Module 11, One-Way Analysis of Variance

Question 1

Between-Group Variability

Answer 1

differences among the mean of the different groups that comprise an independent variable

Question 2

Within-Group Variability

Answer 2

the variability of the dependent variable within each of the groups

Question 3

Between Group & Within Group Variance

Answer 3

• between-group variability must be greater than within-group variability to reject the null hypothesis
• OR the hypothesized effect (systematic variance) must be large enough to overcome the amount of error (random variance) that exists in the data

Question 4

What is wrong with using multiple t-tests?

Answer 4

1) accumulation of the Type 1 error rate (greater probability of making a type 1 error - concluding that an effect exists when it in fact does not when one conducts multiple t-tests)

2) the t-test does not use all information about the population (the estimate of the standard error of the difference only accounts for data from two samples
- estimate of error is from three or more groups

3) multiple t-tests require more time and effort
prefer to do ANOVA for these above reasons

Question 5

Logic of F

Answer 5

• between group variance is composed of the treatment effect plus error
• within group variance is composed of error
• if no treatment effect = error/error = 1
• if treatment effect = effect + error/error > 1

Question 6

F-Ratio Distribution

Answer 6

• characteristics of the F-distribution (changes as a function of sample size; function of number of groups being compare unlike t-test and thus there is a family of F-ratio distribution)
  ◦ non-normal (not symmetrical)
  ◦ positively skewed (starting
  with value of 0 on left and
  extending to infinity on the
  right)
  ‣ ratio of variances, which
  are always positive (values are always positive as variances cannot be expressed as a negative number)
• modality ≅1 (modality approximates one)

Question 7

Null and Alternative Hypotheses

Answer 7

H0: all μs are equal
H1: not all μs are equal

Question 8

Effect Size

Answer 8

• recall that effect size is not affected by sample size, and allows us to compare across samples and studies
• R2: percentage of variance associated with between-group variances (*can be interpreted as the percentage of variance in the dependent variable that can be attributed to the independent variable)
• R2 is going to indicate the percentage of variance in DOMS that can be attributed to the our recovery technique (people are going to vary in their DOMS beyond recovery technique; how much can you attribute back the recovery technique)

Question 9

Effect Size Ranges

Answer 9

a ‘small’ effect produces a R2 of .01
a ‘medium’ effects produces an R2 of .06
a ‘large’ effect produces an R2 of .15 or greater

Question 10

Post Hoc Test: Tukey’s HSD (honestly significant difference)

Answer 10

only conduct if there is a statistically significant finding
= calculates the minimum raw score mean difference that must be attained to declare significance between any two groups
* pair-wise comparisons only
◦ any single group mean may be compared with any other group mean

Question 11

One-Way ANOVA (4) Assumptions

Answer 11

dependent variable assumptions:
1) interval or ratio scale of measurement

2) scores are independent (they come from different people) - assumption of independence (you can only be in one level of the IV)

3) residuals are normally distributed
- Q-Q plot (want all of the dots to be on or close to line
- line is called regression line (want to see dots go along it) - significant deviations from the regression line would appear as an ‘S’ shape

4) homogeneity of variance
- groups should have equal variances (levene’s test) - testing the null hypothesis that the groups have equal variance (want not statistically-significant, p > .05)