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Control in the Design of an Experiment Dr. Penelope Nicholls is interested in exploring a possible connection between high plasma homocysteine (a toxic amino acid created by the body as it metabolizes protein) levels and cardiac hypertrophy (enlargement of the heart) in humans. She realizes that, because there are many complex relationships among human characteristics, it will be difficult to answer her research question unambiguously because there is a significant risk that confounding factors will cloud her inferences. She wants to be as sure as possible that any differences in cardiac hypertrophy are due to high plasma homocysteine levels and not to other hidden factors. Consequently, she needs to design her experiment carefully, so that she controls lurking variables to the extent possible. Therefore, she decides to design a two-sample experiment with independent sampling—one of the groups will be the experimental group, the other a control group. Knowing that there are many factors that can affect the degree of cardiac hypertrophy (the response variable), Dr. Nicholls controls these factors by randomly assigning the experimental units to the experimental or control group. She hopes the randomization will result in both groups having similar characteristics. By controlling the data collection environment and procedures, she also hopes to minimize any situational contaminants within her experimental design. In her preliminary literature review, Dr. Nicholls uncovered an article in which the authors hypothesized that there might be a relationship between high plasma homocysteine levels in patients with end-stage renal disease (ESRD) and cardiac hypertrophy. As her assistant, she has asked you to review this article and to write a brief report detailing your findings. Upon reading the article, you discover that the authors employed a nonrandom process to select a control and an ESRD group. The researchers enlisted 75 stable ESRD patients into their study. All of these patients were on hemodialysis for between 6 and 312 months. The control group was composed of 57 nonuremic members. Nonuremic subjects were chosen so as to eliminate any intergroup differences in terms of mean blood pressure (BP) and gender. Any individuals taking vitamins and any individuals with any type of specified heart-related ailments were excluded from the study. In an effort to minimize situational contaminants, all physical and biochemical measurements were made after an overnight fast. The results of the clinical characteristics and the biochemical findings for the control and ESRD groups are reproduced in the following tables. CASE STUDY Clinical Characteristics (Mean Standard Deviation) Parameters Controls ESRD Subjects 1n = 572 1n = 752 ; Age (years) Sex (M/F ratio) Body Surface Area (m2) Body Mass Index (kg/m2 ) Systolic BP (mmHg) Diastolic BP (mmHg) Mean BP (mmHg) Pulse Pressure (mmHg) Heart Rate (beats/min) 63.0 ; 8.0 70.0 ; 9.0 59.4 ; 15.5 68.6 ; 24.3 104.5 ; 14.2 103.6 ; 17.4 85.0 ; 14.8 80.2 ; 14.3 145.0 ; 15.5 148.8 ; 29.7 26.0 ; 4.70 23.7 ; 3.90 1.85 ; 0.25 1.67 ; 0.20 1.4 ; 0.50 1.4 ; 0.50 49.2 ; 14.7 57.3 ; 15.1 SullStatCH10_Fpp592-653 11/20/02 1:06 PM Page 650 Which type of sampling method, independent or dependent, was used in this experiment? Explain. Using the appropriate hypothesis-testing procedure, ascertain whether the control and ESRD groups have equivalent population means for each of the various clinical and biochemical parameters. Dr. Nicholls requires that you indicate those parameters that have P-values less than 0.05 and those less than 0.01. Detail any assumptions, and the rationale behind making them, that you made while carrying out your analysis. Is there any additional information that you would like to have? Explain. Are there any additional statistical procedures that you think might be useful for analyzing these data? Explain. Based on your findings, does it appear that the control and ESRD groups have similar initial clinical characteristics and biochemical findings? Does it appear that the authors of this article were successful in reducing the likelihood that a confounding effect would obscure their results? Even though Dr. Nicholls does not wish to restrict her research to patients with end-stage renal disease, how might the information presented for this research assist her in designing her own experiment? Write a report for Dr. Nicholls that outlines all of your findings and recommendations. 