Short Answer Practice Questions

Question 1

Write the formula for the independent samples t-test

Answer 1

t = “x bar 1” - “x bar 2” / standard error

Question 2

Write the generic t-test formula

Answer 2

t = sample data - hypothesized pop. parameter / estimated standard error

Question 3

List the three properties of a dataset that contribute to the size of an obtained t-test statistic in the independent samples t-test

Answer 3

1. Sample size
2. Dispersion of means (sd and SE)
3. Effect size

Question 4

Write the formula for the paired samples t-test

Answer 4

t = “D bar” - “Mu D” / “S D bar”

**Can remove “Mu D” because this is the mean difference scores of population which is hypothesized to be 0

Question 5

Write the formula for Cohen’s d for the independent samples t-test

Answer 5

d”s” = “x bar 1” - “x bar 2” / pooled standard deviation

Question 6

Write the formula for Cohen’s d for the paired samples t-test

Answer 6

d”av” = “D bar” / “Avg. S”

Question 7

List the three factors that influence power

Answer 7

1. Alpha
2. Sample size
3. Effect size

Question 8

List the two factors that influence effect size (Cohen’s d)

Answer 8

1. Difference in means

2. Standard deviation

Question 9

Write the formula for the ANOVA F-ratio

Answer 9

F = between variability/ within variability

Question 10

Write the formula for the ANOVA F-ratio with regard to sources of variance

Answer 10

F = treatment effects + individual diffs. + experimental error / individual diffs. + experimental error

Question 11

What are the two analyses that make up analysis of variance for ANOVA?

Answer 11

1. Sums of squares (SS) analysis

2. Degrees of freedom (df) analysis

Question 12

What is the term for variance in ANOVA? What is the formula?

Answer 12

Mean squares

MS = SS/df

Question 13

Write the formula for the ANOVA F-ratio expressed using mean squares

Answer 13

F = MS”between” / MS”within”

Question 14

List the 3 statistical assumptions

Answer 14

1. Groups are independent of each other
2. Sample means are normally distributed
3. Homogeneity of variance between groups

Question 15

What are the 2 effect size indices for ANOVA and their corresponding formula?

Answer 15

Eta squared and Cohen’s f

Eta squared = SSbetween / SSwithin

Cohen’s f = squareroot of SSeffect / SSerror

Question 16

Contrast standard deviation and standard error

Answer 16

Standard deviation is a measure of variability within a sample - the variability between each mean score and the actual mean

Standard error is a measure of variability between samples in a given population - the variability between each sample mean

Question 17

What is an omnibus test?

Answer 17

An omnibus test is one that evaluates a general research question. The ANOVA f test is considered an omnibus test because it provides vague results (a mean difference occurs but not where or how many).

Question 18

Why does ANOVA need follow-up tests?

Answer 18

Since ANOVA is an omnibus test, it needs follow-up tests to identify a more specific research question (to figure out where the mean difference occurs and if there is more than one).

Question 19

Explain why power decreases when alpha becomes more strict

Answer 19

Alpha is the likelihood of finding an effect when no such effect exists, and as alpha decreases and becomes more strict the likelihood of committing this type I error decreases. Essentially, the likelihood of finding an effect decreases and considering that power is the likelihood of finding an existing effect, it will also decrease.

Question 20

What is family-wise error? What tests control for family-wise error?

Answer 20

Family-wise error is the cumulative likelihood of making a type I error. Essentially type I error is inflated.

Both Tukey’s HSD and Bonferroni adjustment control for family-wise error.

Question 21

When can using raw effect size be problematic?

Answer 21

1. When measurement units are difficult to interpret

2. When measurement units differ between samples being compared