ANOVA

Question 1

what does ANOVA stand for?

Answer 1

analysis of variance

Question 2

what is the purpose of ANOVA?

Answer 2

to compare the means of several groups using the variability within and between groups

Question 3

what are the hypotheses in a one-way ANOVA?

Answer 3

H0 : µ1 = µ2 = … = µg
Ha : at least two population means are unequal

Question 4

what are the assumptions for ANOVA?

Answer 4

1. normal population distributions
2. equal standard deviations across groups
3. randomisation in sampling or assignment

Question 5

how is variability partitioned in ANOVA?

Answer 5

between-groups variability: differences between group means
within-groups variability: differences within each group around its mean

Question 6

what is the test statistic for ANOVA?

Answer 6

= between-groups sigma/within-groups sigma

Question 7

how do you calculate the degrees of freedom in ANOVA?

Answer 7

between-groups: df1 = g - 1 (g = number of groups)
within-groups: df2 = N - g (N = total sample size)

Question 8

what does the F distribution signify in ANOVA?

Answer 8

Mean ~ 1 when H0 is true
larger F value indicates stronger evidence against H0

Question 9

how are the mean squares calculated in ANOVA?

Answer 9

mean square between (MSB): sum of squares between (SSB)/df1

mean square within (MSW): sum of squares within (SSW)/df2

Question 10

how is total variability partitioned in ANOVA?

Answer 10

total SS = between-groups SS + within-groups SS

Question 11

when is the F test robust to violations of assumptions?

Answer 11

• if sample sizes are equal or approximately equal
• when population distributions are approximately normal or have similar standard deviations

Question 12

what should you check for extreme violations of assumptions?

Answer 12

box plots or dot plots for skewness or large differences in standard deviations

Question 13

what does the residual standard deviation s represent in ANOVA?

Answer 13

it is the square root of the within-groups variance estimate or mean square error

Question 14

how do you calculate the degrees of freedom for the error in ANOVA?

Answer 14

df2 = N - g

Question 15

what does it mean if a confidence interval comparing two means does not include 0?

Answer 15

it indicates a significant difference between the population means

Question 16

what should you do if the largest standard deviation is more than twice the smallest?

Answer 16

use a confidence interval formula with separate variances instead of pooled variance

Question 17

how many pairwise comparisons are there for g groups in ANOVA?

Answer 17

g(g - 1)/2 = x comparisons

Question 18

what is the main limitation of constructing multiple confidence intervals for mean differences?

Answer 18

the overall confidence level decreases as the number of comparisons increases

Question 19

what is the boneferroni method?

Answer 19

a method that adjusts error probability for each comparison to ensure a high overall confidence level

Question 20

how does the turkey method improve on the boneferroni method?

Answer 20

it provides narrower confidence intervals and maintains the desired overall confidence level

Question 21

when is ANOVA robust to violations of normality?

Answer 21

when sample sizes are large, the normality assumption is less critical