Chapter 13
11. What is the technical name for a distribution that is sometimes referred to as a bell-shaped curve? A) Normal B) Multimodal C) Bimodal D) Skewed
Ans: A Feedback: A normal distribution is a "bell-shaped" distribution that is symmetric, unimodal, and not too peaked. Normal distributions are not bimodal, multimodal, or skewed.
2. In a study on patient compliance, a nurse researcher administered a Questionnaire and asked about the participants' marital status. What is the level of measurement of the variable marital status? A) Nominal B) Ordinal C) Interval D) Ratio
Ans: A Feedback: A person's marital status would be "measured" by providing respondents with several mutually exclusive categories (e.g., 1 = never married, 2 = married, 3 = divorced/separated, 4 = widowed). The numbers associated with each category have no quantitative meaning, which is true of nominal measurements. All other measurement levels involve numeric values with quantitative meaning.
61. Analysis of covariance (ANCOVA) removes the effect of which type of variable before testing whether mean group differences on the outcome are statistically significant? A) Confounding variable B) Mediating variable C) Independent variable D) Dependent variable
Ans: A Feedback: Analysis of covariance (ANCOVA) removes the effect of one or more confounding variables (covariates) before testing whether mean group differences (the independent variable) on the dependent variable are statistically significant. There are no mediating variables in ANCOVA.
66. A nurse researcher develops a scale to measure preparedness for caregiving among family members of palliative care patients. A panel of experts is recruited to assess the relevance of the items, and the results indicated a CVI of .91. What type of validity is being assessed? A) Content validity B) Internal validity C) Criterion validity D) Construct validity
Ans: A Feedback: Content validity is the extent to which the content of the items on a multi-item scale adequately captures the construct. Content validity, unlike criterion or construct validity, can be assessed with feedback from a panel of experts, who rate the relevance of items; the ratings are used to compute a content validity index (CVI). Internal validity concerns the adequacy of the research design for making causal inferences and is unrelated to measurement validity.
6. There are four levels of measurement. Variables measured at which two levels are often called continuous variables? A) Interval and ratio B) Nominal and ordinal C) Ordinal and interval D) Ordinal and ratio
Ans: A Feedback: Continuous variables are ones that take on a range of values, like the scores on a scale (interval) or weight (ratio). Neither nominal-level nor ordinal-level level measures would be considered continuous.
52. In an analysis of variance (ANOVA), what is the test statistic? A) F ratio B) t C) d D) r
Ans: A Feedback: In ANOVA, the F ratio statistic contrasts the variation between three or more groups to the variation within the groups. The t statistic is used in t-tests, r is the statistic used as a correlation coefficient, and d is an effect size statistic.
63. Which of the following is a statistic associated with logistic regression? A) OR B) R2 C) t D) F
Ans: A Feedback: In logistic regression, the analysis yields an odds ratio (OR) for each predictor variable. The OR is the factor by which the odds change for a unit change in the predictors after controlling other predictors. F tests are used in many multivariate analyses (e.g., ANCOVA, multiple regression) but not in logistic regression. Neither R2 nor the t statistic is associated with logistic regression.
21. Which of the following is a characteristic of a normal distribution? A) 95% of the values are within two standard deviations above and below the mean. B) The range of scores is from 20 to 80. C) The values are positively skewed. D) The mean is 50.0.
Ans: A Feedback: In normal distributions, there are roughly three SDs above and below the mean, and 95% of the scores fall within 2 SDs of the mean. The values in a normal distribution are not skewed. The mean of a normal distribution can be any value² not necessarily 50, and the range can also be any value²not necessarily 20 to 80.
64. A researcher is doing a test±retest assessment of a 10-item scale to measure fear of hospitals. What would be the preferred reliability statistic for this situation? A) The intraclass correlation coefficient B) Pearson's r C) Coefficient alpha D) Cohen's kappa
Ans: A Feedback: In test-retest reliability assessments of continuous measures (such as composite scales), the preferred reliability statistic is the intraclass correlation coefficient; it is preferred over the widely used Pearson's correlation coefficient. Coefficient alpha is not used in test-retest reliability assessments. Cohen's kappa is used primarily in interrater reliability assessments.
48. In a sample of 300 adults, a researcher tests the hypothesis that men and women differ in the amount of time (number of hours) they spend exercising weekly. Which of the following statistical tests would the researcher likely use? A) An independent groups t-test B) A chi-squared test C) A dependent groups t-test D) A paired t-test
Ans: A Feedback: In this example, the outcome variable is measured on a ratio scale; the mean number of weekly hours of exercise would be computed for men and women. The means of two separate groups of people are being compared, so an independent groups t-test would be appropriate. Paired (dependent groups) t-tests are used when the means for the same people are compared over time (e.g., before and after an exercise intervention). Chi-squared tests are not used with variables for which mean values would be computed.
