CHOOSING A STATISTICAL TEST – EXERCISE IIREVIEW EACH OF THE FOLLOWING SCENARIOS AND INDICATE WHICH STATISTICAL ANALYSISWOULD BE MOST APPROPRIATE TO TEST THAT SCENARIO. FOR EACH SCENARIO, IDENTIFY THEINDEPENDENT VARIABLE(S) (AND LEVELS, AS APPLICABLE), AND THE DEPENDENT VARIABLE.CHOOSE FROM THE FOLLOWING STATISTICS (EACH ONLY USED ONCE):DEPENDENT-SAMPLES T TESTINDEPENDENT-SAMPLES T TESTONE-WAY ANOVAONE-FACTOR (ONE-WAY) REPEATED MEASURES ANOVAONE-FACTOR (ONE-WAY) ANALYSIS OF COVARIANCEFACTORIAL (TWO-WAY) ANOVASIMPLE LINEAR (BIVARIATE) REGRESSIONSIMULTANEOUS ENTRY MULTIPLE REGRESSIONBLOCK ENTRY (HIERARCHICAL) MULTIPLE REGRESSION1. An educational researcher is studying the influence and relative importance of a student’sreading speed and their aptitude on their overall academic achievement for a group ofrandomly selected fifth graders. Which statistical test would your recommend she use?2. As part of a two-week treatment for phobias, a therapist measured the general anxietylevel of each client four times: before, after one week of treatment, at the end of thetreatment, and four months later. What statistical test would be used to determine theeffectiveness of the treatment?3. Children (mean age = 6 years) who ate breakfast at school participated in an experimentto determine the effect of sugar on activity. On some days a particular child receivedsugar with breakfast and on other days the child did not. This was true for all the childrenin the study. Later in the day each child was observed and activity recorded.4. A group of athletic trainers use a test of physical conditioning that is very comprehensive,but has the disadvantage that its administration is long and complex. A researcherdevelops a shorter, simpler test of physical conditioning and administers both tests to agroup of young adult athletes. The intention is to use the shorter test as a substitute for thelonger, more complex test, but that will depend on how good a predictor the scores on theshort test are of the scores on the long test. Which statistical test would be used to answerwhether the short test can be substituted?5. An experimenter is interested in the effect of expectations and drugs on alertness. Eachparticipant is given an amphetamine (stimulant) or a placebo (an inert substance). Inaddition, half of each group is told that the drug taken was a stimulant and half that thedrug was a depressant. An alertness score for each participant is obtained from acomposite of measures that included a questionnaire and observation.6. The districts high school cafeteria manage is dismayed by the amount of food that is lefton plates. One way to reduce waste is to prepare the food using a tastier recipe. Supposethat three unique recipes for the entrée are served (all other items being equal) at threedifferent school cafeterias (from peer schools). As the plates are cleaned in the kitchen,the amount of entrée left on the plates is recorded. How might the manager gauge thepreference of the recipes?7. Research has shown (indicated) that an individuals performance (success, as measured bytheir final grade) in the ABC Program is a function of what they bring into the programtraining (pre-ability measures) and what they learn while in the program training(acquired ability measures). You have been asked to investigate whether individuals’acquired abilities offer significant additional predictive power beyond that contributed bythe individuals’ pre-abilities. What statistical test would you use for this study?8. A consumer testing group compared two leading laundry detergents to determine whichgot laundry whiter. White towels that had been subjected to a variety of filthy treatmentswere randomly assigned to one of the two detergents. After washing, each set of towelswas tested with a photometer for the amount of light reflected (testing their cleanliness).What is the statistical test that should be used to compare the two detergents?9. Based on research from the National High School and Beyond Study, males have beenshown to have significantly higher mathematics achievement scores than females. Aresearcher wishes to explore this hypothesis; however, she contends that this differencemay be due to differences in the number of math courses taken by the male and femalestudents. What statistical test would she use to test mathematics achievement scoredifferences between males and females controlling for the effect of the number ofmathematics courses that the male and female students had previously taken.CHOOSING A STATISTIC IIPAGE