308 • • CHAPTER 11
fionfertoni adjustment ANOVA (analysis of variance) one-way randomized ANOVA grand mean coe variance
the present text. However. coverage of these tests can be found in more comprehensive statistics texts.
Summary In this chapter, we discussed designs that use more than two leveks of an independent variable. Advantages to such designs include being able to compare more than two kinds of treatment, to use fewer participants, to compare all treatments with a control group, and to use placebo groups. In addition, we discussed the statistical analyses most appropriate for use with these designs—most commonly, with interval-ratio data, an ANOVA. A randomized one-way ANOVA is used for between-subjects designs, and a repeated measures one-way ANOVA is used for correlated-groups designs. Also discussed were appropriate post tux tests (Tukey's HSD) and measures of effect size (eta-squared). After completing this chapter, you should appreciate the advantages of using more compli-cated designs and understand the basic statistics used to analyze such designs.
within-groups variance eta-squared (e) between-groups variance pest hoc test F-ratio Tukey's honestly significant total sum of squares difference (MD) within-gnaupa sum of squat~; one-way repeated betwieregroups sum of squares measures ANOVA Mean square
(Answers to odd-numbered cierci.s appear in Appendix C.) I. What is/arc the advantage(s) of conducting a Andy with three or more levels of the indepen-dent variabk? 2 What is the difference between a randomised ANOVA and a repeated IIIVJNLIMS¦ ANOVA? What does the term one-any mean with respect to an ANOVA? 1 ExpLlin between-groups variance and within- groups variance. a. If a re:caroller decides to use multiple compari-sons in a study with three oanditionc what is the
probability of a Type I error across these com-parisons? Use the Bonferroni adjustment to determine the suggested alpha level 5. If fin S true, what shoidd the F-ratio equal or be dose to? If H. is supported, should the F-ratio be greater than, less than or equal to I? 6. When should post lux comparisons be performed? 7. What information does eta-squared (72) provide? 8. Why is a repented measures ANOVA statisti-cally more powerful than a randomized ANOVA?
Experimental Designs with NOR Than Two Levels of an Independent Wadable •• 309
9. A researcher conducts a study of the effects of amount of sleep on creativity. The creativity series for four levels of sleep (2 hours, 4 hours, 6 tours, and 8 hours) for N = 20 subjects are presented here. 2
3
5
6
2
Amount of Sleep fin hours) II 4 6 8 4 10 10 11 13 8 13 10 3 9 9 2 10 10
a. Complete the following ANOVA summary table. (If ratlf isorructor wanb you to .10.3- 15tC the sums of squares, me the pas...ding data to do so.) Sourer df SS MS F Between groups 187.75 Within groups 5520 Total 242.95
b. Is F„,a saga:bran! at at = 05; at a = DI? e. Perform post hoc comparisons if necessary. d. That corchntoro can be drawn from the F-ratio and the post hoc comparisons? e. What is the effect size. and what does this treat,' f. Graph the mean, 10. Ina study of the effects of sness on ill's., a researcher .1Ird the number of colds people contracted during a 6-month poled as a fon, non of the amount of stseci they reported during that some time period. There were three street kirk: minimal, moderate. and NO stress. The NUms of squares appear in the following ANOVA summary table. The mean for each condition and the number of inthjects per condi-ben are afro noted.
Source df SS MS F Between groups 22.167 Within groups 14.750 Total 36.917 Stress Lerr1 Mean N Minimal 3 4 Moderate 4 4 High 6 4
a Complete the ANOVA summary table. b• k l'ave stsththcant at a = 03; at a = 01e
e. Perform post hoc comparisons if necessary. d. That conchokno can be drawn from the F-ratio and the post Foe comparisons? e. What is the effect sUe, and what does this mean? f. Graph the means. A researcher interested in the effects of exercise on stress had participants exercise for 30, 61 or 90 minutes per day. The mean stress level on a 100-point strew, wale both RV indicating high stress) for each condition appears next, along with the ANOVA S111711714fy table with the sums of squares indicated.
