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statistics for nursing a practical approach
Statistics In Medicine 2nd Edition Robert H. Riffenburgh - Solutions
Name two diseases in which there can be no herd immunity.
From Section 9.2, extract and list the major steps in the evolution of epidemiologic methodology.
How is epidemiology similar to clinical diagnosis? How is it different?
Two types of medication exist to treat a certain medical condition. Medicine A costs x dollars for a course of treatment and has always been successful.Medicine B costs y dollars but is unsuccessful in 1 of 10 cases. When results with medicine B are unsuccessful, medicine A must be used. (There is
What is the coefficient of determination for the data of Exercise 8.5? How is this coefficient of determination interpreted?
What is the equation for the straight-line regression prediction of eNO20 by eNO0 for Exercise 8.5? Lay a thin paper over the scattergram of respiration rate by age and sketch in this line.
Summary statistics for the data in Exercise 8.5 (where subscripts 0 and 20 represent preexercise eNO [0 minutes] and eNO at 20 minutes, respectively)are approximately m0 = 29.3; me0 = 28.1; so = 25.6; s20 = 25.3; and s0,20 = 621.5. Using these values, what is the correlation coefficient between age
In DB14, we investigate if the change in exhaled nitric oxide (eNO) caused by exercise is related to the initial (preexercise) eNO, or if they are independent. The scatter diagram is shown (see accompanying figure). Form a conceptual model. 20-min eNO 150 125- 100- 75 50 25 0 0 25 50 000 75
What is the coefficient of determination? How is this coefficient of determination interpreted?
What is the equation for the straight-line regression of r on a for Exercise 8.1? Lay a thin paper over the scattergram of respiration rate by age and sketch in this line.
Summary statistics for the data in Exercise 8.1 (where subscripts a and r represent age and respiration rate, respectively) are ma -- 10.9; mr = 39.0;Sa = 6.7; Sr = 11.8; and Sar = -15.42. What is the correlation coefficient between age and respiration rate? How is this correlation coefficient
It is believed that respiration rate in infants decreases with age. To exam- ine that belief, respiration rate was recorded for 232 infants from 0 to 24 months.50 The scatter diagram of respiration rate against age is shown (see accompanying figure). Form a conceptual model. 28 o R Respiration Rate
In DB3, the mean for the 16 patients' differences between baseline and 5-day serum theophylline level is 0.993 mg/dl, with standard deviation 3.485. For such a difference to be significant with a = 0.05 and power =0.80, n = 50 pairs would be required [using a formula slightly different from Eq.
Suppose we did not have the exercise-induced bronchoconstriction and exhaled nitric oxide data as in DB14 but found a 5-minute difference standard deviation of 7 parts per billion (ppb) for both healthy subjects and asthmatics. We want to test for a difference in means between these two groups
Suppose we could take a set of International Normalized Ratio (INR) readings from the clinic and another set from the laboratory, as in DB13, but not paired. We want to test for a two-sided difference between means, where a difference of 0.25 INR is clinically relevant. We take a = 0.05 and power=
In DB12, the extent (in centimeters) of the carinal resection appears to affect survival. Using the standard deviations given for surviving (died - 0)and dying (died - 1) patients, estimate the minimum sample size required for a test between means of resection extent of 0.37 cm for those two groups
DB7 contains very small samples of bone density measures for men and women. On the basis of the standard deviations of those samples, estimate the minimum sample size required to detect a difference of 10 units of bone density between the means for men and women with ~ = 0.05 and power =0.80 -
Assess the clinical effects of false-positive and false-negative outcomes and specify whether I3 should be the usual 4c~ in estimating minimum sample size for a test of (a) the effect of ondansetron hydrochloride on nausea after gallbladder surgery in DB2 and (b) a change in plasma silicon level
Should minimum sample size estimation be based on a one-sided or a two-sided test, assuming the underlying distributions are normal, of (a) a difference in nausea scores between ondansetron hydrochloride and placebo in DB2 and of (b) the difference between assay types in DB8?
In DB7, perform a t test to learn if there is evidence that the mean bone density is different between men and women. Compare the result with the result of Exercise 6.6.
In DB3, use the difference between theophylline levels at baseline minus at 5 days and perform a t test to learn if there is evidence that the mean reduction in level caused by the drug differs between men and women.Compare the result with the result of Exercise 6.5.