651 Biological Findings (Mean Standard Deviation) Parameters Controls ESRD Subjects 1n = 572 1n = 752 ; Total Cholesterol (mmol/L) HDL Cholesterol (mmol/L) Triglycerides (mmol/L) Serum Albumin (g/L) Plasma Fibrinogen (g/L) Plasma Creatinine (mmol/L) Blood Urea (mmol/L) Calcium (mmol/L) Phosphates (mmol/L) Source: Jacques Blacher, et al. “Association between Plasma Homocysteine Concentrations and Cardiac Hypertrophy in End-Stage Renal Disease.” Journal of Nephrology 12, 4 (July–August, 1999): 248–255. Article available at 1.03 ; 0.21 1.88 ; 0.38 2.46 ; 0.08 2.45 ; 0.12 6.10 ; 1.20 24.3 ; 2.00 0.10 ; 0.01 0.90 ; 0.13 3.21 ; 0.78 4.75 ; 1.04 44.7 ; 2.60 39.9 ; 3.00 1.39 ; 0.63 1.90 ; 1.02 1.38 ; 0.39 1.07 ; 0.38 5.28 ; 1.04 4.91 ; 1.06 SullStatCH10_Fpp592-653 11/20/02 1:06 PM Page 651 652 DECISIONS Where Should I Invest? Suppose that you have just received an inheritance of $10,000 and you decide that you should invest the money rather than blow it on frivolous items.You have decided that you will invest the money in one of two types of mutual funds. The first type you are considering follows a “large value” approach to investing.This means that the mutual fund invests only in large, established companies that are considered to be a good bargain.The second type of mutual fund you are considering follows a “large growth” approach to investing. This means that the mutual fund invests in large companies that are experiencing solid sales growth. In order to make an informed decision, you decide to research the rate of return of the past three years for each of these types of mutual funds.The mutual fund must have a Morningstar rating of four or five stars.The Morningstar mutual-fund rating system ranks mutual funds, using one to five stars.The stars divide the mutual-fund performance into quintiles—that is, a mutual fund with a one-star rating is in the bottom 20% of mutual funds in its category, a mutual fund with a two-star rating has an investment performance between the and percentile, and so on. These data can be found at or (a) Obtain a simple random sample of at least 15 mutual funds for each investment category. Determine the three-year rate of return for each of the funds. (b) Verify that the three-year rates of return come from a population that is normally distributed.Also, verify that the data have no outliers. If the data do not come from a population that is normally distributed, you’ll have to increase the sample size so that the Central Limit Theorem can be used. (c) Construct a boxplot for the rate of return of each fund category, using the same scale.Which investment category, if any, seems superior? (d) Obtain a 95% confidence interval for the difference between the mean rates of return. Interpret the interval. (e) Write a report that details which investment category seems to be superior. 21st 40th SullStatCH10_Fpp592-653 11/20/02 1:06 PM Page 652 The High Cost of Convenience 653 (d) To test the claim, we used Minitab (release 13.1) to perform a two-sample t-test. The results are shown below. Using the Minitab output, determine the value of the test statistic.What is the P-value of the test? For a recent article, Consumer Reports (December 2001) was interested in comparing a name brand paper towel with a new version packaged in a box.The towels in the box, which cost nearly twice as much as the traditional roll, are marketed for their convenience. Given the difference in cost, one might wonder if the boxed version performs better than the traditional roll. To help answer this question, technicians at Consumers Union subjected both types of towels to 5 physical tests: absorption time in water, absorption time in oil, absorption capacity in water, absorption capacity in oil, and wet strength. For brevity, we will discuss only the results of the absorption time in water test. The absorption time in water was defined as the amount of time necessary for a single sheet to absorb a predetermined amount of water. In order to compare the absorption times of the two types of towels, we tested six randomly selected sheets of paper towels. To avoid potential sources of bias, the individual sheets were taken from different samples of the products and the tests were conducted in a randomly chosen order. The claim being tested is that the water absorption time for the boxed version is less than the water absorption time for the traditional roll. (a) Write the null and alternative hypotheses, letting mbox represent the mean absorption time for the boxed version and represent the mean absorption time for the roll version. (b) Normal probability plots of the water absorption times for the two products are shown below. Based on the normal probability plots, is it reasonable to conduct a two-sample hypothesis test? mroll Note to Readers: In many cases, our test protocol and analytical methods are more complicated than described in these examples. The data and discussions have been modified to make the material more appropriate for the audience. Two-Sample T-Test and CI: Absorption Time In Water, CU CU-Text Box Roll Difference = mu (Box) - mu (Roll) Estimate for difference: -0.0483 95% upper bound for difference: 0.0320 T-Test of difference = 0 (vs <): T-Value = -1.09 P-Value = 0.150 DF = 10 Both use Pooled StDev = 0.0767 Two-sample T for Absorption Time In Water N 6 6 Mean 0.9717 1.0200 StDev 0.0538 0.0942 SE Mean 0.022 0.038 Although they are not discussed here, the other physical tests provided similar results. Write an article that states your conclusion and any recommendations that you would make regarding the purchase of the two products. (c) A boxplot of the water absorption times for the two products is shown below. Does the data set have any outliers? Based on the boxplots, do you think that the absorption times for the boxed version are lower than the absorption times for the roll? SullStatCH10_Fpp592-653 11/20/02 1:06 PM Page 653
Solution Description

Sampling Method Used;
Independent sampling as  two samples selected from the same population, that have no effect on one another.  The outcome for the control group  is assumed to