independent one-way ANOVA

Question 1

when to use an independent one way anova?

Answer 1

Using statistics to examine the influence of an IV (with more than 2 levels) on the DV
-between subjects/ independent design

Question 2

what does a independent one-way anova look at?

Answer 2

Are the mean scores under each IV significantly different?
-if they are, we assume the IV has caused this difference

Interested in whether there is a difference in population means
-examine the difference in sample means to estimate the difference in population means

Question 3

when is a one-way anova used?

Answer 3

Used when we have an IV with more than 2 levels

Question 4

what does a one-way anova estimate?

Answer 4

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

estimate is based on the difference between the measured sample means

Question 5

why use a one-way anova instead of a t-test

Answer 5

When p<.05 we reject the null hypothesis because it’s unlikely to find a difference of the magnitude we’ve measures if the null hypothesis were true

There is still a 5% chance we have made a type 1 error
-measured results from sampling error rather than reflecting a true difference in the underlying population means

With 3 IV levels you would run 3 t-tests
- A vs B, A vs C, B vs C

For each of these t-tests there would be a 5% chance of making a type 1 error

The overall type 1 error rate across all t-tests would be higher

Question 6

what does the family wise error rate adjustment reduce?

Answer 6

the chance of a type 1 error

Question 7

familywise error rate

Answer 7

The probability that at least one of a ‘family’ of comparisons, run on the same data, will result in type 1 error

Provides a corrected significance level (a), expressing the probability of making a type 1 error

Question 8

what control the familywise error rate?

Answer 8

omnibus tests

Question 9

null hypothesis of independent one way anova

Answer 9

there is no difference between the population means under different levels of the IV

H0: U1=U2=U3

Question 10

variance when F value is close to 0

Answer 10

small variance between IV levels relative to within IV levels

Question 11

variance when F value is further from 0

Answer 11

large variance between IV levels relative to within IV levels

Question 12

variance between IV levels t/F ratio (independent)

Answer 12

includes variance ‘caused’ by our manipulation of the IV and error variance

Question 13

variance within IV levels t/F ratio (independent)

Answer 13

includes only error variance

Question 14

total variance (independent one way ANOVA)

Answer 14

total of modal variance and residual variance

Question 15

model variance

Answer 15

variance caused by manipulation and error variance

deviations of the sample means from the grand mean

Question 16

residual variance

Answer 16

only error variance

deviations from the mean of a sample

Question 17

grand mean

Answer 17

sum of the IV level means, divided by the number of IV levels

Question 18

residual variance

Answer 18

sum of squared differences between individual values and the corresponding IV level mean

Question 19

partitioning the variance

Answer 19

1) Calculates the means for each IV level

2) Calculates the grand mean
-sum of the 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

Question 20

assumption of independent one way ANOVA

Answer 20

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

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

Equivalent sample size

Independence of observations

Question 21

independence of observations

Answer 21

scores under each level of the IV should be independent

Question 22

what can correct for heterogeneity of variance independent one way anova

Answer 22

welches f statistic

Question 23

what is the levene’s test null hypothesis

Answer 23

there is no difference between the variance under each level of the IV (homogeneity)

Question 24

what do we do when levene’s p value is <0.05

Answer 24

we reject the null hypothesis (heterogeneity)

Question 25

which column of levene’s statistic do we read from?

Answer 25

based on mean

Question 26

what should we report for independent one way anova when homogeneity is violated

Answer 26

welch’s F instead of ANOVA F

degrees of freedom have been adjusted to make the test more conservative

Question 27

non parametric equivalent independent one way anova

Answer 27

Kruskal Wallis Test

Question 28

model sum of squares (SS M)

Answer 28

sum of squared differences between IV means and grand mean

Question 29

residual sum of squares (SS R)

Answer 29

sum of squared differences between individual values and corresponding IV level mean

Question 30

df for independent one-way anova

Answer 30

The difference between the number of measurements made and the number of parameters estimated

We need to calculate df for our estimates of:
-between IV level (model) variance
-within IV level (error/residual) variance

N is total sample size, K is number of IV levels

Between: df(model): k-1

Within: df(residual): N-k

Question 31

post hoc tests (independent one way ANOVA)

Answer 31

Secondary analyses used to assess which IV level mean pairs differ

Only used when F value is significant

Run as a t-test but include correction for multiple comparisons

Choice corrections, vary in their risk of type I and type II errors

Question 32

Tukey honestly significant difference (HSD) type I error risk

Answer 32

low

Question 33

Tukey honestly significant difference (HSD) type II error risk

Answer 33

high

Question 34

Tukey honestly significant difference (HSD) classification

Answer 34

reasonably conservative

Question 35

partial n2

Answer 35

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