Name:
HOMEWORK 9
Two-Way ANOVA (Between-Subjects, Within-Subjects, & Mixed-Factorial)
1. / (20 pts) A physiological psychologist is investigating the effect of a new drug-terpinol on motor skills. She suspects that the drug will affect the basal ganglia and block motion feedback control during fine positioning tasks. She also thinks sex will affect the outcome measure as well. She divides 40 experimental participants (20 males and 20 females) into independent groups by random assignment. Each group contains 5 males and 5 females and receives different amounts of the drug (0,1,5, and 10 mg respectively). She then asks the participants to drop 59 clothes pins into a small rectangular box. He records the number of times the participant dropping the clothes pin misses the container. The data are contained below. Can he conclude that sex and the drug effects motor skills from this analysis? Use an -level of 0.01.
0mg / 1mg / 5mg / 10mg
Male / 0 / 0 / 4 / 13
1 / 2 / 6 / 15
2 / 1 / 3 / 16
1 / 3 / 7 / 20
3 / 2 / 4 / 12
Female / 1 / 0 / 8 / 17
4 / 2 / 12 / 15
0 / 1 / 14 / 13
0 / 0 / 10 / 12
1 / 0 / 8 / 17
  1. (2 pts) What test is appropriate for this analysis?
  2. (3 pts) State the null hypothesis/es:
  3. (3 pts) State the alternative hypothesis/es:
  4. (2 pts) Calculate the obtained statistic:
  5. (3 pts) Make a decision/s:
  6. (5 pts) What does your decision mean? Describe what is going on in your plot here.
  7. (2 pts) Produce a plot of the data. Paste below:

2. / (20 pts) A psychologist would like to evaluate the effect of Cognitive-Behavioral Therapy and antidepressant use on depression. He obtains 10 clinical participants for a period of 2 months. During the first month, the participants are given no therapy; half the participants are given an anti-depressant and the other half receive a placebo. This is followed by a diagnostic Depression test (0-10). During the second month, those same participants continue treatment, but now all receive CBT. This is then again followed by a diagnostic depression test (0-10). Below is the data. Evaluate the effect of both CBT and antidepressant-use on Depression.
Pre-CBT / Post-CBT
Placebo / 8
7
9
8
9 / 7
6
9
3
4
Anti-depressant / 8
4
8
9
7 / 3
4
2
5
5
  1. (2 pts) What test is appropriate for this analysis?
  2. (3 pts) State the null hypothesis/es:
  3. (3 pts) State the alternative hypothesis/es:
  4. (2 pts) Calculate the obtained statistic:
  5. (3 pts) Make a decision/s:
  6. (5 pts) What does your decision mean? Describe what is going on in your plot here.
  7. (2 pts) Produce a plot of the data. Paste below:

3. / (20 pts) A researcher would like to know whether taking vitamin C and getting a flu shot affect the number of instances of illness in a year. She finds 28 people such that half got the flu shot, and half did not. She also makes sure that half of the people who got a flu shot took vitamin c, while the other half did not, and the same for the individuals who did not get the flu shot. She asks each person to report the number of colds they had during a one-year period. The data are below. Test her hypothesis using an alpha level of .05.
Flu Shot / No Flu Shot
Vitamin C / 2
1
3
2
0
1
0 / 6
5
8
7
9
8
7
No Vitamin C / 0
1
2
4
1
2
3 / 12
10
6
14
12
9
10
  1. (2 pts) What test is appropriate for this analysis?
  2. (3 pts) State the null hypothesis/es:
  3. (3 pts) State the alternative hypothesis/es:
  4. (2 pts) Calculate the test statistic:
  5. (3 pts) Make a decision/s:
  1. (5 pts) What does your decision mean? Describe what is going on in your plot here.
  1. (2 pts) Produce a plot of the data. Paste below:

4. / (20pts) Atypingspecialistwouldliketoevaluatetheeffectoftask-switching (askingsomeonetoswitchbetweenvarioustasks) androomlightingonreactiontime (milliseconds) inagroupof 5 studentsinhisclass. Heasksthese 5 studentstocompleteacomputertaskinwhichtheyaretojudgewhetherornotanumberisoddorevenbypressingacertainkeyonthekeyboard. Hefirsthasthemcompletethistasksinaroomwithverydimlighting, andthen, anhourlater, bringsthembacktocompletethesametaskinabrightly-litroom. Hesendsthemhome, andasksthemalltoreturnonthefollowingday, atwhichpointtheycompleteataskwhichalternatesbetweenaskingthemtoidentifyaneven/oddnumberandidentifyingwhetherornotthenumberislessthanorgreaterthan 5 (thus, therearetwodifferenttasksincorporatedintotheprogram). Hehasthemdothisinadimly-litroom, andagain, afteranhour, callsthembacktodoitagaininabrightly-litroom. Useanalphalevelof .05 toassesstheeffectoftask-switchingandlightingonreactiontime.
NoTask-Switching / Task-Switching
Dimlighting / 980
800
900
950
800 / 1100
1200
1010
1000
1200
Brightlighting / 500
600
600
500
600 / 1000
1200
900
800
1200
  1. (2 pts) What test is appropriate for this analysis?
  2. (3 pts) State the null hypothesis/es:
  3. (3 pts) State the alternative hypothesis/es:
  4. (2 pts) Calculate the test statistic:
  5. (3 pts) Make a decision/s:
  6. (5 pts) What does your decision mean? Describe what is going on in your plot here.
  7. (2 pts) Produce a plot of the data. Paste below:

5. / (8 pts) For each of the following examples, assume we have created an experiment in which we test to see whether the color of light and the temperature affect how well students perform on a Statistics exam. We ask 100 students to participate in this experiment: 50 students take a stats exam in a room lit with red light (half of them are in a cold room, while the other half are in a hot room). The other 50 students take the exam in a room lit with blue light (half in a cold room, half in a hot room). Below are tables that contain the mean score for each of the possible groups of students. You will notice that some cells are left blank. Fill each blank in with a number that makes the indicated condition true:
  1. No main effect of Room Color:
Red / Blue
Hot / 80
Cold / 70 / 60
b. No main effect of Temperature:
Red / Blue
Hot / 75 / 85
Cold / 80
c. No interaction between room color and temperature.
Red / Blue
Hot / 70 / 90
Cold / 80
d. No main effect of Room Color and no main effect of Temperature:
Red / Blue
Hot / 85
Cold / 60 / 85
6. / (12 pts) Write your own research vignettes (in one short paragraph), describing a hypothetical study for one of each of the following research designs: Between-Subjects, Within-Subjects, and Mixed Factorial. You should limit your example to two independent variables (the # of levels of each variable is up to you, but to keep things simple, feel free to keep it to two levels).
  1. Between-Subjects Two-Way ANOVA:
  2. Within-Sibjects Two-Way ANOVA:
  3. Mixed-Factorial Two-Way ANOVA: