Ch. 11 Understanding Statistics in Research

57. A researcher correlates self-confidence measures with obesity rates and determines an r value of 0.8. What can the reviewer conclude when evaluating this research? a. There is a 36% chance that variation in one score is the result of variation in the other score. b. There is a 64% chance that variation in one score is the result of variation in the other score. c. There is a 64% chance that variation in one score is the result of variation in something other than the other score. d. There is a weak correlation between these two variables.

ANS B Explained variance is a score that is r2 which, in this case, is 0.64, or 64%. This means that there is a 64% chance that the variation in one score affects the variation in the other score. The other three options are incorrect statements.

9. To measure test-retest reliability of an instrument, a researcher may use the a. Cronbach alpha coefficient. b. Fischer's exact test. c. Kuder-Richardson score. d. Pearson's correlation statistic.

ANS D The t-test, or Pearson's correlation statistics, may be used to determine test-retest reliability. Cronbach's alpha coefficient is used to determine reliability in a single study. Fischer's exact test measures statistical significance, usually in small samples. The Kuder-Richardson score measures internal reliability.

3. A parameter is a characteristic of a. a population. b. a frequency distribution. c. a sample. d. a normal curve.

ANS: A A parameter is a numerical characteristic of a population. A frequency distribution describes the occurrence of scores or categories in a study. A sample is a subset of a population. A normal curve is a theoretical frequency distribution of all possible values in a population, with a 95% probability that any value from that population will fall within 2 standard deviations of the mean.

23. When a researcher concludes that study findings are applicable to the total population, this is an example of a. generalization. b. inference. c. probability. d. significance.

ANS: A Generalizations are made when information gained from a specific instance is generalized to the general population. A statistical inference is made from the study findings obtained from a specific sample and applied to the target population. Probability refers to the likelihood that a variable fall at a certain point in the range of data scores. Significance is a value indicating the chance that values are from different groups when the value of one group is not within the range of values of another group.

42. Which is true about a sample that is heterogeneous? a. It has a wide variation in scores. b. Scores will be clustered around the mean. c. The measure of range will be small. d. The standard deviation cannot be calculated.

ANS: A Heterogeneous samples have a wide variation in scores. Such samples will have a wide standard deviation, with scores that can be far from the mean score.

14. The nurse researcher understands that nonparametric analyses are conducted if the variables are measured at what two levels? a. Nominal and ordinal b. Nominal and interval c. Nominal and ratio d. Ordinal and ratio

ANS: A If the variables are measured at the nominal and ordinal levels, nonparametric analyses are conducted. If variables are at the interval or ratio level of measurement, and the values of the study participants for the variable are normally distributed, parametric analyses are conducted.

35. A researcher wishes to present data identifying pain scores for a group of subjects using a grouped frequency distribution table. Which is true about using this method? a. Each group must have equivalent ranges in scores. b. Ranges may overlap from one group to the next. c. Some data may not fit into any group. d. There should be no more than five groups of scores.

ANS: A In grouped frequency distribution tables, each group of scores must have equivalent ranges. Ranges should be discrete without overlapping so that each datum will fit into only one group. The ranges must be exhaustive so that all data will fit into a group. There should be at least 5 and no more than 20 groups.

10. Which describes an outlier? a. A data point with a value outside what is predicted by other data points b. Any data point far from the median point, but still within 2 standard deviations from the mean c. A study result that is directly attributable to randomness d. A study score from a subject lost to attrition after the study begins

ANS: A Outliers are subjects or data points with extreme values that seem unlike the rest of the study sample. Outliers may be within or outside standard deviations. Outliers are not directly attributable to randomness. Outliers are data collected from subjects in the study.

15. After a clinical drug trial to measure the effects of atorvastatin administration on low-density lipoprotein levels, which of the following conclusion statements is acceptable in the research report? a. Findings of clinical drug tests suggest that atorvastatin works to reduce low-density lipoprotein levels in study subjects. b. Results of this clinical drug trial demonstrate that atorvastatin works to reduce low-density lipoprotein levels in all adults over age 65. c. The negative correlation between atorvastatin administration and low-density lipoprotein levels indicates that atorvastatin causes a decrease in LDL levels. d. The study proved that atorvastatin decreases low-density lipoprotein levels.

