Chapter 18

Question 1

ANOVA

Answer 1

• Used to compare 2 or more means (typically used for 3+)
• “omnibus test”
• Closely related to t-test -> you could use ANOVA instead of t-test in a 2-mean design and get the same results (F = t^2)
• Always non-directional

Question 2

treatment conditions

Answer 2

different values/levels of the IV -> “k”

Question 3

treatment effect

Answer 3

differences among groups caused by difference in treatment conditions (H0 is false)

Question 4

2 types of variation

Answer 4

• Within-groups variation: variation of scores around the mean of a single treatment condition; due to inherent variation/chance (aka: error)
• Between-groups variation: variation among the means of different treatment conditions; due to inherent variation/chance and treatment effect (if one exists)

Question 5

grand mean

Answer 5

• mean of all scores in all the treatment conditions

- Obtained by adding all the scores in all populations and dividing by the total number of scores

Question 6

SS within vs. SS between

Answer 6

• SSwithin: reflection of inherent variation/chance

- SSbetween: reflection of inherent variation/chance + treatment effect

Question 7

f-ratio

Answer 7

• Ratio of within and between groups variance
• If H0 is true, F should be approx 1, if H0 is false, F should exceed 1
• Ranges from 0 to infinity - F can never be less than 0 since variance estimates are never negative

Question 8

ANOVA assumptions

Answer 8

• Same as those for independent samples t-test:
• • Populations are normally distributed
• • Variance of populations are the same (homogeneity of variance)
• • Selection of elements for each sample is independent
• • Samples are drawn randomly and with replacement

Question 9

effects of violating ANOVA assumptions

Answer 9

• Normal distribution: moderate departure is okay, especially if n is large (problematic if highly skewed
• Homogeneity of variance: disregarded if sample sizes are equal
• Independent samples: problematic – this ANOVA procedure is only appropriate for independent samples
• Random sampling: research usually use random assignment rather than random sampling – it’s okay, but random sampling allows us to generalize to population

Question 10

effect sizes

Answer 10

• eta squared and omega squared

- Both members of the r family (not the d family)

Question 11

eta squared

Answer 11

• measure of effect size
• Aka: correlation ratio
• Measures strength of association between independent and dependent variables -> gives a proportion of total variance due to the independent variable
• .01 = small, .06 = medium, .14 = large
• Biased in an upward direction

Question 12

omega squared

Answer 12

• measure of effect size
• Unbiased
• Estimates proportion of variance in the dependent variable that is due to k levels of treatment
• .01 = small, .06 = medium, .14 = large

Question 13

power

Answer 13

• Factors affecting power in ANOVA are similar to those of the t-test:
• • Actual differences among population means
• • Variance that is not attributable to treatment effect
• • Degrees of freedom in numerator and denominator (more groups/subjects = more power)
• • Level of significance (probability of a type-1 error); alpha = .05 -> more power