30. The use of inferential statistics permits researchers to: A) draw conclusions about a population based on data from a sample. B) describe data obtained from a population. C) interpret parameters. D) interpret the laws of probability.
Ans: A Feedback: Inferential statistics, based on the laws of probability, provide a means for drawing conclusions about a population, given data from a sample. Inferential statistics are not used to interpret parameters (descriptive indexes from a population) or the laws of probability. Inferential statistics is used to make inferences about a population, not to describe data from a population²data are almost always from samples, not populations.
68. An instrument's ability to correctly identify a case is its: A) sensitivity. B) specificity. C) content validity. D) ROC curve.
Ans: A Feedback: Sensitivity is a measure's ability to identify a "case" correctly, that is, to screen in or diagnose a condition or trait correctly (the true positive rate). Specificity is the measure's ability to identify non-cases correctly, that is, to screen out those without the condition (the true negative rate). ROC curves are sometimes used to plot sensitivity against specificity. Content validity is unrelated to an instrument's ability to correctly identify a case.
53. A researcher tested the hypothesis that patients in the ICU who were administered a silicone border foam dressing would be less likely than those without the dressing to experience incontinence-associated dermatitis. Which statistical test would the researcher likely use? A) A chi-squared test B) A paired t-test C) ANOVA D) An independent groups t-test
Ans: A Feedback: The chi-square ( 2) test is used to test hypotheses about group differences in proportions or percentages. In this example, there are two groups (those with and without the dressing), and the dependent variable (dermatitis vs. no dermatitis) is a nominal-level variable for which percentages would be computed. Neither ANOVA nor t-tests could not be used in this situation because the outcome variable is not on an interval or ratio scale (i.e., the researcher is not comparing group means).
34. Which statement about standard errors of the mean (SEM) and sampling distributions is true? A) One component in the formula for estimating SEMs is the standard deviation for the sample. B) Researchers construct sampling distributions from their study data. C) A sampling distribution of the mean is positively skewed. D) The larger the SEM, the more accurate are sample means as estimation of population means.
Ans: A Feedback: The formula for estimating SEMs involves two pieces of information²the SD for the sample and sample size. Sampling distributions are theoretical and are not based on actual data. The accuracy of parameter estimates is enhanced when SEMs are smaller, not larger. Sampling distributions are unimodal and normal; they are not skewed.
29. A researcher wants to estimate how many people would need to receive a fall prevention intervention to prevent one fall. What index would the researcher compute? A) Number needed to treat B) Odds ratio C) Absolute risk reduction D) Absolute risk
Ans: A Feedback: The number needed to treat (NNT) represents an estimate of how many people would need to receive an intervention (here, a fall prevention intervention) to avoid one undesirable outcome (here, a fall). The other three indexes terms²the odds ratio, absolute risk, and absolute risk reduction²are risk indexes that provide different types of information about risk.
44. If a power analysis indicated that for a given sample size, the power was .50, which would be true? A) The risk of a Type II error would be 50%. B) The results would be statistically significant 50% of the time. C) The 95% CI would have a range of 50 points. D) The risk of a Type I error would be 50%.
Ans: A Feedback: The probability of committing a Type II error can be estimated through power analysis. When power equals .80 (the standard criterion), the risk for a Type II error is 20%. For a given sample size, if the power was estimated to be .50, there would be a 50% probability of a Type II (not a Type I) error²that is, wrongly concluding that the null hypothesis was correct. A power analysis is not related to particular CI values or to the probability that results would be significant a specified percentage of the time.
23. In analyzing scores on an anxiety scale, a nurse researcher found the scores were distributed from 62 to 98 in the research sample. What is the range? A) 36 B) 62 C) 98 D) 160
Ans: A Feedback: The range is simply the highest score minus the lowest score in a distribution. In this example, 98 minus 62 equals 36.
12. In a sample of 250 patients with cancer, the scores on a scale that measured resilience ranged from 10 to 70. There were two peaks in the distribution, at the scores of 25 and 55. What would this distribution be called? A) Unimodal B) Bimodal C) Asymmetric D) Normal
Ans: B Feedback: A bimodal distribution has two high peaks, which in this example occurred at the scores of 25 and 55. Normal distributions are unimodal, and a unimodal distribution only has one peak. The distribution of scores in this example might be asymmetric, but there is no information about whether this is the case.