ANS: A Researchers can never prove things using inferential reasoning; they can never be certain their reasoning is correct. Findings can never be applied to all humans. Correlation does not equate with causation. The study cannot prove that something is the case; it can only support the likelihood.

48. Based on study data, a researcher predicts that a population mean will fall within a specific range of data. This is called the a. confidence interval. b. range. c. standard deviation. d. validity measure.

ANS: A The confidence interval is the probability of including the value of the population within an interval estimate. The range is the full range of all data, from the smallest to the highest number. Standard deviations define the variability of data. Validity is a measure of the extent to which the measure represents the real word data.

31. The median scores of two groups participating in a study are exactly the same for a particular variable. This suggests that the a. average score is the same for both groups. b. the middle score is the same for both groups. c. the most frequent score is the same for both groups. d. groups are very much alike in relation to the variable.

ANS: A The median is a measure of central tendency and indicates the middle score of a group, but does not indicate the variability of the scores around the mean. A measure of dispersion is required to demonstrate the distribution of scores. The same median score does not mean the average score, or the mean, is the same. The same median score does not mean that the most frequent, or mode, is the same. The same median does not equate to sameness in other ways.

41. A researcher conducts a study and calculates a mean value of 100 in a set of scores ranging from 90 to 300. Which other measure will the researcher report when describing central tendency in this data set? a. Median b. Mode c. Range d. Variance

ANS: A The median value is not affected by extreme scores and should also be reported. The mean is most affected by outliers in a study. In this case, the mean value is very close to values at one end of the scale and not toward the center, indicating that a normal curve is not present. The mode will describe the most frequent score. The range and variability will be reported, but do not describe central tendency.

33. A researcher collects scores measuring weight among school-age children who are in an obesity prevention program and notes that several students are morbidly obese with most students falling within or below the 85th percentile for weight. The scores from the morbidly N R I G B.C M obese children will affect whicUh mSeasuNre oTf centrOal tendency the most? a. Mean b. Median c. Mode d. All the above are affected equally.

ANS: A The mode and median are not as affected by outliers as is the mean. The other three statements are incorrect.

38. A researcher studying subjects who have pulmonary disease presents a data set to describe the different conditions the subjects experience and reports the following data. Which number represents the mode for this data set? Asthma 4 COPD 6 Chronic bronchitis 4 Pulmonary hypertension 7 a. 4.0 b. 5.25 c. 6.5 d. 7.0

ANS: A The mode is the number that occurs most frequently in a data set. In this case, there are two groups of 4, so 4 is the mode. The other three statements are incorrect.

43. A researcher is analyzing the following data set. Which value represents the range? a. 43 b. 46 c. 46 d. 57 e. 67 f. 69 g. 78 a. 35 b. 46 c. 57 d. 58

ANS: A The range represents the difference between the lowest and the highest scores. 46 is the mode, or the most frequently recorded value. 57 is the median, or the data point in the middle of all the data when they are placed in order. 58 is the mean, or the average number of all the data.

26. In a study to examine motivational techniques to help adolescent smokers to quit smoking, the null hypothesis states that the intervention will have no effect on this population. The researcher establishes a level of significance of 0.01. When analyzing the data, the researcher concludes that there is a significant difference between subjects receiving the intervention and those who do not. In this study, a type I error means there is a a. 1% chance that the conclusion is wrong. b. 1% chance that the conclusion is correct. c. 99% chance that the conclusion is wrong. d. 99% chance that the null hypothesis is correct.

ANS: A Type I error occurs when the null hypothesis is rejected when it is actually correct. A significance of 0.01 indicates a 1% chance that the null hypothesis is correct when it is rejected. There is a 99% chance, in this study, that the conclusion is correct and the null hypothesis is incorrect.

1. Which of the following are true statements about the research outcome addressing implications for nursing'? Select all that apply. a. Implications for nursing are the meanings of conclusions from scientific research for the body of nursing knowledge. b. Implications for nursing include replications or repeating the design with a different or larger sample using different measurement methods. c. Implications for nursing include the formation of hypotheses to further test the framework in use. d. Implications for nursing are restrictions or problems in a study that may decrease the generalizability of the findings. e. Implications for nursing provide specific suggestions for implementing the findings in nursing.

