WorksheetsCh11_3000
Total questions: 19
Worksheet time: 10mins
What is the main purpose of a one-way ANOVA?
To compare a sample mean to a population mean
To test whether scores change within the same individuals across two time points
To compare the means of two independent groups
To test whether three or more group means are equal
Which interpretation of the F ratio is correct?
F shows whether variability between group means (MSB) is large relative to random error (MSW)
F always equals 1 under the alternative hypothesis
F is the same as a t statistic squared in all cases with k>2
Which formula correctly gives the ANOVA F statistic?
F = MSB / MSW, where MSB = SSB / dfB and MSW = SSW / dfW
F = SSB / SSW (no df or MS involved)
F = (grand mean) / (group mean)
F = (SSW / dfW) / (SSB / dfB)
When the null hypothesis (H₀) is true, what value is the F ratio expected to approximate?
0
1
Greater than 1
Less than 1
What does a large F value (MSB ≫ MSW) suggest in ANOVA?
Group means differ more than would be expected by chance (evidence against H0)
Within-group variability is larger than between-group variability
The grand mean explains most variation inside groups
All groups have equal means
Compute df for an ANOVA with k = 3 groups and total N = 15. (Formulas: dfB = k − 1; dfW = N − k.) Which are dfB and dfW?
dfB = 3, dfW = 15
dfB = 2, dfW = 15
dfB = 3, dfW = 12
dfB = 2, dfW = 12
What does MSB measure in a one-way ANOVA?
Total variance across all scores
Variability among participants within each group
Variability among group means due to treatment or condition differences
Easy computation (SSB → MSB). Group means: M1 = 5 (n1 = 4), M2 = 7 (n2 = 4), M3 = 9 (n3 = 4). Grand mean MG = 7. Use SSB = Σ nj(Mj − MG)². Compute SSB and then MSB (MSB = SSB / dfB with dfB = k − 1 = 2). Which MSB is correct?
SSB = 32, MSB = 16
SSB = 48, MSB = 24
SSB = 16, MSB = 8
SSB = 64, MSB = 32
What does MSW measure in a one-way ANOVA?
Effect due to treatment or experimental manipulation
Variability between group means
Variability among participants within each group
Easy computation (SSW → MSW). Suppose SSW = 24, total N = 12, k = 3.
Use dfW = N − k and MSW = SSW / dfW.
Which MSW is correct?
MSW = 24 / 8 = 3.00
MSW = 24 / 9 = 2.67
MSW = 24 / 6 = 4.00
MSW = 24 / 12 = 2.00
Compute MSB and MSW then F. Given MSB = 16 (already computed) and MSW = 2.67.
Use F = MSB / MSW. Which is correct?
F ≈ 4.00 → marginal evidence only
F ≈ 6.00 → evidence against H₀
F ≈ 1.50 → fail to reject H₀
F ≈ 0.17 → no evidence
Suppose you have F ≈ 6.00 with dfB = 2 and dfW = 9; Fcrit(2,9) ≈ 4.26.
What do you conclude?
Reject H₀ (6.00 > 4.26)
Fail to reject H₀ (6.00 < 4.26)
Need p-value to decide
Compute MSB again
If your one-way ANOVA yields F(2, 27) = 6.45, p < .01, what does this result indicate?
At least one group mean differs significantly from the others.
All three group means differ significantly from each other.
The within-group variance is larger than the between-group variance.
The null hypothesis is true.
Why is one-way ANOVA preferred to multiple independent-samples t tests when comparing 3+ groups?
It increases the chance of Type I error.
It decreases the chance of Type I error.
It controls the Type I error rate across comparisons.
After a one-way ANOVA, when should post hoc tests (e.g., Tukey’s HSD) be conducted?
Always, regardless of the F test.
Only when the overall F test is significant.
What is the main purpose of a post hoc test like Tukey’s HSD?
To verify that the assumptions of ANOVA are met.
To replace the F test entirely.
To determine which specific group means differ after finding a significant overall F.
A researcher conducted a one-way ANOVA and obtained F(3, 24) = 5.12, p = .007, η² = .39. Which is the correct APA-style interpretation?
Group differences were not significant, F(3, 24) = 5.12, p = .007.
The effect size was small, η² = .39.
The F value indicates homogeneity of variance was met.
There was a significant effect of group on the dependent variable, F(3, 24) = 5.12, p = .007, η² = .39.
If F(2, 21) = 1.24, p = .31, what is the proper APA-style statement?
The result supports rejecting H₀.
The effect of group was significant, F(2, 21) = 1.24, p = .31.
There was no significant effect of group on the dependent variable, F(2, 21) = 1.24, p = .31.
If F(2, 27) = 3.89, p = .034, what should be done next?
Fail to reject H₀.
Conduct post hoc comparisons (e.g., Tukey’s HSD) to locate which group means differ.