In DB12, the sample is large enough to take the sample standard deviation as if it were a population standard deviation ~r. For convenience, carry the calculations to only two decimal places. Perform a normal (z) test to learn if there is evidence that (a) mean age and (b) extent of carinal
Using DB14, plot the frequency distributions of the 5-minute exhaled nitric oxide (eNO) differences for male and female subjects. Is this distribution close enough to normal in shape to use a t test? Rank the differences and use the rank-sum test to learn if there is a response difference between
In DB7, rank bone density and perform the rank-sum test to learn if there is evidence that the bone density is different between men and women.
In DB3, calculate the difference: serum theophylline level at baseline minus at 5 days; assign ranks to this new variable and perform the ranksum test to learn if there is evidence that the reduction in level caused by the drug differs between men and women.
Using the results of Exercise 6.4, term a patient in range as negative and out of range as positive. The laboratory results are taken as "truth," so the properly formatted result forms a truth table. For the clinic's test results, calculate and state the interpretation of (a) the false-positive
A general surgeon noted a number of errors in his hospital's diagnosis of appendicitis. Of the next 200 patients with abdominal pain, 104 turned out to have had appendicitis and 96 turned out not to have had appendicitis.Of those with appendicitis, 82 were correctly diagnosed; of those without
In DB13, combine below-range with above-range result categories (last two columns) to form an out-of-range category. Form an in-range versus out-of-range 2 • 2 contingency table and use )~2 to decide if clinic and laboratory result categories were discrepant.
In DB2, test the 2 x 2 contingency table using chi-square to decide whether or not nausea score is reduced by the drug.
In DB6, test the contingency table using chi-square to decide whether or not titanium-containing tattoo ink is harder to remove than other inks.
In DB4, test the contingency table using chi-square to decide whether or not access to protease inhibitors has reduced the rate of pulmonary admissions.
From DB13, we want to learn if our clinic results agree with those of the laboratory. Follow the first nine steps of Section 5.5 in setting up a test.
Using the 2 x 2 table in DB2, follow the first nine steps of Section 5.5 in setting up a test to learn if the drug reduces nausea score.
From DB14, set up tables as in Section 5.4: (a) EIB frequency by sex;(b) for the six EIB patients, 5-minute eNO differences by sex as ranks;(c) for the six EIB patients, 5-minute eNO differences by sex as continuous measurements.
In DB10, rank the seconds to perform the triple hop for the operated leg, small to large.
Of what data type is: (a) The variable Respond versus Not Respond in DB6? (b) The variable Nausea Score in DB2? (c) The variable Platelet Count in DB9?
In DB14, healthy subjects showed a mean decrease of 2.15 ppb exhaled nitric oxide (eNO) from before exercise to 20 minutes after exercise.A 5 % significant test of this mean against a theoretical mean of 0 (paired t test) yielded p = 0.085. Make an argument for the two interpretations of this
A clinical hypothesis arising from DB5 might be: The variances (or standard deviations) of plasma silicon level before and after implant are different. (a) What probability distribution is associated with this hypothesis?(b) What assumptions about the data would be required to investigate this
A clinical hypothesis arising from DB9 might be: The standard deviation of platelet counts is 60,000 which gives an approximate 95% confidence range of 240,000 [mean +2 • 60,000]); this hypothesis is equivalent to supposing that the variance is 60,0002 - 3,600,000,000. (a) What probability
A clinical hypothesis arising from DB3 might be: The mean serum theophylline level is greater at the end of the antibiotic course than at baseline.(a) What probability distribution is associated with this hypothesis?(b) What assumptions about the data would be required to investigate this
In DB14, we ask if the mean ages of patients with and without exerciseinduced bronchoconstriction (EIB) are different. Write down the null and alternate hypotheses.
In DB4, a hypothesis to be investigated is that protease inhibitors reduce pulmonary admissions. Is this a clinical or a statistical hypothesis? What would be a statement of the other type of hypothesis?
Using the sample sizes and standard deviations given in Exercise 4.9, find 95% confidence intervals on the standard deviation of the baseline data for each treatment. Are they similar?
