as...?

Model Sum of Squares (SSM)

What is Model Sum of Squares (SSM)?

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

Sum of squared differences between individual values and corresponding IV level mean (i.e. within IV level variance) This is known as...?

Residual Sum of Squares (SSR)

What is Residual Sum of Squares (SSR)?

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

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

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

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

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

What is the F value formula on SPSS?

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

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

2 - df model (between IV levels) - df residual (within IV levels

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

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

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

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

Between IV level variance is known as...?

Model variance

Within IV level variance is known as...?

Error/Residual variance

N (sample size) - k (number of IV levels) This is the formula to calculate the df for...?

Within IV levels or df residual

This is the formula to calculate the df for...? k (number of IV levels) - 1

Between IV levels or df model

What are Post-hoc tests?

Secondary analyses used to assess which IV level mean pairs differ

Secondary analyses used to assess which IV level mean pairs differ This is known as...?

Post-hoc tests

When are Post-hoc tests used?

When F-value is significant

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

Correction for multiple comparisons

What are the 3 types of Post-hoc tests?

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

What is the Type I Error risk for Bonferroni? a. Very high b. High c. Low d. Very low

d. Very low

What is the Type I Error risk for Least Significant Difference (LSD)? a. Very high b. High c. Low d. Very low

b. High

What is the Type I Error risk for Tukey Honestly Significant Difference (HSD)? a. Very high b. High c. Low d. Very low

c. Low

What is the Type II Error risk for Bonferroni? a. Very high b. High c. Low d. Very low

a. Very high

What is the Type II Error risk for Least Significant Difference (LSD)? a. Very high b. High c. Low d. Very low

c. Low

What is the Type II Error risk for Tukey Honestly Significant Difference (HSD)? a. Very high b. High c. Low d. Very low

b. High

What is the classification for Bonferroni?

“very conservative”

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

“liberal”

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

“reasonably conservative”

This post-hoc test is classified as “reasonably conservative” a. Bonferroni b. Least Significant Difference (LSD) c. Tukey Honestly Significant Difference (HSD)

c. Tukey Honestly Significant Difference (HSD)

This post-hoc test is classified as “liberal” a. Bonferroni b. Least Significant Difference (LSD) c. Tukey Honestly Significant Difference (HSD)

b. Least Significant Difference (LSD)

This post-hoc test is classified as “very conservative” a. Bonferroni b. Least Significant Difference (LSD) c. Tukey Honestly Significant Difference (HSD)

a. Bonferroni

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. Bonferroni

This post-hoc test has a high Type I Error risk a. Bonferroni b. Least Significant Difference (LSD) c. Tukey Honestly Significant Difference (HSD)

b. Least Significant Difference (LSD)

This post-hoc test has a low Type I Error risk a. Bonferroni b. Least Significant Difference (LSD) c. Tukey Honestly Significant Difference (HSD)

c. Tukey Honestly Significant Difference (HSD)

This post-hoc test has a low Type II Error risk a. Bonferroni b. Least Significant Difference (LSD) c. Tukey Honestly Significant Difference (HSD)

b. Least Significant Difference (LSD)

This post-hoc test has a high Type II Error risk a. Bonferroni b. Least Significant Difference (LSD) c. Tukey Honestly Significant Difference (HSD)

c. Tukey Honestly Significant Difference (HSD)

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. Bonferroni

What are the 2 different effect sizes calculated for ANOVA?

1. Partial n2 2. Cohen's d

How much variance in the DV is explained by the manipulation of the IV overall What effect size is this?

Partial n2

The magnitude of the difference between pairs of IV level means, expressed in SD units What effect size is this?

Cohen's d

What does partial n2 tell us?

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

What does Cohen's d tell us?

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

What is considered a small effect size of partial n2?

> .01

What is considered a medium effect size of partial n2?

> .06

What is considered a large effect size of partial n2?

> .14

What proportion of the variance in the DV is accounted for by the manipulation of the IV? This is known as...?

Partial eta^2

What does partial eta^2 tell us?

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

What is the formula for partial eta^2?

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)

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

3 d.p.

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

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

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)