Chapter 7: Paired samples 4/7/07

Review Questions

1. Provide synonyms for paired samples. 
2. Describe ways to get paired samples.
3. How do independent samples differ from paired samples?
4. What symbol denotes the mean difference parameter?
5. True or false? The confidence interval for the mean difference parameter tries to locate _d.
6. The power of a test is the probability of avoiding a type ____ error.
7. F(0) = ? [Calculation not necessary.]
8. A type II error occurs when you _______________________________________ [complete the sentence]

Exercises

7.1 Placebo effect in Parkinson's disease  (de la Fuente-Fernandez et al., 2001).  The placebo effect occurs when patients experience a benefit after given a pharmaceutically inert substance which they think is active. This effect can be effective because of expectation of a benefit. To understand this phenomenon, investigators conducted a placebo-controlled blinded study in which Parkinson's disease patients did not when they were receiving placebo or an active ingredient (apomorphine). These are paired samples because each data point in the placebo sample is matched to a unique point in the control sample. Chemical measurements were made at a key point in the brain of n = 6 patients. The six differences showed  _d = -0.326 with s_d = 0.181 Test the difference for significance.

7.2  Social faux pas, high school students (fictitious; data stored in fauxpas.sav). Eight (8) junior high school students were taken to a shopping mall to test the efficacy of a program designed to promote social skills. The number of socially inappropriate behaviors (faux pas) such as put-downs and other unlovable behaviors exhibited by each student was counted before and after the program. Data are shown below. .

(A) Calculate changes in the number of faux pas within individuals (DELTA). 
(B) Explore the differences with a stemplot. Describe the results. 
(C) Would you use a t procedure on these data? [Consider whether the Normality assumption has been violated.]
(D) Test to see if the mean decline is significant. Use a two-sided test. Show all steps. 

7.3 OC & BP. Thirty (30) women between 20- and 24-years of age not currently using oral contraceptives have their systolic blood pressure checked. They begin taking an oral contraceptive an,d after five months, have their blood pressure checked again. Blood pressure is 1.4 mm Hg higher on average at the second reading (s_d = 2.6). 

(A) Calculate a 95% confidence interval for the mean change in systolic blood pressure. 
(B) From information provided, can you determine the effect of this formulation in individuals? [Brief narrative response.]

7.4 Fertility after discontinuing contraception. We are interested in the effect of contraceptive methods on fertility following discontinuation and want to compare how long it takes to become pregnant in former oral contraceptive users and intra-uterine device users (IUD) users contraception is stopped. Twenty oral contraceptive users are matched to 20 IUD users on age, race, parity, and socioeconomic status. Subjects attempt to conceive after discontinuing their contraceptives. On average, oral the contraceptive users became pregnant 5 months earlier than IUD users (s_d = 8 months). Determine whether the observed mean difference is significant. Show all hypothesis testing steps. 

7.5 Water fluoridation A study looked at the number of cavity-free children per 100 in 16 North American cities BEFORE and AFTER water fluoridation projects. Data are shown below and are stored online in ../datasets/fluoride.sav).   

(A) Calculate the changes (DELTAs) within each city. Construct a stemplot of these differences, and then interpret the stemplot.  
(B) What percentage of cities showed an improvement in their cavity-free rate? 
(C) The mean decrease in the cavity-free rate (_d) for these data is 12.21 (s_d = 13.62). Estimate the mean change in the cavity-free rate in all similar cities with 95% confidence.

7.6 Is caffeine dependence real? (Under development. See EESEE story by this name;  Moore, 2004, p. 435; Strain et al., 1994).

7.7 Salivary cotinine. Cotinine is a chemical synthesized by the body from nicotine. Since cotinine can be made only from nicotine, and since nicotine comes primarily from cigarette smoke, cotinine is an objective marker of exposure to cigarettes. People who do not smoke and are not exposed passively to environmental tobacco should have no measurable cotinine levels. Data from a study of the decline in salivary cotinine levels in seven volunteers are shown below. Measurements are taken 12- and 24-hours following last cigarette use. Determine the mean change in cotinine levels in these 7 volunteers. (Let DELTA = 12hours - 24hours.) Then, calculate a 95% confidence for the mean change. (Assume the sampling distribution of _d  is approximately Normal.) 

    ID    12hours   24hours
    ---   --------  -------
     1      83        34
     2      68        27
     3      68        29
     4      98        29
     5      30        14
     6      24         9
     7      41        11

7.8  Vitamin C and the common cold. An investigator wishes to determine whether vitamin C reduces the frequency of the common cold by pairing children from the same family and randomly assigns to one of the children in each pair high daily doses of vitamin C. The other pair-member receives a  placebo that looks and tastes the same as the vitamin C pill. The number of days in which upper respiratory symptoms are observed during the year of the study are shown. Test the data for significance.

    Pair   VitC  Placebo
    -----  -----  ------
    1        2      3
    2        5      4
    3        7      9 
    4        0      3
    5        3      6 
    6        3      5 

7.9 Benign prostatic hyperplasia (Source: Joanne Morales; data stored in bph-samp.sav). Benign prostatic hyperplasia is a non-cancerous enlargement of the prostate gland that causes restriction of urine flow, adversely affecting the quality of life of millions of men. A study of a minimally invasive procedure for the treatment for this condition determined pre-treatment quality of life (QOL_BASE) and quality of life 3 months on treatment (QOL_3MO). Data for 10 patients chosen at random from the study are shown below.  

(A) Calculate differences in quality of life scores after 3 months on therapy (DELTA = QOL_3MO - QOL_BASE). Explore the differences with a stemplot, and discuss what you see.
(B) Test the change in scores for a significant difference Show all calculations and hypothesis testing steps. [Note: n =  10, _d = 1.70 s_d = 1.494] 

 Variables: 

• QOL_BASE = quality of life at baseline scored: 0 = Delighted, 1 = Pleased, 2 = Mostly Satisfied, 3 = Mixed, 4 = Mostly Dissatisfied, 5 = Unhappy, 6 = Terrible.

• QOL_3Mo = Quality of life after 3 months of treatment

• MAXFLO_B = maximum urine flow at baseline

• MAXFLO3M= maximum urine flow after 3 months of treatment

7.10 Power. A researcher fails to find a significant difference in mean blood pressure in 36 matched-pairs exposed and not exposed to environmental tobacco smoke. The standard deviation of the differences was 5 mm Hg. What was the power of the test to detect a mean difference of 2.5 at a = .05 (two-sided)? 

7.11 NASA experiment (Data from Adam Seddiqi; stored in seddiq.sav).. A NASA study was set up to compare two methods of determining white blood cell counts in laboratory animals. Method 1 is the CELDYNE method and method 2 was the UNOPETT method. Data representing white blood cell counts (×1000/dL) by these methods are shown in 42 laboratory rates. Calculate differences for each observation (DELTA) and make a stemplot of the differences. How consistent were the results? [Look carefully at the spread of the distribution. This is not a test of means.]

Key to Odd Numbered Problems                    Key to Even Numbered Problems (may not be posted)