The emergency department physician of Exercise 4.8 is concerned not only about the average heart rate of the trauma patients but also about the variability. Even if the mean is satisfactory, if the standard deviation is too large, outlying patients would be at risk. Recall that n - 8, m - 67.75
The surgeon referenced in Exercise 4.3 is concerned about the variability of time to full feeding in neonates. Even if the mean is satisfactory, if the variability is too large, the outlying neonates on the longer side of the scale would be at risk. Recall that n = 20, m = 6.56 hours, and s = 4.57
In the kidney cooling data of DB15, the baseline (time 0) means are ml =34.40 for saline infusion and m2 = 36.12 for ice slush, each based on 12 readings. (Use two decimal places throughout for easier calculation.) The respective estimated standard deviations are sl - 3.25 and s2 - 1.17.Find 95 %
An emergency medicine physician samples the heart rate of n = 8 patients after a particular type of trauma. The mean is m - 67.75 beats/min, and the standard deviation is s - 9.04 beats/min. What is the 95 % confidence interval on the mean?
Among the indicators of patient condition after pyloromyotomy (correction of stenotic pylorus) in neonates is time (hours) to full feeding. 21 A surgeon wants to place a 95 % confidence interval on mean time to full feeding. He has readings from n = 20 infants. Some of the data are 3.50, 4.52,
For the laboratory INR values of Exercise 4.4, find the 95% confidence interval on the mean.
The orthopedist in the Nitronox example in Section 4.5 also is interested in the patients' pain, which he has measured using the CHEOPS rating form.For his n = 50 patients, m = 9.16 and a = 2.04. Find the (a) 95%, (b) 99%, and (c) 90% confidence intervals on mean pain rating.
In DB13, let us take the standard deviation of the 104 laboratory International Normalized Ratio (INR) values as the populationa. Find m anda. Find the 95% confidence interval on an individual patient. Does this confidence interval match the patient "in-range" interval?
In DB12, the age distribution of patients undergoing carinal resections is approximately normal with mean = 47.8 years and standard deviation =14.8 years. The sample is large enough to take the standard deviation as if it were the populationa. You have a 12-year-old patient whose tracheal carina
For the N(2,9) distribution, what are the values on the x-axis (horizontal)that enclose 95 % of the area under the curve?
A probability distribution for variable x is expressed as N(2,9). How would you transform it to N(0,1), the standard normal distribution for variable z?
From DB14, construct a 3-D bar chart of 20-minute eNO change by age using 5-year intervals for age and 10-unit intervals for eNO change.
From DB14, construct a scattergram of 20-minute eNO change by age.
From DB3, construct a scattergram of serum theophylline level at 10 days depending on level at baseline.
From DB14, construct (a) a mean-and-standard-error chart (4-1.96 SEM)and (b) a box-and-whisker chart of eNO for EIB patients across time.
From DB3, construct (a) a mean-and-standard-error chart (+1.96 SEM)and (b) a box-and-whisker chart for serum theophylline levels at baseline, 5 days, and 10 days.
From DB14, construct a line chart for eNO means over time for groups with and without EIB.
From DB11, construct a line chart of number rats surviving malaria by day number for the three treatments.
From DB14, construct a pie chart ofthe four categories: male with exerciseinduced bronchoconstriction (EIB), female with EIB, male without EIB, and female without EIB.
From DB14, construct a histogram of the 20-minute eNO change with all values greater than 5 in one interval.
From DB14, construct a bar chart of the 20-minute eNO change.
From DB7, construct pie charts of patients' (a) sexes and (b) ages (grouped 17-19, 20-22, 23-25, >25).
From DB7, construct a histogram of bone density in the intervals 80 to
From DB7, construct a bar chart of patient ages.
From DB14, find the correlation coefficient of exhaled nitric oxide (eNO)between before exercise and 20 minutes after.
From DB10, find (a) the covariance and (b) the correlation coefficient of seconds to perform the hops between the operated and nonoperated legs.
From DB10, find (a) the covariance and (b) the correlation coefficient of distance covered between the operated and nonoperated legs.
From DB10, find the two-sample SEM of distance covered using the operated leg sample and the nonoperated leg sample.
From DB12, find the mode age.
From DB15, find the (a) mean, (b) median, (c) variance, (d) standard deviation, (e) 1st quartile, (f) 3rd quartile, and (g) SEM of temperatures at depth I for each treatment.
From DB10, find the (a) mean, (b) median, (c) variance, (d) standard deviation, (e) 1st quartile, (f) 3rd quartile, and (g) SEM of the distance covered in a triple hop on the operated leg.
From DB7, find the (a) mean, (b) median, (c) variance, (d) standard deviation, (e) 1st quartile, (f) 3rd quartile, and (g) SEM of the bone density.Round all answers to one decimal place after calculation.
