Chapter 12: Intro to Analysis of Variance (ANOVA)

Question 1

What is analysis of variance (ANOVA)?

Answer 1

• a hypothesis testing procedure used to evaluate mean differences between two or more populations
• The purpose of ANOVA is similar to t-tests

Question 2

What are the advantages of ANOVA?

Answer 2

• Can examine more than two groups at the same time
• Protects researchers from excessive risk of a Type I error in situations when comparing more than two population means (it automatically adjusts for the effect testing multiple hypotheses has on Type I errors)

Question 3

What is a factor?

Answer 3

• The independent variable that splits participants into groups is called a factor (ANOVA can be used with multiple factors at the same time)

Question 4

What is a level?

Answer 4

• The individual conditions or values that make up a factor are called levels
• Number of levels is indicated by k

Question 5

The test statistic for ANOVA

Answer 5

• Is an F-ratio (a ratio of two sample variances)
• In ANOVA, sample variances = mean squares, or MS values
• The top of the F-ratio (MSbetween/Signal) measures the size of mean differences between samples
• The bottom of the F-ratio (MSwithin/Noise) measures the magnitude of differences expected without any effects of the IV

Question 6

F-ratio compared to t-statistic

Answer 6

F= Msbetween / Mswithin
-Which equals: obtained mean differences (including treatment effects) / differences expected by chance (without treatment effects)

Question 7

Between groups variability

Answer 7

• MSbetween measures the size of the differences between the sample means
• For example, suppose a factor has three levels, each with n=25 subjects. The level means are M1=1, M2=2, M3=3.
• The three sample means are different (variable)
• By computing the variance of the means (MSbetween) we can test the size of the differences

Question 8

Where can the differences (or variance) between means be caused from?

Answer 8

1. Effects of the IV: could cause the mean for one level to be higher (or lower) than the mean for another level
2. Chance or Sampling Error: If there is no effect of the IV at all, we would still expect some differences in the DV values between levels due to random, unsystematic sampling error.

Question 9

Within-Groups Variability

Answer 9

• MSwithin measures the size of the differences that exist inside each of the treatment levels.
• Because the individuals in each group experienced exactly the same level of the independent variable (ex. all took drug X, drug Y, or drug Z), any variance within a sample cannot be caused by the independent variable’s effects
• Only explanation: random chance or sampling error