ANS: A, E Implications for nursing are the meanings of conclusions from scientific research for the body of nursing knowledge. Implications are based on but are more specific than conclusions; they provide specific suggestions for implementing the findings in nursing. Recommendations for further study may include replications or repeating the design with a different or larger sample, using different measurement methods, or testing a modified or new interventions. Recommendations may also include the formation of hypotheses to further test the framework in use. Limitations are restrictions or problems in a study that may decrease the generalizability of the findings. Study limitations often include a combination of theoretical and methodological weaknesses.

47. A data set is found to approximate a normal curve and has a mean of 72.5 and a standard deviation of 10.8. In which range of numbers will 99% of the scores fall? a. 35.8 - 112.6 b. 44.6 - 100.4 c. 51.3 - 93.7 d. 61.7 - 83.3

ANS: B

54. A review of demographic data shows that mothers with higher levels of education have fewer children. This represents which type of relationship? a. Asymmetrical b. Negative c. Positive d. Symmetrical

ANS: B A negative relationship exists when higher scores of one variable are correlated to lower scores of another. Asymmetry refers to skewness in the data set. In a positive relationship, high scores on one variable are correlated to high scores on another variable. Symmetrical means that the analysis given no indication of the direction of the relationship.

55. A review of demographic data shows that mothers with higher levels of education have fewer children. In this example, the r value is likely to be a. =0. b. <0. c. >0. d. not definable.

ANS: B A perfect negative correlation is -1. A perfect positive correlation is +1. Negative correlations are less than zero and positive correlations are greater than zero. The other three options are incorrect statements.

21. A researcher studies the effects of a nursing intervention on a desired patient outcome and discovers a statistically significant difference between groups receiving the intervention and those not receiving the intervention. The researcher concludes that the intervention is effective. This researcher has made a a. generalization. b. statistical inference. c. type I error. d. type II error.

ANS: B A statistical inference is made from the study findings obtained from a specific sample and applied to the target population. Generalizations are made when information gained from a specific instance is generalized to the general population. A type I error occurs when a researcher incorrectly states that something is significant when it is not. A type II error occurs when a researcher declares the null hypothesis to be true when it is not.

61. A researcher conducts an experimental study on patients at different outpatient clinics, including clinics in inner city, suburban, and rural locations. To help ensure that differences in scores are not related to clinic location, the researcher will apply which technique? a. ANOV A b. ANCOV A c. Bivariate correlation analysis d. Factor analysis

ANS: B Analysis of covariance, or ANCOVA, is used to examine the effect of a treatment apart from the effect of one or more potentially confounding variables, such as clinic location. ANOVA is used to examine differences among three or more groups and tests for difference in variance. Bivariate correlation measures the extent of relationship of two variables. Factor analysis examines interrelationships among large numbers of variables to identify clusters of variables most closely linked.

19. Which of the following is not one of the components of power analysis? a. Effect size b. Error type c. Power d. Sample size

ANS: B Error type is not a component of power analysis. Cohen identified four parameters of a power analysis: the level of significance, sample size, power, and effect size.

2. A reviewer reads a research report and notes that the number of subjects in the original sample is larger than the number in the final analysis. Besides attrition of subjects, this discrepancy is likely because a. data from the control group are not included in the analysis. b. essential data is missing from subjects no longer included. c. subjects producing outlying data have been excluded from the results. d. the final analysis usually discusses data from the experimental group only.

ANS: B If enough data are missing for certain variables, researchers may have to exclude analyses using these variables and may sometimes have to exclude some subjects from data analysis. The analysis discusses data from both the experimental and the control groups. Outlying data are not excluded from study results; such data must be discussed. A final analysis will discuss data from both the experimental and control group.

16. In a discussion that includes the analysis of data collected during a pilot study, the researcher discusses the relationships and differences in data sets and makes predictions based on this analysis. The researcher will use which process? a. Descriptive analysis b. Inferential analysis c. Reliability testing d. Validity testing

ANS: B Inferential analysis techniques focus on relationships and differences in data, along with predictions based on the data. Descriptive analysis is used to examine all the data descriptively and to identify variation among data and whether outliers exist. Reliability and validity testing are measures used to evaluate whether measurement tools are effective.