24. A nurse researcher wants to describe the relationship between marital status (married vs. unmarried) and having a diagnosis of postpartum depression (yes vs. no). Which of the following would the researcher use to describe the data? A) Pearson's product-moment correlation coefficient B) A crosstabs table C) A correlation matrix D) Spearman's rho
Ans: B Feedback: A crosstabs table is a two-dimensional frequency distribution in which the frequencies of two nominal-level variables (or ordinal level variables with few values) are crosstabulated. In this example, both marital status and postpartum depression status are nominal level, which would make Pearson's r, Pearman's rho, and a correlation matrix inappropriate.
41. What is the least conservative alpha that is considered acceptable? A) .10 B) .05 C) .01 D) .001
Ans: B Feedback: An alpha of .05 is considered a minimum threshold acceptable in most situations for declaring that a result is statistically significant. An alpha of .10 is not sufficiently stringent (a 1 in 10 chance of a Type I error) and both .01 and .001 are more conservative than .05.
60. A researcher wants to compare male and female oncology patients in terms of scores on a depression scale, controlling for age and severity of illness. The analysis would likely involve which test? A) Multiple regression B) ANCOVA C) Logistic regression D) Repeated measures ANOVA
Ans: B Feedback: Analysis of covariance (ANCOVA) is used to compare group means (here, mean scores on a depression scale for male and female patients) while statistically controlling confounding variables (age and illness severity) to "equalize" groups being compared. Multiple regression and logistic regression are used to predict a dependent variable using two or more predictor (independent) variables, which did not occur in this example. Repeated measures ANOVA is used to test mean differences over time, and there is no suggestion that depression was measured more than once.
50. A researcher compared the mean anxiety levels of patients who had been randomly assigned to a soothing music group, a massage group, or a control group. Which of the following statistical tests was likely used to test group differences in anxiety scores? A) t-Test B) ANOVA C) ANCOVA D) Chi-squared test
Ans: B Feedback: Analysis of variance (ANOVA) is the statistical procedure used to test mean group differences for three or more groups. A t-test is used to compare means for two groups, not three. ANCOVA is used when a confounding variable is controlled, and no confounder is mentioned in this example. Chi-squared tests are not used with variables on an interval scale, as is the case in this example.
37. A 95% confidence interval is associated with how many standard deviation (SD) units? A) 0.95 B) 1.96 C) 2.58 D) Depends on the sample size
Ans: B Feedback: In a normal distribution, 95% of the scores lie within about 2 SDs (more precisely, 1.96 SDs) from the mean. To calculate a 95% CI, the value of 1.96 is multiplied to the standard error of the mean, and that value is added to and subtracted from the sample mean to arrive at a range of scores within which the population value has a 95% probability of lying. For a 99% CI, the value is 2.58 SDs. The CI calculation does not depend on the sample size.
17. A nurse researcher reported that, for scores on a 12-item scale of empathy, = 43. What does the symbol represent? A) An effect size B) A mean C) Total sample size D) An individual score
Ans: B Feedback: In research articles, the mean is often symbolized as M or . An individual score might be written as X, without the overbar. Total sample size is often designated as N in research reports. There are several effect size indexes (such as the d statistic), but is not one of them.
15. Here are five score values: 5, 6, 9, 10, 10. Which measure of central tendency for this distribution would have a value of 9? A) The mode B) The median C) The mean D) The mode, median, and mean would be equal²all would be 9.
Ans: B Feedback: In this example, the median is equal to 9²it is the value above which and below which 50% of the cases fall. The mode in this example is 10, and the mean is 8.0 (40 ÷ 5 = 8.0).
59. In terms of measurement levels for variables in a multiple regression analysis, which of the following is true? A) Nominal-level variables cannot be used as predictors in multiple regression analysis. B) Infant birth weight is measured at an acceptable level for use as either a predictor or a dependent variable in multiple regression. C) Smoking status (smoker vs. nonsmoker) is measured at an acceptable level for use as either a predictor or a dependent variable in multiple regression. D) The dependent variable in multiple regression can be measured at any measurement level.
Ans: B Feedback: Infant birth weight is on a ratio scale and could be used as either a predictor or a dependent variable in multiple regression. Dependent variables in multiple regression analysis should be measured on an interval or ratio scale, not on a nominal scale (e.g., smoking status). Predictor variables can be either continuous or nominal-level variables.