In DB3, the two related variables baseline and 5-day theophylline levels vary jointly. If we were to calculate a measure of how one varies relative to the other, what would it be called?
In DB10, the difference in time to perform between legs has mean = 0.16 and standard deviation - 0.2868. Calculate the SEM.
Calculate the sample SEM of the rounded GAG levels (0.7, 0.4, 0.3, 0.2)for type i assay in DB8.
If we wished to make an inference about the proportion of patients in DB12 who died after 2 cm or less of carinal resection, what distribution would we be using?
If we wished to make an inference about the proportion of patients experiencing any nausea in DB2, what distribution would we be using in this inference?
Assign ranks (small to large) to the bone density values in DB7. Patient 18 has a bone density reading far less than that for the others. What effect does this have on the distribution of readings? Is this effect also true for the rankings of the readings?
Assign ranks (small to large) to the platelet counts in DB9.
If we were to make an inference about the mean of differences between clinic and laboratory INR readings in DB13, what would be the dr?
If we were to make an inference about the mean of differences between preoperative and postoperative plasma silicon levels in DB5, what would be the dr? To make this mean into a t statistic, we subtract what value, and then divide by what statistic? To decide if t is significantly larger than zero,
For INR readings from the clinic in DB13, plot the frequency distribution in intervals of 0.25 in width. (This may have been done in Exercise 2.3.)Is it more similar to a normal or a chi-square probability distribution?
The squares of the 60 plasma silicone levels in DB5 are (• 9 225, 169, 1521, 400, 1521, 1764, 576, 324, 144, 676, 100, 121,225, 361,729, 784, 121, 121, 324, 324, 576, 2304, 484, 729, 361,324, 1024, 961,361, 441,441, 576, 100, 144, 784, 625, 484, 441,529, 484, 484, 576, 1444, 2025, 529, 484, 324,
As an investigator, you wish to make an inference from DB14 about whether or not the difference in exhaled nitric oxide from before exercise to 20 minutes after is zero. From Section 2.7, what steps would you go through?
As an investigator, you wish to make an inference from DB3 about whether or not the drug affects serum theophylline level (5 days). From Section 2.7, what steps would you go through?
For computational ease, use the glycosaminoglycans (GAG) levels for type 2 assay in DB8 rounded to 1 decimal place: 0.5, 0.5, 0.4, 0.3. Calculate(a) the variance and (b) the standard deviation.
Calculate(a) the variance and (b) the standard deviation.
For computational ease, use the glycosaminoglycans (GAG) levels for type 1 assay in DB8 rounded to 1 decimal place: 0.7, 0.4, 0.3,
For INR readings from the laboratory in DB13, (a) select intervals for a tally, (b) tally the data, (c) find the median, and (d) convert the tally into a relative frequency distribution. (e) What does the median compared with the mean = 2.28 say about symmetry?
For International Normalized Ratio (INR) readings from the clinic in DB13, (a) select intervals for a tally, (b) tally the data, (c) find the median, and (d) convert the tally into a relative frequency distribution. (e) What does the median compared with the mean = 2.40 say about symmetry?
Does the median converge to the final median? (d) Convert the tally into a relative frequency distribution. (e) Comment on whether the distribution appears by eye to be near normal. If not, in what characteristics does it differ?(f) Give a visual estimate (without calculation) of the mean and
For patient age in DB12, (a) select intervals for a tally and (b) tally the data. In tallying, (c) record the median when data for 25 patients have been tallied, then for 50, 75, 100, and all patients. Plot the median depending on the number of data sampled similar to the plot of Fig.
For extent of carinal resection in DB12, (a) select intervals for a tally,(b) tally the data, (c) find the median, and (d) convert the tally into a relative frequency distribution. (e) Comment on whether the distribution appears by eye to be near normal. If not, in what characteristics does it
In the tattoo removal database (DB6), to what population would the dermatologist prefer to generalize his results? From the information given, is he justified in doing so?
Which database contains ratings that could be treated as categorical, ranked, or continuous data?
In the warfarin International Normalized Ratio (INR) database (DB13), which variables are (a) categorical and (b) continuous? (c) Can the differences in INR be ranked?
In the femoral neck fracture database (DB7), which variables are (a) categorical and (b) continuous? (c) Can bone density be ranked?
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