Chapter 12- ANOVA

Question 1

When would you use an ANOVA vs. a t-test?

Answer 1

When you are examining more than two groups at the same time

Question 2

What are the strengths of using an ANOVA over multiple t-tests?

Answer 2

• Protects researches from excessive risk of a Type I error in situations when comparing more than two population means… automatically adjusts for the effect testing multiple hypotheses has on Type I errors

Question 3

What is the logic behind the f-ratio?

Answer 3

• Msbetween / Mswithin
• Ms= mean squares (or MS values)
• MSbetween measures the size of mean differences between samples
• MSwithin measures the magnitude of differences expected without any effects of the IV
• =obtained mean differences (including treatment effects) / differences expected by chance (without treatment effects)

Question 4

Msbetween (between group variance)

Answer 4

• measures the size of the differences between each level’s sample mean
• the differences/variance between means can be cause by effects of the independent variable, or by random chance/sampling error

MSbetween= SSbetween / df between (K-1)

Question 5

MS within

Answer 5

• measures the size of the differneces that exist inside each of the treatment levels
• Because the individuals in each group experienced exactly the same level of the independent variable, any variance within a sample cannot be cause by the independent variable’s effects
• only explanation is random chance or sampling error

Question 6

Hypotheses for ANOVA

Answer 6

• Ho: μ1=μ2=μ3
• H1: There is at least one mean difference
• When H0 is true and there are no differences between levels, the F-ratio is balanced (when the effect of the IV i zero, the top and bottom of the F-ratio only measure random variance…. so we should expect an F-ratio near 1.00
• When the F-ratio is near 1.00, we conclude that there is no significant effect of the IV…a large effect produces a large F-ratio
• We reject the null hypothesis and conclude there is at least on significant difference between groups when we get a large F-ratio (far from 1)

All hypotheses in ANOVA are non-directional because F is a ratio of variances and variances cannot be negative (there is always a single tail to the distribution)

Question 7

How to identify critical region?

Answer 7

• Find where dfbetween (columns) and dfwithin (rows) intersect
• Bold is for a=.01, normal is for 1=.05
• dfbetween=k-1
• dfwithin=n-k

Question 8

Why are post hoc tests conducted after ANOVAs and do they tell you?

Answer 8

• Hoc tests need to be conducted because ANOVA simply states that difference exists, it does not indicate which levels are different
• Hoc tests determine exactly which groups are different and which are not
• Tukey and Scheffe tests are common post hoc tests
• Are done after an ANOVA where H0 is rejected
• The tests compare the treatments two at a time to test the mean differences while correcting for concerns about experiment-wise Type 1 error inflation

Question 9

How to calculate effect size for ANOVA?

Answer 9

• compute the percentage of variance counted for by the independent variable
• identified as η2
• η2= SS between / SS total

.02-.12 is small effect, .13-.25 is medium effect, .26+ is large effect