43. A 95% CI in parameter estimation corresponds to which alpha value in a hypothesis testing framework? A) An alpha of .95 B) An alpha of .05 C) An alpha of .99 D) An alpha of .01
Ans: B Feedback: Levels of significance are analogous to the CI values²an alpha of .05 is analogous to the 95% CI, and an alpha of .01 is analogous to the 99% CI. By convention, the minimal acceptable alpha level is .05. An alpha of .01 is more stringent than an alpha of .05²just as a CI of .99 is more stringent than a CI of .95.
7. Which of the following is a parameter? A) The average birth weight of a sample of 2,000 infants B) The average age of an accessible population of 50,000 nursing home residents in New York City C) The percentage of male and female in a sample of 5,000 patients D) The grade point average of nursing students responding to an Internet survey
Ans: B Feedback: Parameters are descriptive indexes (such as averages and percentages) calculated using data from a population. All of the other responses reference data obtained from a sample. A descriptive index from a sample is called a statistic.
58. A researcher found a multiple correlation of .40 (R = .40) between candy intake, age, and income on the one hand and dental caries on the other. How much variability in dental caries, the dependent variable, can be accounted by the three predictor variables? A) 4% B) 16% C) 40% D) Cannot be determined
Ans: B Feedback: R, when squared, can be interpreted as the proportion of the variability in the outcome variable that is explained by the predictors. In predicting dental caries by candy intake, age, and income, an R of .40 results in an R2 = .16. Thus, the predictors accounted for 16% (not 4% or 40%) of the variation in dental caries.
70. In reporting the results of a statistical test in a research article, which would not be reported? A) The computed value of the test statistic B) The theoretical value of the test statistic C) Degrees of freedom D) The probability (p) value
Ans: B Feedback: Research articles usually provide certain information about statistical tests, including (1) which test was used, (2) the value of the calculated statistic, (3) degrees of freedom, and (4) level of statistical significance. The theoretical value of the test statistic would not be reported.
42. A researcher controls the risk of a Type I error by: A) selecting a sufficiently large sample. B) setting the level of significance. C) computing confidence intervals rather than using hypothesis testing. D) using the appropriate sampling distribution.
Ans: B Feedback: Setting the significance level (alpha) allows researchers to decide how much risk they are willing to accept that there will be a Type I error. Sample size affects the risk of Type II (not Type I) errors. Type I and Type II errors can occur with confidence intervals as well as with hypothesis tests. Researchers do not select sampling distributions; this is a function of which statistical test is used.
28. In a randomized controlled trial testing the effect of a smoking cessation program with 75 experimental group members and 75 control group members, which index would be a measure of the proportion of individuals in the control group who presumably would have stopped smoking had they received the intervention? A) Absolute risk B) Absolute risk reduction C) Odds ratio D) Number needed to treat
Ans: B Feedback: The absolute risk reduction index is an estimate of the proportion of people in the control group who could have been spared an undesirable outcome (here, continued smoking) had they been exposed to the intervention. Absolute risk is the proportion of people who experience an undesirable outcome in each group. The odds ratio measures the proportion of subjects who experienced an undesirable outcome relative to those who experienced a desirable outcome. The number needed to treat index estimates how many people would need to receive an intervention to prevent one undesirable outcome.
In a study on patients' fear of falling, a nurse researcher administered a questionnaire; one question asked about the participants' educational attainment (1= high school, 2 = some college, 3 = college degree, 4 = graduate degree). In this example, what is the level of measurement of the variable educational attainment? A) Nominal B) Ordinal C) Interval D) Ratio
Ans: B Feedback: The researcher operationalized educational attainment as an ordinal-level variable. Respondents were asked to choose one of several categories that were rank ordered according to the amount of education attained. The numbers associated with the categories do not indicate how much greater one category is than the other (i.e., this is not interval and ratio measurement). Unlike nominal measurement, however, the numbers (1, 2, 3, and 4) do convey quantitative information.
31. Which of the following is the standard deviation of a sampling distribution of means? A) Sampling error B) Standard error of the mean C) Mean difference D) Square of the standard deviation
Ans: B Feedback: The standard error of the mean (SEM)²the standard deviation of a theoretical sampling distribution of means²indicates the degree of average error of a sample mean. Sampling error occurs when sample values differ from population values. A mean difference is the difference between two group means and is unrelated to sampling distributions. The square of an SD is another index of variability (known as the variance) and is also unrelated to sampling distributions.
13. What is the most frequently occurring score in a distribution called? A) Average B) Mode C) Median D) Mean
Ans: B Feedback: There are several indexes of central tendency. The mode is the value that occurs most frequently in a distribution, the median is the point above and below which 50% of the cases fall, and the mean is the arithmetic average of all scores (called The "average" in lay terms).
