25: Two Means t Test Flashcards
The ANOVA is based on all of the following assumptions except:
a. Groups should show homogeneity of variance.
b. Data should be drawn from populations with normal distributions. c. Data should be at the interval/ratio level.
d. Participants are chosen through a random sampling procedure.
D
Rationale: It is preferable that groups be randomly assigned, but it is not required that the sample be chosen at random.
An effect size for the independent samples one-way ANOVA analysis can be calculated by:
a. Dividing the between-groups sum of squares by the total sum of squares.
b. Dividing the within-groups sum of squares by the total sum of squares.
c. Dividing the within-groups sum of squares by the between-groups sum of squares.
d. Dividing the between-groups sum of squares by the within-groups sum of squares.
A
Rationale: The effect size index 2 = SSb/SSt.. The effect size index f = (SSb/SSe).
All of the following can be used as effect size indices for the ANOVA except: a. 2 c. p
b. f d. 2
ANS: C
Rationale: The p value is not an effect size.vAll others choices are effect sizes that can be used for ANOVA
A study is designed to examine the effect of exercise (against no exercise) on knee pain, with
measurements taken at 1 week, 3 weeks, and 6 weeks. Participants are randomly assigned to one of
the exercise conditions. The appropriate design would be:
a. Two-way analysis of variance.
b. One-way analysis of variance.
c. Two-way analysis of variance with one repeated measure.
d. One-way repeated measures analysis of variance.
C
Rationale: The design has two independent variables. Exercise has two levels, and time is a repeated measure with three levels. This is also called a mixed design.
An ANOVA is run to determine if there is a difference among five treatment groups for relief of shoulder pain in a sample of 65 patients. The analysis results in F = 2.41. The critical value and significance of this result is:
a. Critical F = 2.37; the test is not significant.
b. Critical F = 2.37; the test is significant.
c. Critical F = 2.53; the test is not significant.
d. Critical F = 2.53; the test is significant.
C
Rationale: The critical value (see Appendix Table A-3) is 2.53 with dfb = 4, dfe = 60 (dfb = k-1, dfe = N-k)
In an ANOVA, the value of F is calculated by:
a. MSb / MSe c. SSb / dfb
b. SSb / SSe d. SSe / dfe
A
Rationale: The F statistic is the between-groups mean square divided by the error mean square.
As the distance of group means from the grand mean gets larger, what happens to the value of F?
a. It will stay the same. c. It will decrease.
b. It will increase. d. It depends on sample size.
B
ANS: B
Rationale: The F value will increase as the distance of means from the grand mean increases, indicating that they are farther apart.
A researcher studied the performance on a memory task in students who had <4 hours of sleep the night before versus 4-6, or >6 hours. The effect was also monitored for those who had high versus low reading skills. The graph above shows the distribution of scores among the 6 groups. The ANOVA showed a significant effect. Which of the following statements is not a reasonable interpretation of this result?
a. High reading scores are associated with higher memory scores.
b. There is no interaction effect present.
c. Higher reading score with > 6 hours sleep produces the best memory score.
d. There is an interaction between reading and hours sleep on memory score.
A
Rationale: The graph shows an interaction, with the best combination of higher reading score and >6 hrs sleep. High reading scores are only associated with higher memory scores with >6 hrs sleep.
A study was designed to compare three groups on balance scores following three types of balance
training. 33 patients are randomly assigned to the two groups in a pretest-posttest design. An ANOVA resulted in F (2, 30) =3.25, p = .07, 2 = .09. What is your reasonable conclusion?
a. The F value is significant, and there is a difference among the three types of training.
b. The F value is not significant, and there is no difference in the three types of training.
c. The F value is significant, and power is sufficient to demonstrate that the difference is meaningful.
d. The F value is not significant, but power may be low and differences may be present with a larger sample.
D
Rationale: The critical value of F(2,30) = 3.32, which is close to the calculated F. The eta squared of .09 is considered a medium effect. It will translate to power of 22% (using G*Power), which is quite low. The p value is close to .05, and therefore, a larger sample might produce a significant result.
Which of the following is true about conducting a two-way ANOVA?
a. Interaction effects should only be considered if main effects are significant.
b. Multiple comparisons are only necessary follow-up tests for main effects.
c. The significance of a main effect is only considered if the interaction effect is
significant.
d. Main effects may be ignored if there is a significant interaction effect.
D
Rationale: Both main and interaction effects are considered. However, main effects are often ignored if interaction is significant, as it is the combination of levels that is usually the primary interest. Main effects would be considered if interaction was not significant. Multiple comparisons can be used a follow-up analyses for both main and interaction effects (see Chapter 26).
In a one-way repeated measures analysis of variance, the total variance is composed of:
a. Between-subjects, main effect, and interaction effect variance.
b. Between-groups variance and within-groups variance.
c. Between-subjects variance, between-treatments variance, and error variance.
d. Between-groups variance and within-subjects variance.
C
Rationale: In a one-way repeated measures ANOVA, the total variance is partitioned into between-subjects and within-subjects variance. The within-subjects variance is further partitioned into treatment and error variance.
A study is designed to test the effect of four different drugs on frequency of migraine headache in 50 patients. A one-way ANOVA was used to test the difference across four randomly assigned groups. In the ANOVA, which of the following degrees of freedom would be used with each source of variance?
a. Between-groups = 3 df; Error = 46 df; Total = 49 df
b. Between-groups = 4 df; Error = 46 df; Total = 50 df
c. Between-groups = 3 df; Error = 47 df; Total = 50 df
d. Between-groups = 2 df; Error = 47 df; Total = 49 df
A
Rationale: Between groups = k – 1 df; Error = N – k df; Total = N – 1 df.
A study was done to test the effect of four exercise routines and two program schedules on improving endurance. The two program schedules were 3x/week or 5x/week. Which of the following is not a question that can be answered in a two-way ANOVA?
a. What is the independent effect of the exercise routines on endurance?
b. What is the independent effect of program schedules on endurance?
c. What is the combined effect of exercising 3x/week and 5x/week?
d. What is the combined effect of exercise routine and program schedule on
endurance?
C
Rationale: The research questions refer to the exercise and program variables, not the individual levels of program schedule.