Source Between groups Within groups Total
Everette Lem) 30 minutes 60 manner 90 attendees
df SS MS F 4,68927 E2,604.20 87213 47
Mean 75.0 44.7 632
10 10 10
s Complete the ANOVA samrnary table. h B F., sigrificant at = .05; at a = .01? c. Perform post toe comparisons if recessnly. d. What cenchoions can be drawn from the F-ratio and the post hoc comparisons' e. What is the effect Mae, and what does this mean? Graph the means. 12 A researcher conducted an esperiment on the effects of a new 'drug,' on del-m.99.n The researcher had a control poop that recessed nothing, a placebo group. and an experimental group that remand the "drug- A depression inventory that provided a measure of depression an a 50-point scale was used 00 indicates that an individual is very high on the deprecion vari-able). The ANOVA summary table appears rest, along with the mean depression score for each condition. Source df SS MS F Between groups 1202.313 Within groups 2,11800 Total 3,320313
COrlditiOn Control Placebo °Drag-
Mean 3626 3333 24.13
15 15 15
310 • • CHAPTER 11
a. Complete the ANOVA summary table. b. 6 Fun, significant at a = .05, at a = .01? c. Perform pest hoc comparisons if neceaary. d. That conclusions can be drawn from the F-ratio and the pmt hoc comparkora? c. What is the effect size, and what do. the mean? I Graph the swarm 13. A researcher is interested in the effects of practice on accuracy ina signalskaction task. Subjects are tested with no practice after 1 hour of practice, and after 2 hours of practice. Each pers., partiopatc in all three conditiea. The following data indicate how many signals each participint detected accu-rately at each Iced of practice. Amount of Pratko
Subject 1 2 3 4 5 6 No Proetior 3 4 2 1 3 3 2 1 Horn 4 5 3 3 6 4 3 2 Hours 54 5 7 6 4
Source. df 5$ MS F Subject 16.27 Between 3.81 Error 457 Total 46.95
a Complete the ANOVA summary table. (11 your indriseter wanes you to calculate the sums of sparnti use the preceding data to do so.) b. Is F,,,„ signiiront at a = .05, at o i= .01? c. Perform pmt hoc comparisons if nccnsmrv. d. What concluxions can be drawn from the Faistio and the put hoc comparisons? e. What is the effect size, and what do. O. mean? I Graph the means. 14. A researcher has been hired by a pizzeria to determine whah type of crust autoireirs prefer. The restaurant offers three types of at.: hand-ttissed, thick, and thin. Following are the mean number of 1-inch pieces of pizza eaten for each condition from 10 subjects who had the oppor-tunity to eat as many pia. with each typed mat as they desired. The ANOVA summary table also follows. Source df 55 MS Subject 2.75
Between 180.05 Error 21.65 Total 204A5 OW* Type Man Hand-tossed 273 10 Thick 4.20 10 Thin 8.50 10
a. Complete the ANOVA summary table b. 6 sithificant at a — .05, at a — DI? c. Perform post hoc comparisons if necessary. d. Wt.( conclumons can be drawn from the Fratio and the post hoc comparisons? e. Whet is the effect ,iac, and what doe the mean' f. Graph the means. 15. A researcher is interested in whether massed or spaced studying has a greakr impact on grades in a course. The researcher has her class study for 6 hours all in one day for one main (massed study condition). She Ixns then, study for 2 hours each day for 3 days for another exam (3-day spaced condition). Last, she has them study for 1 hour a day for 6 days for a third exam (6-day spaced condition). The mean exam score (out of a possible 100 points) for each condition appears nest, along with the ANCNA summary table Source df SS MS F Subject 136.96 Between 3,35d% Error 49903 Total 398695
Study CondWort Mein Massed 69.13 15 3-day spaced 79.33 15 6-day spaced 91127 15
a. Complete the ANOVA summary table. b. Is stithificant at a — .0.5; at DI? c. Perform post hoc comparisum if necessary. d. Whit conchraom ore be drawn Ewen the F-ratio and the post hoc comparisons? e. What is the effect sae, and what des the mean? L Graph the means.