20. A group of 500 elders completed a test of cognitive functioning. The mean score was 85, the standard deviation was 5, and scores were normally distributed. Approximately what percentage of the 500 scores fell between 80 and 90? A) 34% B) 68% C) 95% D) Impossible to determine
Ans: B Feedback: When scores are normally distributed, about 34% of the scores fall within 1 standard deviation (SD) above the mean, and another 34% fall within 1 SD below the mean. In this case, 34% of the scores would be between 80 and 85 (the mean), and another 34% would be between 85 and 90, for a total of 68% of scores between 80 and 90. About 95% of the scores would be between 75 and 95²that is, 2 SDs above and below the mean of 85.
27. In a sample of patients with peripheral neuropathy, a researcher found that the correlation between pain scores and age was .02. What does this mean? A) The older the patient, the much greater the pain score. B) Older patients had pain scores 2% higher than younger patients. C) Older patients had pain scores similar to younger patients. D) The relationship between pain scores and age was perfect.
Ans: C Feedback: A correlation coefficient communicates both magnitude and direction of a relationship. A correlation of .02 is very small²signifying virtually no relationship at all. Thus, in this analysis, younger and older patients had similar scores. A correlation of 1.00 (or ±1.00) signifies a perfect relationship. Correlations do not "translate" to percentages - there is no way to know if scores were 2% higher among older patients.
36. Which of the following could not be a point estimate of a population parameter? A) .05% B) 520 C) 18.0 to 22.0 D) .95
Ans: C Feedback: A point estimate is a single statistic that is used to estimate a population parameter²it is not a range of values. The values of 520 and .95 could be point estimates of population means, and .05% could be a point estimate of a population percentage.
35. Confidence intervals (CIs) address a question relating to the appraisal of evidence. Which of the following questions do CIs address? A) What is the quality of the evidence? B) What is the magnitude of effects? C) How precise is the estimate? D) What is the cost of applying the evidence?
Ans: C Feedback: Confidence intervals provide an estimate of how precise estimates of effects are² They indicate the range of values within which the "true" effect probably lies, with a given probability. The smaller the interval, the more precise the estimates. CIs do not answer questions about the quality of evidence, the magnitude of effects, or costs of applying evidence.
67. A nurse researcher developed a new scale to measure stress in adolescents and Calculated a Pearson's r between scale scores and a gold standard, wake-up salivary free cortisol levels. What type of validity is being assessed? A) Content validity B) Internal validity C) Criterion validity D) Construct validity
Ans: C Feedback: Criterion validity is the extent to which the scores on a measure are a good Reflection of a "gold standard," which in this example is a biophysiological indicator of stress, wake-up salivary free cortisol levels. When scores on both measures are continuous, as in this example, Pearson's r is the statistic used to evaluate criterion validity. Content validity and construct validity do not rely on a "gold standard" criterion. Internal validity concerns the adequacy of the research design for making causal inferences and is unrelated to measurement validity.
26. A nurse researcher wants to describe the relationship between patients' age and their scores on a 20-item social support scale. Which of the following would the researcher use in this descriptive analysis? A) A crosstabulation B) Spearman's rho C) Pearson's r D) A correlation matrix
Ans: C Feedback: In this example, age is a ratio-level variable, and scale scores would be considered Interval level. A correlation could be computed between the two, using Pearson's r. Spearman's rho would be used if both variables were ordinal level. A correlation matrix presents correlation coefficients for three or more variables, not two as in this example. Crosstabs tables are used to describe relationships between two nominal-level variables.
65. Which measurement property of a multi-item composite scale is estimated with coefficient alpha? A) Stability/reproducibility B) Interrater reliability C) Internal consistency D) Construct validity
Ans: C Feedback: Internal consistency is the extent to which the items on a multi-item scale are measuring the same attribute, and internal consistency is most often estimated with coefficient alpha (Cronbach's alpha). Stability/reproducibility and interrater reliability are different types of reliability, neither of which involves coefficient alpha. Construct validity also does not involve the computation of coefficient alpha.
62. A researcher wanted to predict whether nursing home residents would or would not experience a fall within 6 months of admission based on four predictors (e.g., age, vision acuity, cognitive functioning, and having had a prior fall). The analysis would involve which of the following? A) Multiple regression B) ANCOVA C) Logistic regression D) MANOVA
Ans: C Feedback: Logistic regression analyzes the relationships between multiple independent variables and a nominal-level dichotomous outcome²here, whether or not a resident experienced a fall within 6 months of admission. None of the other types of analyses is appropriate for situations in which the outcome variable is dichotomous.
