CHOOSING A STATISTICAL TEST – EXERCISE II – KEYREVIEW 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?Multiple linear regression analysis (simultaneous entry) would be used,with one set of independent (predictor) variables (reading speed andaptitude) and one dependent (criterion) variable (academic achievement).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?A one-factor repeated-measures ANOVA will help evaluate the treatment.Here the dependent variable is anxiety level and the independent variabletreatment times, with four occasions (before, after one week of treatment,at the end of the treatment, and four months later).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.A paired-samples (dependent) t test allows you to determine if activity (thedependent variable) depends on whether or not a child eats sugar atbreakfast (the independent variable). The samples are paired – each childserves in both conditions.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?Simple linear (bivariate) regression analysis (used for prediction) would beused, with one Independent (Predictor) Variable (Short Test) and oneDependent (Criterion) Variable (Long Test).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.A 2  2 factorial ANOVA. The two independent variables are drug type(two levels; amphetamine and placebo) and information (two levels; told itwas a stimulant and told it was a depressant), with the alertness scorebeing the dependent variable.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?One-way Analysis of Variance – with the dependent variable being theamount of entrée left, and the independent variable being type of entrée(with three levels).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?Multiple linear regression analysis (hierarchical, block entry) would beused, with the first (control) set of Independent (Predictor) Variables beingthe pre-ability measures and the second set of Independent (Predictor)Variables being the acquired ability measures. The one Dependent(Criterion) Variable would be the performance (success).CHOOSING A STATISTIC II – KEYPAGE 28. 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?An independent-samples t test, with cleanliness as the dependent variableand laundry detergent as the independent variable (two levels; the twoleading brands).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