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essentials of statistics
Statistics And Data Analysis For Nursing Research 2nd Edition Denise Polit - Solutions
A5. Suppose that a researcher regressed surgical patients’length of stay in hospital (Y ) on a scale of functional ability measured 24 hours after surgery (X). Given the following, solve for the value of the intercept constant and write out the full regression equation: Mean length of stay 6.5
A4. In a random sample of 100 people, the correlation between amount of daily exercise and weight was found to be.21. What would be the likely effect on the absolute value of the correlation coefficient under the following circumstances:(a) The sample is restricted to people who weighed under 180
A3. For each coefficient of determination below, calculate the value of the correlation coefficient:(a) r 2 .66(b) r 2 .13(c) r 2 .29(d) r 2 .07
A2. For each correlation coefficient below, calculate what proportion of variance is shared by the two correlated variables:(a) r .76(b) r .33(c) r .91(d) r .14
B6. Run Crosstabs for four outcomes in the Polit2SetC dataset.(Note that this is a different file than for the previous exercises.) The four outcomes are responses to a series of questions about whether the women had experienced different forms of abuse in the prior year: verbal abuse,
B5. In this analysis, you will be running a Kruskal-Wallis test, comparing women in the four BMI categories (bmicat)with regard to the number of miscarriages they had ever had (miscarr). Number of miscarriages in a ratio-level variable, but it is skewed, with most women having had no miscarriages.
B4. For this exercise, you will be running a Mann-Whitney U test, comparing smokers and nonsmokers on an ordinallevel variable, drunk. This variable measures how frequently in the prior month the woman had consumed enough alcohol to get drunk (drunk), from never (code 1)to 10 times (code 5). Begin
B3. In this exercise, we will be testing the null hypothesis that smoking status (smoker) is unrelated to having a health limitation. Because we want “cell a” to be the cell with the risk factor and the unfavorable outcome, we will recode smoker (which is coded 1 for smokers and 0 for
B2. Within SPSS, it is possible to introduce a third categorical variable into a Crosstabs analysis, to see if the relationship between two variables is consistent for different levels of a third variable. In this exercise, run the same analysis that you ran in Exercise B1, except this time enter
B1. For Exercises B1 to B5, you will be using the SPSS dataset Polit2SetB. Begin by running a crosstabs (Analyze ➜Descriptive Statistics ➜ Crosstabs) for the variables bmicat and hlthlimit. The first is a variable that uses the women’s body mass index (BMI), computed from their height and
A7. Using the information provided, indicate which test you think should be used for each of the following situations:(a) Independent variable: normal birthweight versus low birthweight infants; dependent variable: 1-minute Apgar scores (0 to 10 scale); sample size: eight infants per group(b)
A6. Match each of the nonparametric tests in Column A with its parametric counterpart in Column B:
A5. Assume that a researcher has conducted a pilot intervention study and wants to use the pilot results to estimate the number of participants needed in a full-scale study to achieve a power of .80 with a .05. For each of the hypothetical pilot results presented below, how many study participants
A4. Given each of the following situations, determine whether the calculated values of chi-square are statistically significant:(a) x2 3.72, df 1, a .05(b) x2 9.59, df 4, a .05(c) x2 10.67, df 3, a .01(d) x2 9.88, df 2, a .01
A3. Using the statistical information from the first two exercises, write a paragraph summarizing the results of the analyses.
A2. This question was intentionally removed from this edition.
A1. Calculate the chi-square statistic and degrees of freedom for the following set of data for 300 elders exposed to different interventions to encourage flu shots:Is the value of chi-square statistically significant at the .05 level? Based on the (O E)2 /E components contributing to chi-square,
B6. Run one-way ANOVAs for two outcomes in the Polit2SetA dataset: overall satisfaction with material well-being, which is already completed if you did Exercise B1 (satovrl), and rating of neighborhood as a good place to live and raise children(nabrqual, Variable #18). Be sure to look in the
B5. For the next analysis, run a two-way ANOVA in which the dependent variable will again be satovrl, the women’s overall degree of satisfaction with their material well-being. The two dichotomous independent variables will be whether or not the woman was working at the time of the
B4. Do another one-way ANOVA for the same independent variable (hprobgrp) and dependent variable (satovrl), this time using Analyze ➜ Compare Means ➜ Means. On the second dialog box, click the box for ANOVA table and eta.What is the value of eta-squared for this analysis? Would this be
B3. Now run a one-way ANOVA with hprobgrp as the independent (group) variable, using the variable satovrl (overall satisfaction with material well-being, Variable #43) as the outcome variable. This variable is a summated rating scale variable for women’s responses to their degree of satisfaction
B2. In this exercise, you will create a new variable (call it hprobgrp) that divides the sample into three groups based on number of housing problems. The new variable will be coded 1 for no housing problems, 2 for one housing problem, and 3 for two or more housing problems. Click Transform (upper
B1. For these exercises, you will be using the SPSS dataset Polit2SetA, which contains a number of variables relating to material hardships and social–environmental health risks. Eight variables in this file (from utilcut to badstove, which are Variables #25–32) are responses to a series of
A10. This question was intentionally removed from this edition.