39. Which statement about errors in statistical decision making is true? A) A Type I error occurs when a researcher concludes that there is no relationship between variables when there is one. B) A Type II error occurs when a researcher concludes that there is no relationship between variables when there is none. C) A Type II error occurs when a researcher concludes that there is no relationship between variables when there is one. D) A Type I error occurs when a researcher concludes that there is a relationship between variables when there is one.
Ans: C Feedback: Researchers make a Type II error (not a Type I error) by accepting a null hypothesis that is, in fact, not true²i.e., concluding that there is no relationship when a relationship does exist between variables. Two of the response alternatives to this question are not errors at all²the researcher came to the correct conclusion.
4. A nurse researcher administered a 30-item scale that measured the severity of caregiver burden. What is the level of measurement of the scores on the scale? A) Nominal B) Ordinal C) Interval D) Ratio
Ans: C Feedback: Scores on a psychosocial scale are considered to be interval-level measures. The scores are ordered to indicate increasing amounts of caregiver burden in equal intervals (and so, not ordinal measurement), but there is no rational zero point (and so, not ratio measurement). Unlike nominal measurement, the numbers in this example (scores) would convey quantitative information.
22. Which statement about standard deviations (SDs) is true? A) In a normal distribution, there are roughly 2 SDs above and below the mean. B) In a normal distribution, 1 SD above the mean accounts for 68% of the cases. C) The SD represents the average amount of deviation of scores from the mean. D) An SD of 10 indicates a distribution that is more heterogeneous than one with an SD of 20.
Ans: C Feedback: The SD represents the average amount of deviation from the mean. In normal distributions, there are roughly 3 SDs above and below the mean, not 2, and 1 SD above the mean would account for about 34% of the cases in the sample (68% would be the amount for 1 SD above AND 1 SD below the mean). If a distribution had an SD of 10, it would be less heterogeneous (less varied) than if the SD were 20.
49. A researcher compared an experimental and control group on scores on a quality-of-life scale. The value of the calculated t statistic was ±2.50 and the theoretical t value (for df = 6- and a = .05) is 2.00. The researcher would: A) conclude that a Type II error had been made. B) accept the null hypothesis. C) reject the null hypothesis. D) use a different level of significance.
Ans: C Feedback: The absolute value of the calculated t (±2.50) is larger than the theoretical value of t (2.00). Thus, the null hypothesis can be rejected²that is, the group means are significantly different at p < .05. The value of the test statistic indicates that the null hypothesis is "improbable." A different level of significance does not need to be selected - nor would that be appropriate once the results are "in". Given the significant results, a Type II error (false negative) was not made.
55. Which of the following is an effect size index? A) t B) F C) d D) 2
Ans: C Feedback: The d statistic is an effect size index that summarizes the strength of the difference in two means. The other answers are statistics used in statistical tests to compare groups and are not effect size indexes.
16. Which measure of central tendency is the most stable? A) Mode B) Median C) Mean D) The mode, the median, and the mean are equally stable.
Ans: C Feedback: The mean is usually the preferred measure of central tendency because of its stability. Modes and medians are more likely than means to fluctuate in value from one sample to another drawn from the same population.
69. Which statistical test result would not be considered statistically significant? A) r = .19, p = .05 B) 2 = 12.33, p < .001 C) t = 1.70, p = .09 D) F = 3.23, p < .05
Ans: C Feedback: The standard criterion for statistical significance is a probability value of less than .05. All of the results reported in the response alternatives are statistically significant except for the t-test, where the p value is .09²i.e., greater than .05.
47. When a statistical test has been performed, the computed p value is compared to the: A) theoretical distribution for the test statistic. B) values for the 95% CI. C) specified value of alpha. D) specified value of the power criterion.
Ans: C Feedback: The value of alpha is the researcher's criterion for statistical significance. The p value is the actual probability that the null hypothesis is false, and so the p value is compared to alpha. The p value is not compared to a theoretical distribution, CI values, or the power criterion.
3. Which measure exemplifies ratio-level measurement? A)Scores on a depression scale B) Apgar scores C) Urine output in milliliters per hour D) Employment status
Ans: C Feedback: Urine output in milliliters per hour is measured on a ratio-level scale; it has a rational zero, and values would be equidistant. Scores on a depression scale would likely be considered interval-level, Apgar scores are ordinal, and employment status could be nominal (e.g., working/not working) or ordinal (e.g., not working, working part-time, working full-time).