18. When critically appraising a study, the researcher understands that the data analysis process involves the management of numerical data and the statistical analysis of these data to produce study results. Which statement is true regarding the steps of the data analysis process? a. Researchers always use computers for data analysis. b. Researchers present as complete a picture of the sample as possible in their report. c. Researchers need to report the validity of the measurement methods used in their study. d. Researchers typically do not indicate whether outliers are identified during data analysis.

ANS: B Researchers present as complete a picture of the sample as possible in their research report. Except in very small studies, researchers almost always use computers for data analyses. Researchers need to report the reliability of the measurement methods used in their study. Researchers usually indicate whether outliers are identified during data analysis and how these were managed.

4. A researcher identifies that 2 subjects in an experimental group had scores like those in the control group, while the other 20 experimental group subjects had scores far different from those in the control group. The researcher would consider the scores for the two subjects as a. control group findings. b. outlier scores. c. unexpected findings. d. ungrouped participants.

ANS: B Subjects with extreme values that seem unlike the rest of the sample are called outliers. Subjects who receive the experimental group intervention remain part of the experimental group regardless of their scores. Unexpected findings can occur with or without outliers. Subjects can be grouped into categories or not; the process may highlight outliers, but would not define them.

28. In a data set that has a normal distribution what percent of scores will be within two standard deviations above or below the mean? a. 34 b. 68 c. 95 d. 99

ANS: C In the normal curve, 95% of the scores will be within two standard deviations above or below the mean. The other three statements are incorrect.

50. Which is true about a Z-score? a. It identifies the confidence interval for a group of data. b. It is a method for calculating variance. c. It is a standardized score used when data measures use different scales. d. It represents the median data point in any set of data.

ANS: C When study results use different scales to report data, it is necessary to standardize the scores into a more general meaning. This standardized score is a Z-score. The Z-score does not identify the confidence interval, variance, or median.

17. A nurse conducts a study to evaluate the likelihood that single adolescent mothers will breastfeed their newborn infants if they are given materials about the benefits of breastfeeding. The results show a P value of .18. The nurse may conclude that a. the value is too low to be able to draw meaningful conclusions. b. there is an 18% probability that this population will breastfeed their infants. c. there is an 18% probability that this population will not breastfeed their infants. d. there is an 82% probability that this population will breastfeed their infants.

ANS: B The P value expresses the probability that an event will occur. In this case, the P value is .18, or 18%, and the researcher can predict this probability based on study results. The P value does not have a required range of value to be considered relevant. The P value expresses the probability that an event will occur. In this case, the P value is .18, meaning that there is an 18% chance that adolescent mothers will breastfeed their infants.

46. A researcher has calculated a variance of 9 for a data set. What is this data set's standard deviation? a. 1 b. 3 c. 4 d. 5

ANS: B The variance is the standard deviation squared. The square root of 9 is 3. The other three options are incorrect.

12. The analysis of a nondirectional hypothesis is called a a. one-tailed test of significance. b. two-tailed test of significance. c. three-tailed test of significance. d. no-tailed test of significance.

ANS: B With nondirectional hypotheses, researchers assume that an extreme score can occur in either tail of the normal curve. The analysis of a nondirectional hypothesis is called a two-tailed test of significance. In a one-tailed test of significance, the hypothesis is directional, and extreme statistical values that occur in a single tail of the curve are of interest. The other two options are incorrect.

56. A researcher calculates a Pearson product-moment coefficient of 0.2. The reviewer understands that this value represents a. a moderate positive correlation. b. a moderate negative correlation. c. a weak positive correlation. d. a weak negative correlation.

ANS: C A r value between -0.3 and +0.3 is considered to indicate a weak relationship. A positive number indicates a positive relationship, so this value is a weak positive correlational value. The other three options are incorrect statements.

52. A researcher wishes to display scores representing the relationship between two variables. Which will the researcher use? a. Grouped data table b. Pie chart c. Scatterplots d. Z-score

ANS: C A scatterplot may be used to illustrate the relationship between variables and will show either a negative or positive relationship. Grouped data tables and pie charts show the frequency of data. The Z-score is a standardized score calculated to compare data when measures use different scales.