A9. Suppose we used a crossover design to test for differences in bruising from subcutaneous sodium heparin injections at three sites (arm, leg, and abdomen) in a sample of 15 medical–surgical patients. Surface area of the bruises(in mm2) is measured 72 hours after each injection, which are
A8. Interpret the meaning of the F tests from question A7. (Note:higher scores on the self-esteem scale mean higher selfesteem.) Write a few sentences summarizing the results.
A7. Suppose we were interested in studying the self-esteem of men versus women (Factor A) in two exercise status groups—nonexercisers versus exercisers, Factor B—with 20 people in each of the four groups. Use the following information to compute three F tests, and determine which, if any, is
A6. For each of the following F values, indicate whether the F is statistically significant, at the specified alpha level:(a) F 2.80, df 4, 40, a .01(b) F 5.02, df 3, 60, a .001(c) F 3.45, df 3, 27, a .05(d) F 4.99, df 2, 150, a .01(e) F 2.09, df 2, 250, a .05
A5. Write a few sentences that could be used to describe the results of the analyses from questions 2–4.
A4. For the data in question A2, what is the value of h2? What is the approximate estimated power for this ANOVA?Explain what the h2 and estimated power indicate.
A3. Using the data from question A2, compute three protected t tests to compare all possible pairs of means. Also, forα .05, what is the value of LSD? Which pairs are significantly different from one another, using this multiple comparison procedure?
A2. Suppose we wanted to compare the somatic complaints (as measured on a scale known as the Physical Symptom Survey or PSS) of three groups of people: nonsmokers, smokers, and people who recently quit smoking. Using the following data for PSS scores, do a one-way ANOVA to test the hypothesis that
A1. For each of the following situations, indicate whether ANOVA is appropriate; if not appropriate, the reason why not; and, if appropriate, the type of ANOVA that would be used (i.e., one-way, repeated measures, etc.):(a) The independent variable (IV) is age group—people in their 60s, 70s, and
B6. Run independent groups t tests for three outcomes in the Polit2SetC dataset: cesd and the two subscale score variables for the SF-12 scale. In these t tests, you will be testing the null hypotheses that women who do not have a high school education have the same scores on these three health
B5. Almost all of the data in the three datasets included are from interviews conducted with adult women in 2001, in the second wave of a longitudinal study. We have, however, included CES-D scores based on data collected in the Wave I interview for a small subsample of these women.This variable is
B4. Using information about the pooled standard deviation for the cesd variable from the output in Exercise 1 (or from a separate “Descriptives” analysis for the cesd variable), compute the value ofd, indicating the effect of being nonemployed on levels of depression in this population. Then do
B3. Now run a t test to test the hypothesis, using the commands Analyze ➜ Compare Means ➜ Independent Samples T Test. Move the variable cesd into the slot for Test Variable(s). Then move the variable worknow into the slot for Grouping Variable. To run this analysis, you must X2 13.2 SD2 2 15.21
B2. Suppose we wanted to test the hypothesis that the employment status of these disadvantaged women(i.e., whether they were working or not working at the time of the interview) was related to their level of depression.(a) Formally state the null and alternative hypothesis for this situation. (b)
B1. For these exercises, you will be using the SPSS datasetPolit2SetC, which contains a number of mental health variables. Most of our analyses involving t tests will involve the variable cesd, which are the women’s scores on a 20-item scale called the Center for Epidemiologic
A10. Suppose we wanted to test whether the number of hours in labor was different for women in their 20s and women
A9. The following are data for subcutaneous oxygen tension(PSCO2, measured in mmHg) 12 hours after the start of two protocols, administered to the same 10 healthy subjects in random order—a bed rest protocol and a high activity protocol:Subject Bed Rest High Activity 1 67 63 2 68 62 3 70 69 4 66
A8. For a post hoc power analysis, assume that d .60, a.05 for a two-tailed t test, and the number of people in each of two groups 30. What was the approximate power of the t test, and what was the risk of a Type II error? For the same effect size (.60), approximately what n per group would be
A7. State the critical (tabled) value of t that would be used to reject the null hypothesis of equality of population means, for an independent groups t test under each of the following conditions:(a) H1: m1 m2; n1 20, n2 20; a .05(b) H1: m1 m2; n1 30, n2 30; a .01(c) H1: m1 m2; n1 10, n2 10; a
A6. For each of the following t values, indicate whether the t is statistically significant for a two-tailed test, at the specified alpha:(a) t 2.40, df 25, a .01(b) t 2.40, df 25, a .05(c) t 5.52, df 10, a .01(d) t 2.02, df 150, a .05
A5. For question A3, assume that the pooled SD for the two groups is 7.05. Calculate the value ofd. Given the result, approximately what was the power of the statistical test—and conversely, approximately what is the probability of a Type II error ()?
