## PSY-520 Module 7 Exercises – Graduate Statistics GCU

PSY-520 Module 7 Exercises – Graduate Statistics GCU

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Chapter 15:4. When doing an experiment with many groups, what is the problem with doing t tests between all possible groups without any correction? Why does use of the analysis of variance avoid that problem?

The problem with utilizing a t-test with many groups is that there is an increase in the probability of a Type I error occurring. Yet, when we use the analysis of variance (ANOVA) method, it is specifically designed to be used when there are two or more groups. It allows researchers to evaluate the mean of the single hypothesis through an a-level and reduces the potential of a Type I error occurring.

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8. What are the assumptions underlying the analysis of variance?

10. Find Fcrit for the following situations:a. df(numerator) = 2, df(denominator) = 16, ? = 0.05

b. df(numerator) = 3, df(denominator) = 36, ? = 0.05

c. df(numerator) = 3, df(denominator) = 36, ? = 0.01What happens to Fcrit as the degrees of freedom increase and alpha is held constant? What happens to Fcrit when the degrees of freedom are held constant and alpha is made more stringent?

12. What are the variables that affect the power of the one-way analysis of variance technique?

13. For each of the variables identified in Question 12, state how power is affected if the variable is increased. Use the equation for Fobt on p. 421 to justify your answer.

20. Assume you are a nutritionist who has been asked to determine whether there is a difference in sugar content among the three leading brands of breakfast cereal (brands A, B, and C). To assess the amount of sugar in the cereals, you randomly sample six packages of each brand and chemically determine their sugar content. The following grams of sugar were found:

a. Using the conceptual equations of the one-way ANOVA, determine whether any of the brands differ in sugar content. Use ? = 0.05.

b. Same as part a, except use the computational equations. Which do you prefer? Why?c. Do a post hoc analysis on each pair of means using the Tukey HSD test with ? = 0.05 to determine which cereals are different in sugar content.

d. Same as part c, but use the .

e. Explain any differences between the results of part c and part d.

23. Assume you are employed by a consumer-products rating service and your assignment is to assess car batteries. For this part of your investigation, you want to determine whether there is a difference in useful life among the top-of-the-line car batteries produced by three manufacturers (A, B, and C). To provide the database for your assessment, you randomly sample four batteries from each manufacturer and run them through laboratory tests that allow you to determine the useful life of each battery. The following are the results given in months of useful battery life:

a. Use the analysis of variance with ? = 0.05 to determine whether there is a difference among these three brands of batteries.

b. Suppose you are asked to make a recommendation regarding the batteries based on useful life. Use the Tukey HSD test with ? = 0.05 to help you with your decision.

26. A university researcher knowledgeable in Chinese medicine conducted a study to determine whether acupuncture can help reduce cocaine addiction. In this experiment, 18 cocaine addicts were randomly assigned to one of three groups of 6 addicts per group. One group received 10 weeks of acupuncture treatment in which the acupuncture needles were inserted into points on the outer ear where stimulation is believed to be effective. Another group, a placebo group, had acupuncture needles inserted into points on the ear believed not to be effective. The third group received no acupuncture treatment; instead, addicts in this group received relaxation therapy. All groups also received counseling over the 10-week treatment period. The dependent variable was craving for cocaine as measured by the number of cocaine urges experienced by each addict in the last week of treatment. The following are the results.

a. Using ? =0.05, what do you conclude?

b. If there is a significant effect, estimate the size of effect, using .

c. This time estimate the size of the effect, using ?².

d. Explain the difference in answers between part b and part c.

Chapter 16:11. It is theorized that repetition aids recall and that the learning of new material can interfere with the recall of previously learned material. A professor interested in human learning and memory conducts a 2 X 3 factorial experiment to investigate the effects of these two variables on recall. The material to be recalled consists of a list of 16 nonsense syllable pairs. The pairs are presented one at a time, for 4 seconds, cycling through the entire list, before the first pair is shown again. There are three levels of repetition: level 1, in which each pair is shown 4 times; level 2, in which each pair is shown 8 times; and level 3, in which each pair is shown 12 times. After being presented the list the requisite number of times and prior to testing for recall, each subject is required to learn some intervening material. The intervening material is of two types: type 1, which consists of number pairs, and type 2, which consists of nonsense syllable pairs.After the intervening material has been presented, the subjects are tested for recall of the original list of 16 nonsense syllable pairs. Thirty-six college freshmen serve as subjects. They are randomly assigned so that there are six per cell. The following scores are recorded; each is the number of syllable pairs from the original list correctly recalled.

a. What are the null hypotheses for this experiment?

b. Using ? =0.05, what do you conclude? Plot a graph of the cell means to help you interpret theresults.

12. Assume you have just accepted a position as chief scientist for a leading agricultural company. Your first assignment is to make a recommendation concerning the best type of grass to grow in the Pacific Northwest and the best fertilizer for it. To provide the database for your recommendation, having just graduated summa cum laude in statistics, you decide to conduct an experiment involving a factorial independent groups design. Since there are three types of grass and two fertilizers under active consideration, the experiment you conduct is 2 X 3 factorial, where the A variable is the type of fertilizer and the B variable is the type of grass. In your field station, you duplicate the soil and the climate of the Pacific Northwest. Then you divide the soil into 30 equal areas and randomly set aside 5 for each combination of treatments. Next, you fertilize the areas with the appropriate fertilizer and plant in each area the appropriate grass seed. Thereafter, all areas are treated alike. When the grass has grown sufficiently, you determine the number of grass blades per square inch in each area. Your recommendation is based on this dependent variable. The “denser” the grass is, the better. The following scores are obtained:

a. What are the null hypotheses for this experiment?

b. Using ? = 0.05, what are your conclusions? Draw a graph of the cell means to help you interpret the results.

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13. A sleep researcher conducts an experiment to determine whether a hypnotic drug called Drowson, which is advertised as a remedy for insomnia, actually does promote sleep. In addition, the researcher is interested in whether a tolerance to the drug develops with chronic use. The design of the experiment is a 2 X 2 factorial independent groups design. One of the variables is the concentration of Drowson. There are two levels: (1) zero concentration (placebo) and (2) the manufacturer’s minimum recommended dosage. The other variable oncerns the previous use of Drowson. Again there are two levels: (1) subjects with no previous use and (2) chronic users. Sixteen individuals with sleep onset insomnia (difficulty in falling asleep) who have had no previous use of Drowson are randomly assigned to the two concentration conditions, such that there are eight subjects in each condition. Sixteen chronic users of Drowson are also assigned randomly to the two conditions, eight subjects per condition. All subjects take their prescribed “medication” for 3 consecutive nights, and the time to fall asleep is recorded. The scores shown in the following table are the mean times in minutes to fall asleep for each subject, averaged over the 3 days:

a. What are the null hypotheses for this experiment?

b. Using ? = 0.05, what do you conclude? Plot a graph of the cell means to help you interpret the results.

**References**

Academic Web Services (n.d.). The Visual Learner – Statistics. Retrieved from: http://lc.gcumedia.com/zwebassets/courseMaterialPages/psy520_the-visual-learner-v1.1.php. Pagano, R. (2013). Understanding Statistics in the Behavioral Sciences (10th ed.). Wadsworth-Cengage Learning. PSY-520 Module 7 Exercises – Graduate Statistics GCU