14. A researcher reported the age of onset of Alzheimer's disease in a sample of residents in a memory care facility. What index of central tendency is likely to best communicate the information? A) The average B) The mode C) The median D) The mean
Ans: C Feedback: When a distribution is skewed, as it would be for the residents' age at onset in this sample, the preferred index is the median²the value that divides the cases is half. The mean, which is the same as the average, is the sum of all values divided by the Number of people; the mean would distort what is a "typical" age at onset because there would be a negative skew, with some having an early age at onset but most having a later age. The mode is not the preferred index of central tendency with continuous variables.
56. A researcher tested the hypothesis that a person's decision to have a colonoscopy was related to his or her perceived risk for colorectal cancer. With a = .05, the hypothesis was not supported. What might be a cause of this result? A) There were too many degrees of freedom. B) The alpha level was too conservative. C) The test had inadequate power. D) A researcher did not use an appropriate conceptual framework.
Ans: C Feedback: When a researcher uses too small a sample, statistical tests are underpowered, and there is a risk of a Type II error (falsely concluding there is no relationship when there is one), as is likely to be the case in this example. There can never be too many degrees of freedom, as it is a function of sample size and a large sample improves statistical power. The a level of .05 is the least conservative level considered appropriate. A conceptual framework is unlikely to affect the results of a statistical test.
9. Which of the following would be an example of a positively skewed attribute in general populations? A) Age at diagnosis of dementia B) Typical number of hours of sleep C) Number of years of education D) Age at retirement
Ans: C Feedback: With a positive skew, the bulk of values are at the lower end of the distribution. Educational attainment is typically positively skewed²most people have low or moderate amounts of education, whereas fewer people have advanced degrees such as a PhD, DNSc, or MD, which involve many years of schooling. Age at diagnosis of dementia, typical number of hours of sleep, and age at retirement are attributes that are most often negatively skewed, with most values in the upper ranges and the tail pointing to the left.
10. Which of the following is the most likely distribution for the variable height in a population of adults? A) Bimodal B) Positively skewed C) Negatively skewed D) Normally distributed
Ans: D Feedback: A normal distribution is symmetric, unimodal, and not very peaked. Many human attributes, such as height, approximate a normal curve, with most people having "average" height, and comparable percentages being much shorter or much taller than average. Such distributions are not skewed, nor are they bimodal (two peaks, or values with high frequencies).
38. Consider the following hypothesis: The amount of daily daylight is unrelated to levels of depression in older adults. What type of hypothesis is this? A) Research hypothesis B) Alternative hypothesis C) Parametric hypothesis D) Null hypothesis
Ans: D Feedback: A null hypothesis predicts the absence of a relationship between variables, as in This example ("unrelated"). The research (or alternative) hypothesis for this example might be as follows: The greater the amount of daily daylight, the lower the levels of depression among older adults. There is no such thing as a parametric hypothesis.
46. Which of the following is not one of the steps involved in hypothesis testing? A) Selecting the appropriate statistic to be used B) Specifying a level of significance C) Computing a test statistic D) Calculating the theoretical distribution for the test statistic
Ans: D Feedback: Each statistical test can be used with specific kinds of data, but the overall hypothesis-testing process is similar for all tests: (1) selecting a test statistic, (2) specifying the level of significance, (3) computing a test statistic, (4) determining degrees of freedom, and (5) comparing the test statistic to a theoretical value. Hypothesis testing does not involve calculating a theoretical distribution for the test statistic.
40. For which level of significance is the probability of committing a Type I error lowest? A) .10 B) .05 C) .01 D) .001
Ans: D Feedback: For hypothesis testing, researchers select a level of significance, which is the probability of making a Type I error. The smaller the probability, the lower the risk, and in this example, the smallest value is .001. With a .001 significance level, we would accept the risk that out of 1,000 samples from a population, a true null hypothesis would be wrongly rejected only 1 time.
33. The standard error of the mean (SEM) gets smaller as which occurs? A) The mean gets smaller B) The sample size gets smaller C) The mean gets larger D) The sample size gets larger
Ans: D Feedback: Larger samples increase the precision of estimates of the population mean, and so larger samples are associated with smaller standard errors of the mean (SEMs). The value of the SEM is unrelated to the value of the means.
5. There are four levels of measurement. What is ordinal measurement? A) A level in which characteristics are classified into discrete, mutually exclusive categories B) A level with equal distances between ordered values and a true meaningful zero point C) A level in which an attribute is ordered on a scale with equal distances between points on the scale but with no rational zero D) A level in which an attribute is rank ordered on a scale with unequal distances between points on the scale.
