assumptions in between subject anova

Question 1

define normality

Answer 1

refers to a normal distribution

in between subject ANOVA, it is assumed that the random variable Eij has a normal distribution in all groups

normality justifies the use of the F distribution to evaluate the observed F statistic

Question 2

which tests are used to assess normality

Answer 2

descriptive and inferential statistics:
- tests for skewness
- kolmogorov-smirnov and shapiro wilk tests

visual methods:
- histograms
- normal quantile (q-q) plot

Question 3

skewness

Answer 3

skewness represents symmetry and whether the distribution has a long tail in one direction

should be about 0
>0 = positive/right skew
<0 = negative/left skew

Question 4

kolmogorov smirnov (k-s) test

Answer 4

• very general, but usually less power than S-W
• conceptually, compares sample scores to a set of scores generated from e.g., a normal distribution with a sample mean and standard deviation

Question 5

shapiro wilk (s-w) test

Answer 5

usually more powerful than k-s test, but only for normal distributions

Question 6

how to use histograms to assess normality

Answer 6

construct separate histograms for each group and judge it the plots are roughly symmetric

Question 7

how to use a normal quantile plot to assess normality

Answer 7

1. compute percentile rank for each score
   (sort from smallest to largest, what percentage of scores are below score x)
2. calculate theoretical z scores from percentile rank - if scores were normal, what would the z score b
3. calculate actual z scores
4. plot the observed vs theoretical z scores

if data are close to normal then the points will look like a straight line

Question 8

what happens when the assumption of normality is not met

Answer 8

type 1 error rates that are lower than the nominal value

usually not as concerning as a violation that results in excessive type one error rates

Question 9

define homogeneity of variance (i.e., homoscedasticity)

Answer 9

an assumption that states that the variance of the random variable Eij is the same for all groups - a bit of variance is okay, refers to systematic causes that would lead different groups to have different variances

Question 10

which tests are used to assess homogeneity of variance

Answer 10

• Fmax test
• Levene’s test
• Brown and Forsythe test

Question 11

Fmax test

Answer 11

calculate the sample variance for each group and find the largest and smallest variances

Fmax= maxs^2g÷mins^2g

Fmax value is compared against a critical value

assumes each group has an equal number of observations (wont use)

Question 12

levene’s test

Answer 12

measures how much each score deviates from its group mean

Uses absolute deviation scores, Zij, instead of the original scores to run ANOVA

Zij=Yij-Yj

Question 13

what happens when homogeneity of variance is violated

Answer 13

excessive type 1 error rates (inflates the observed value of the F statistic)

increases in sample size and having equal groups can alleviate some of the inflation

more problematic when smaller groups have larger variance