51. A researcher presents data to examine the relationship between income and weight and uses a scatterplot to display the results. The researcher places income level intervals along the vertical line in the graph. The reviewer knows that a. data about income represent the independent variable. b. income data are presented along the X axis. c. the plot will show whether the relationship is negative or positive. d. weight values will occur along the Y axis.

ANS: C A scatterplot may be used to illustrate the relationship between variables and will show either a negative or positive relationship. This is correlational data; neither variable is independent. The Y axis is the vertical axis.

27. A researcher develops a study to examine the effects of Keep Yourself Safe Screening (KYSS) on the incidence of intimate partner violence (IPV). The study level of significance is 0.05. The null hypothesis, that KYSS will have no effect on IPV, is found to be true. When reviewing the study for type II errors, the reviewer understands that a. a level of significance of 0.01 would decrease the risk of a type II error. b. the level of significance does not affect the chance of a type II error. c. there is a 5% chance that the null hypothesis is false. d. there is a 5% chance that the null hypothesis is true.

ANS: C A type II error occurs when the null hypothesis is regarded as true but is actually false. A level of significance of 0.05 indicates a 5% chance of a type II error. The risk of a type II error increases when the level of significance is less. A level of significance of 0.05 indicates a 5% chance of a type II error that occurs when the null hypothesis regarded as true but is actually false but does not affect the likelihood that the null hypothesis is true or false.

60. Which circumstance will call for the use of analysis of variance (ANOVA)? a. A researcher wishes to compare differences in means between four groups. b. A researcher wishes to compare the difference in variance between two groups. c. A researcher wishes to compare the difference in variance among four groups. d. A researcher wishes to compare the difference in correlation between two groups.

ANS: C ANOVA is used to examine differences among three or more groups and tests for difference in variance. ANOVA does not test differences in means. ANOVA is used to examine differences among three or more groups. ANOVA does not examine differences in correlation.

53. Which is true about a correlational analysis technique? a. It is most desirable for small samples with homogeneous scores. b. It is used to determine cause and effect among sets of variables. c. It measures the relationship among variables. d. It usually involves comparing data from two subjects.

ANS: C Correlational analysis techniques are used to measure the relationship among variables. These techniques are most desirable with large, heterogeneous samples. Correlational analysis does not determine cause and effect. Correlational analysis occasionally compares data from two subjects.

30. The concept of degrees of freedom refers to a. the level of significance for a study. b. the standard deviation from the mean among data. c. the variability of a given score based on other scores. d. whether statistical analysis is one- or two-tailed.

ANS: C Degrees of freedom involve the freedom of a score value to vary given the other existing scores. Degrees of freedom do not directly affect the level of significance, standard deviation, or tailedness.

11. What is the purpose of using exploratory analysis in a research report? a. To compare control and experimental groups b. To develop testable hypotheses c. To examine and describe data d. To identify theoretical constructs

ANS: C Exploratory analysis is used to examine all the data descriptively and to identify variation among data and whether outliers exist. Statistical analysis is used to compare control and experimental groups, as well as to develop testable hypotheses. Theoretical constructs are discussed in the theoretical framework.

13. An important goal of inferential statistical analysis is to a. analyze and describe data collected during a study. b. determine whether theoretical constructs are valid. c. generalize results from the study to the target population. d. measure the reliability and validity of measurement tools.

ANS: C Inferential statistical analysis is performed for generalizing findings from the study sample to appropriate accessible and target populations. Descriptive data analysis is performed to analyze and describe data collected during a study. Inferential statistics are not performed to determine the validity of theoretical constructs. Other analyses are conducted to examine the reliability and validity of measurement tools.

58. Clinicians now can calculate a person's myocardial infarction risk by evaluating several known risk factors, such as cholesterol levels and diabetes. This is possible because of a. bivariate correlation analysis. b. factor analysis. c. multiple regression analysis. d. simple linear regression analysis.

ANS: C Multiple regression analysis is used to analyze study data that include two or more independent variables to predict the value of one variable when the value of the independent variables is known. Bivariate correlation measures the extent of relationship of two variables. Factor analysis examines interrelationships among large numbers of variables to identify clusters of variables most closely linked. Simple linear regression analysis is used when one independent variable is used to predict a dependent variable.