Ans: D Feedback: Ordinal measurement assigns numerical values that are rank ordered (unlike nominal measurement), but the distances between points on the scale are not equal (interval measurement), nor is there a rational zero point (ratio).
54. A researcher tested the hypothesis that weight gain during pregnancy was associated with infant birth weight. Which statistical test would be appropriate? A) A paired t-test B) ANOVA C) Chi-squared test D) Pearson's r
Ans: D Feedback: Pearson's r, the most widely used correlation coefficient, is used to test whether there is a relationship between the two variables that are measured on an interval or ratio scale, as is the case in this example (here, both ratio-level variables). The chi-squared test and ANOVA involve comparisons of groups (proportions and means, respectively), and there are no groups in this example. A paired t-test involves comparing means for a group under two circumstances or at two points in time.
51. A researcher tested the effects of prenatal yoga on the mean stress levels of 100 pregnant women at three points in time²at baseline and at two points of follow-up. Which statistical procedure did the researcher likely use? A) Paired t-test B) Chi-squared test C) Analysis of variance (ANOVA) D) Repeated measures ANOVA
Ans: D Feedback: Repeated measures ANOVA compares means for one or more groups at three or more different points in time. A paired t-test can be used to test mean differences for a group at two different points of data collection. ANOVA is used to test the means of three or more independent groups²that is, different groups of people, which is not the case in this example. A chi-squared test is used to test differences in proportions, not mean differences.
32. The tendency of sample values (statistics) to fluctuate from one sample to another reflects: A) a Type I error. B) measurement error. C) a sampling bias. D) a sampling error.
Ans: D Feedback: Statistics are rarely exactly the same values as population parameters; the fluctuations in sample values result in sampling error. Sample bias concerns how well the sample reflects population characteristics, and measurement error concerns the reliability of measures used to collect data. A Type I error is one of two broad classes of errors in statistical decision making.
18. Which is an index of variability that takes into account all score values? A) The range B) The median C) The mean D) The standard deviation
Ans: D Feedback: The most widely used variability index is the standard deviation. Like the mean, which is a central tendency index and not a variability index, the standard deviation is calculated based on every value in a distribution. The median is not an index of variability. The range is the highest score minus the lowest score in a distribution and does not take all scores into account.
19. For a distribution of scores on a quality of life scale, the standard deviation was computed to be 4.0. What is the value of the range? A) 2.0 B) 4.0 C) 16.0 D) Insufficient information to determine
Ans: D Feedback: The range is the highest value in the distribution minus the lowest value. The range for the scale in this example cannot be determined with the information provided.
25. Below is a correlation matrix for four variables (labeled A, B, C, and D). For which pair of variables in the matrix is the relationship strongest? A B C D A B .64 C ±.59 .45 D ±.65 .52 ±.27 A) A with B B) B with C C) B with D D) A with D
Ans: D Feedback: The strongest correlation is between variables A and D: ±.65. The minus sign indicates the direction of the relationship (negative), but the absolute value of the number indicates the strength of the relationship, and the largest number in the matrix is .65. All the other correlation coefficients in the matrix indicate weaker relationships.
45. When a researcher reports that a result is statistically significant, what does this mean? A) The result is clinically meaningful. B) The result does not contain a Type I or Type II error. C) The result was consistent with the null hypothesis. D) The obtained result likely was not the result of chance.
Ans: D Feedback: The term "statistically significant" means that results are not likely to have been due to chance at some specified level of probability. In this context, "significant" does not mean important or clinically meaningful. Any results could contain Type I or Type II errors²there is always some possibility of a statistical error. Statistically significant results indicate that the null hypothesis was rejected as probably being wrong.
57. What is the range of the multiple correlation coefficient (R)? A) -0.10 to 0.00 B) -1.00 to +100 C) 0.00 to -1.00 D) 0.00 to +1.00
Ans: D Feedback: Unlike Pearson's r, R does not have negative values. R varies from .00 to +1.00, showing the strength of the relationship between several independent variables and a dependent variable, but not the direction.
8. A researcher administered a self-esteem scale to a sample of 500 12-year-old children. The bulk of scores were at the upper end of the distribution. How would the frequency distribution for the scores be described? A) Normal B) Bimodal C) Positively skewed D) Negatively skewed
Ans: D Feedback: When more people are at the upper end of the distribution, the longer tail points to the left, and the distribution has a negative skew, not a positive skew. A normal distribution is symmetric, which is not true in this example. There is nothing in the description to suggest that the distribution is bimodal, with two peaks.