A4. Write one or two sentences that could be used to report the results obtained for the t test in question A3.
A3. Suppose we wanted to test the hypothesis that a control group of cancer patients (Group 1) would report higher mean pain ratings than an experimental group receiving special massage treatments (Group 2). Using the following information, compute a t statistic for independent groups:What are the
A2. For which of the following situations is the dependent groups t test appropriate (if inappropriate, indicate why)?(a) The independent variable (IV) is presence or absence of conversation directed to comatose patients; the dependent variable (DV) is the patients’ intracranial pressure.(b) The
A1. For which of the following situations is the independent groups t test appropriate (if inappropriate, indicate why)?(a) The independent variable (IV) is a type of stimulation for premature infants (auditory versus visual versus tactile); the dependent variable (DV) is cardiac responsiveness.(b)
B7. Using the variable poverty as the row variable in a Crosstabulation analysis, calculate RRs and ORs between the women’s poverty status and four to five other dichotomous outcomes of your choosing in the Polit2SetB dataset. Create a table presenting the results, and write a brief paragraph
B6. Set up a table to display the results from Exercise B5, using Table 3 as a model. Then write a few sentences summarizing the results.
B5. This question was intentionally removed from this edition.
B4. Create a graph that presents the statistics from Exercise B3. Click on Graphs ➜ Legacy Dialogs ➜ Error Bar. The dialog box that pops up is set to a default for type of graph (Simple) that you should run. Click the pushbutton Define.In the next dialog box, move bmi into the slot for Variable
B3. Within Explore, you can instruct the computer to compute CIs around the means of a dependent variable for different subgroups. Run Explore for the variable bmi again, but on the opening dialog box, in the slot labeled “Factor List,”enter the variable for the woman’s poverty status
B2. Now, have SPSS compute the same CIs around the mean of bmi by using the Analyze ➜ Descriptive Statistics ➜Explore procedure. In the opening dialog box, Insert the bmi variable into the Dependent Variable list. Next, click “Statistics” at the bottom left, then click on the Statistics
B1. For the exercises in this chapter, you will again be using the SPSS dataset Polit2SetB. First, run a descriptive analysis for the variable bmi, the body mass index for study participants.Do this within Analyze ➜ Descriptive Statistics ➜Descriptives. Move the variable bmi (variable #19) into
A10. For the problem in Question A9, would the obtained result be statistically significant with .05 for a one-tailed test (i.e., for H1: m 55)?
A9. Suppose you wanted to test the hypothesis that the average speed on a highway—where the maximum legal speed is 55 mph—is not equal to 55 mph (i.e., H0: m 55; H1: m 55). Speed guns are used to measure the speed of 50 drivers, and the mean is found to be 57.0, SD 8.0. What is the calculated
A8. Suppose we obtained data on vein size after application of a nitroglycerin ointment in a sample of 60 patients.The mean vein size is found to be 7.8 mm with an SD of 2.5. Using the t distribution in Table 2 of Appendix:Theoretical Sampling Distribution Tables (because information on the true
A7. Population A and Population B both have a mean height of 70.0 inches with an SD of 6.0. A random sample of 30 people is selected from Population A, and a random sample of 50 people is selected from Population B.Which sample mean will probably yield a more accurate estimate of its population
A6. Compute the mean, the standard deviation, and the estimated standard error of the mean for the following sample data: 3, 3, 4, 4, 4, 5, 5, 5, 5, 5, 5, 6, 6, 6, 7, and 7.
