10th Edition

ISBN: 9780321989178

Author: Neil A. Weiss

Publisher: PEARSON

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A new framework of data analysis where the new statistical methods are used for interpreting the results and analyzing the data is known as estimation in statistics.

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Textbook Question

Chapter B.3, Problem 68E

Mental Tasks and Drugs. In the text Statistical Theory and Methodology in Science and Engineering (New York: Wiley. I960). K. A. Brownlee provides data on an experiment involving a person's ability to perform a mental task before and after taking one of four drugs. Fifty-six subjects performed a task that involved mental addition. The subjects were then randomly divided into four groups. Each group drank a beverage containing one of four drugs, labeled A, B, C, and D. After a period of time for the drugs to take effect, each subject repeated the mental addition test. We want to relate the after test score (after) to the before test score (before) and the drug that was taken. The data from the experiment are presented in the following table.

Chapter B.3, Problem 68E, Mental Tasks and Drugs. In the text Statistical Theory and Methodology in Science and Engineering , example 1

In this study, the drug labeled B was a placebo, that is, it contained no drug and should have no effect on a person’s ability to perform a mental task. Define three indicator variables as follows:

$d r u g a = { 1 , if drug A is taken ; 0 , if drug A is not taken . d r u g c = { 1 , if drug C is taken ; 0 , if drug C is not taken . d r u g d = { 1 , if drug D is taken ; 0 , if drug D is not taken .$

a. Output B.57 on page B-93 provides a plot of after versus before, using a different plot symbol for each drug. Bases on this plot, does it appear that drug is a useful predictor variable? Explain your answer.
b. We obtained the regression analysis of after on before and the three indicator variables druga, drugc, and drugd, as shown in Output B.55 on page B-93. Conduct the t-tests for the individual utility of the four predictor variables at the 5% level of significance. Interpret your results.
c. Explain what the t-test for the utility of the indicator variable druga means in terms of comparing the effect of drug A to the effect of the placebo on the after mental task scores.
d. Which drugs have on effect on the after mental task score that is different from the placebo?
e. Based on Output B.58, obtain 1he regression equations relating after to before for each of the four drugs.
f. Outputs B.59(a)–(f) provide, respectively, plots of residuals versus fitted values, residuals versus before, and residuals versus each indicator variable, and a normal probability plot of the residuals. Perform a residual analysis to assess the appropriateness of the regression equation, constancy of the conditional standard deviations, and normality of the conditional distributions. Check for outliers and influential observations.
g. Output B.60 on page B-95 provides a scatterplot of after versus before with the regression lines for the four drugs. Based on this output and your residual analysis in part (f), do you feel that this model fits the data well? Explain your answer.
h. To check for possible interactions between the before score and. the drug, we obtained the regression analysis of after on before, druga, drugc, drugd, druga·before, drugc·before and drugd·before. The output is in Output B.61 on page B-96. Is there an interaction between drug and before, that is, are any of the cross-product terms useful predictor variables in the regression equation that contains the other terms in the model? Use α = 0.05.

Chapter B.3, Problem 68E, Mental Tasks and Drugs. In the text Statistical Theory and Methodology in Science and Engineering , example 2

Regression Analysis: AFTER versus BEFORE, DRUDA, DRUGC, DRUGD

Analysis of Variance

Chapter B.3, Problem 68E, Mental Tasks and Drugs. In the text Statistical Theory and Methodology in Science and Engineering , example 3

OUTPUT B.58 Regression output for Exercise B.68

Chapter B.3, Problem 68E, Mental Tasks and Drugs. In the text Statistical Theory and Methodology in Science and Engineering , example 4

Chapter B.3, Problem 68E, Mental Tasks and Drugs. In the text Statistical Theory and Methodology in Science and Engineering , example 5

Regression Analysis: AFTER versus BEFORE, DRUDA, DRUGC, DRUGD, DRUGA*BEF, DRUGC*BEF, …

Analysis of Variance

Chapter B.3, Problem 68E, Mental Tasks and Drugs. In the text Statistical Theory and Methodology in Science and Engineering , example 6

OUTPUT B.61 Regression output For Exercise B.68

Features Features Normal distribution is characterized by two parameters, mean (µ) and standard deviation (σ). When graphed, the mean represents the center of the bell curve and the graph is perfectly symmetric about the center. The mean, median, and mode are all equal for a normal distribution. The standard deviation measures the data's spread from the center. The higher the standard deviation, the more the data is spread out and the flatter the bell curve looks. Variance is another commonly used measure of the spread of the distribution and is equal to the square of the standard deviation.

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Chapter B.3, Problem 67E

Chapter B.3, Problem 69E

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Chapter B Solutions

Introductory Statistics (10th Edition)

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Solution Summary: The author explains that the variable drug seems to be a useful predictor variable, based on the after versus before plot in Output B.57.

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