A5. If a sampling distribution of the mean had an SEM equal to 0.0, what would this suggest about the sample means drawn from the population—and about the scores in the population?
A3. Given a normal distribution of scores with a mean of 100 and an SD of 10, compute z scores for the following score values: 95, 115, 80, and 130.A4. Based on Figure 2, which shows a normal distribution of children’s heights with a mean of 60.0 and an SD of 5.0, approximately what is the
A2. Draw a histogram that graphs the probability of drawing a spade, a club, a heart, or a diamond from a normal deck of 52 cards. Shade in the area showing the probability of drawing a red card.
A1. What is the probability of drawing a spade from a normal, shuffled deck of 52 cards? What is the probability of drawing five spades in a row (i.e., the probability of getting a flush in five-card poker)?
B6. Select several interval-level or ratio-level variables from the Polit2SetB dataset and do some basic descriptive statistics (means, SDs, etc.) for the selected variable. Then do a correlation matrix to explore relationships among the variables. Write a paragraph summarizing what you learned
B5. Run crosstabs to describe the relationship between women’s current employment status and health-related characteristics in this sample of low income women, using the following variables in the Polit2SetB dataset: currently employed(worknow), does not have health insurance (noinsur), smokes
B4. Create a correlation matrix with four variables in the Polit2SetB dataset. The four variables are Variables #11, 18, 44, and 45: Number of visits to the doctor in the past 12 months(docvisit); body mass index (bmi); standardized score on the Short-Form Health Survey or SF12, Physical health
B3. This exercise involves producing risk index statistics, again using the dataset Polit2SetB. Run the SPSS Crosstabs procedure, using poverty status (poverty) as the risk exposure variable—i.e., inserting it as the row variable. Then find Variable #43 toward the end of the variable list
B2. Using the same SPSS dataset (Polit2SetB), run a crosstab between poverty status (poverty) and current smoking status (smoker, Variable #15, which is coded 0 for nonsmokers and 1 for smokers). This time, check the box on the opening dialog box that says “Display clustered bar charts.” Run
B1. The SPSS dataset Polit2SetB has a number of healthrelated variables. Use this dataset to create a contingency table that crosstabulates the women’s poverty status (poverty, coded 1 for those below the poverty line and 2 for those above it) with a four-category ordinal variable indicating how
A5. Compute the correlation coefficient (Pearson’s r) to summarize the relationship for the blood pressure data presented in question A4. How accurate was your verbal description of the scatterplot, as compared to the value of the coefficient?
A4. Below are values for diastolic and systolic blood pressure for 10 people:Diastolic 90 80 90 78 76 78 80 70 76 74 Systolic 130 126 140 118 114 112 120 110 114 116 Construct a scatterplot that shows the relationship between the variables. Verbally describe the direction and magnitude of the
A3. The contingency table below presents fictitious data regarding an intervention to reduce pressure ulcers in nursing home residents. Using these data, compute ARE, ARNE, ARR, RR, RRR, OR, and NNT.
A2. Examine the results in Table 7. (a) Are the percentages shown in this table row percentages or column percentages? (b) Compute the percentages the opposite way, and then answer this question: Given that males represent 7.5%of all licensed nurses in Missouri, which (if any) infractions in the
A1. The following data designate whether or not patients complied with a medication regimen (1 yes, 2 no), for an experimental group that participated in a special intervention designed to promote perceived mastery over health events, and a “usual care” control group:Construct a contingency
B6. Select a variable from the Polit2SetB dataset that is an interval-level or ratio-level variable. Do some basic descriptive statistics (means, SDs, etc.) for the selected variable, and run the Explore procedure to examine outliers. Write a paragraph summarizing what you learned about the
B5. Run descriptive statistics on the following variables in the Polit2SetA dataset: age, age1bir, higrade, hhsize, and income. Create a table summarizing the results, using Table 2 as a model—or elaborate on it by adding other descriptive statistics. Then write a paragraph summarizing the
B4. In this exercise, you will create a new variable (crowded)and then generate z scores for that variable. The new variable will be an index of how crowded participants were in their residences. To create crowded, you will instruct the computer to divide the number of rooms in the household(rooms)
B3. In this next exercise, perform analyses relating to outliers, again with the variable age1bir. Using the Explore procedure(Analyze ➞ Descriptive Statistics ➞ Explore) put age1birth into the Dependent List when the dialog box appears, and put Identification number in the box that says
B2. Now, for the same variable (age1bir), determine the median, mode, and quartile values, using the Frequencies procedure (Analyze ➞ Descriptive Statistics ➞ Frequencies).When the dialog box appears, “uncheck” the box that says“Display Frequency Tables.” (Why do you think we
B1. Using the SPSS dataset Polit2SetA, determine the mean, range, standard deviation, and variance for the variable age1bir (Participants’ age at first birth). To do this, click on Analyze (on the top toolbar menu), then select Descriptive Statistics from the pull-down menu, then Descriptives.
A5. For each blood pressure value in question A4, compute a z score. Then, transform these z scores to standard scores with a mean of 500 and an SD of 100.
A4. The following ten data values are systolic blood pressure readings. Compute the mean, the range, the SD, and the variance for these data.
A3. For which distribution in question A2 would the median be preferred to the mean as the index of central tendency?Why?
A2. Find the medians for the following distributions:(a) 1 5 7 8 9(b) 3 5 6 8 9 10(c) 3 4 4 4 6 20(d) 2 4 5 5 8 9
A1. The following numbers represent the scores of 30 psychiatric inpatients on a widely used measure of depression(the Center for Epidemiologic Studies-Depression scale).What are the mean, the median, and the mode for these data?If the values of these indexes are not the same, discuss what they
B8. Run Frequencies for the following three demographic/background variables in the dataset: educational attainment(educatn, variable number 5); currently employed (worknow, variable 7); and current marital status (marital, variable 9).Create a table (in a word processing program or by hand)that
B7. To examine the issue of outliers, use the SPSS Explore command by clicking on Analyze in the top toolbar, then selecting Descriptive Statistics, then Explore. Move the variable higrade (highest grade completed) into the Dependent Variable list using the arrow; then move the variable
B6. Re-run the frequency distribution for higrade a third time.Now, when the initial dialog box opens, click the pushbutton for “Charts.” When a new dialog box appears, click on“Histogram” and “With normal curve.” Return to the main dialog box and click on OK. Examine the resulting
B5. Re-run the frequency distribution for higrade. This time, when the dialog box comes up, click the pushbutton for“Statistics.” When a new dialog box appears that asks which statistics you would like, click the “Skewness” and“Kurtosis” options that appear in the lower right section
B4. Now focus on missing data for the variable higrade, using the same frequency distribution output as in Exercise B3.Answer these questions:(a) How many cases altogether had valid information, and what percentage of the overall sample did these cases represent?(b) How many different types of
B3. Now execute the SPSS Frequency command once again for the variable higrade, highest grade of education for participants (Variable 6). (If you do this analysis right after the previous one, you will need to remove the variable racethn from the variable list with the arrow push button, and then
B2. Re-run the frequency distribution for racethn. This time, use the toolbar with icons that is second from the top. Put the mouse pointer over the icons, from left to right. Find the icon(likely to be the fourth one) that has a “Tool Tip” that reads“Recall recently used dialogs” when you
B1. Using the SPSS dataset Polit2SetA, create a frequency distribution for the variable racethn. You can do this by clicking on Analyze (on the top toolbar menu), then select Descriptive Statistics from the pull-down menu, then Frequencies.This will bring up a dialog box (this is true in almost all
A5. If you wanted to display information on patients’ age using the data in Table 5, would you construct a histogram, bar graph, frequency polygon, or pie chart? Defend your selection, and then construct such a graph.
A4. Describe the shape of the frequency distribution drawn in Exercise A3 in terms of modality and skewness. Is the number of falls normally distributed?
A3. Draw a frequency histogram for the data shown in Exercise A1. Now superimpose a frequency polygon on the histogram. Using a ruler, measure the height and width of your graphs: Is the height about two thirds of the width?
A2. Using information from the frequency distribution for Exercise A1, answer the following:(a) What percentage of the nursing home residents had at least one fall?(b) What number of falls was the most frequent in this sample?(c) What number of falls was the least frequent in this sample?(d) What
A1. The following data represent the number of times that a sample of nursing home residents who were aged 80 or older fell during a 12-month period. 0341020120 1001250101 0210113210 1311046101 Construct a frequency distribution for this set of data, showing the absolute frequencies, relative
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