62. In a study comparing weight gain between small-for-gestational-age (SGA) infants who were breastfed and SGA infants who were fed formula, researchers noted increased weight gain in infants who were held more regardless of how they were fed. This finding is an example of a a. mixed result. b. nonsignificant result. c. serendipitous result. d. significant result.

ANS: C Serendipitous, or unexpected results, are relationships found between variables that were not hypothesized and not predicted prior to beginning the study. Mixed results occur when some but not all predicted relationships are demonstrated. Nonsignificant results are negative results, indicating only that the study failed to find a significant relationship. Significant results are results that statistically show a significant difference among variables and which help to build a body of knowledge.

20. In statistical analysis of data, the alpha value is used to a. describe the degree of generalizability of the findings. b. determine the risk of a type I error. c. reveal whether the P value meets criteria for statistical significance. d. speculate on the frequency distribution of study values.

ANS: C The alpha, or the level of statistical significance, is the probability level at which the results of statistical analysis are judged to indicate a statistically significant difference between the groups. The alpha value does not address generalizability of findings. The P value is used to calculate the probability of a type I error. The normal curve provides information on the frequency distribution of study values.

45. Which is true about the variance for scores in a data set? a. A larger variance value usually indicates a smaller dispersion of scores. b. It can be calculated for nominal scores. c. The calculated score has no absolute value. d. The variance indicates the range of scores.

ANS: C The calculated variance value has no absolute value and can be compared only with data obtained using similar measures. A larger variance value usually indicates a greater dispersion of values. Variance can only be calculated for nominal and ratio level of measurement. The variance indicates the spread or dispersion of the scores, not the range.

8. An appropriate level of significance for nursing research is either a. 0.5 or 0.1. b. 0.03 or 0.003. c. 0.05 or 0.01. d. 0.005 or 0.001.

ANS: C The level of significance selected for most nursing studies is 0.05. In some studies, the more rigorous level of significance of 0.01 may be chosen. The other three options are incorrect: 0.5 or 0.1 values are too high. 0.03 or 0.003 values are not generally accepted levels of significance. 0.005 or 0.001 values would be too rigorous.

40. What is the mean value in the following set of scores? a. 128 b. 128 c. 130 d. 135 e. 144 a. 128 b. 130 c. 133 d. 132.8

ANS: C The mean is the average of the scores, or the sum of all scores divided by the number of scores. 128 is the mode. 130 is the median.

39. A researcher collects the following scores on a set of ranked data. Which is the median score? a. 2 b. 5 c. 6 d. 7 e. 10 f. 15 g. 18 h. 21 a. 7 b. 10 c. 8.5 d. 10.5

ANS: C The median score is the midpoint score in a data set. In an even number of scores, the midpoint is calculated by averaging the two central scores. In this case, 7 + 10 = 17/2 = 8.5. All other options are incorrect.

29. A researcher conducts a power analysis for a study in which there was no difference between control and experimental group scores and identifies a power level of 0.75 and a level of significance of 0.05. What will this researcher do? a. Alter measurement methods to detect larger changes in scores. b. Conclude that the null hypothesis is true. c. Consider repeating the study using a larger sample. d. Lower the level of significance to 0.01.

ANS: C The minimum acceptable power level is 0.80. To improve this, a larger sample size may be necessary. Because the level of power is too low, the researcher cannot draw valid conclusions about the data. Measurement methods that measure large changes decrease the effect size, which decreases the power. The level of significance does not indicate whether the null hypothesis is true or false, merely the probability of making an error in judging whether it is true or false. Lowering the level of significance lowers the power.

49. A researcher analyzes scores from two studies in which patients' temperatures were measured after antipyretic medications are given. One study measures temperatures in centigrade and the other in Fahrenheit. The researcher will a. calculate standard deviationUmeSasuNresTfor eachOstudy using their scale values. b. compile all data regardless of scale and calculate measures of central tendency. c. determine a Z-score and then calculate measures of central tendency. d. realize that studies using different measures cannot be compared.

ANS: C When study results use different scales to report data, it is necessary to standardize the scores into a more general meaning. This standardized score is a Z-score. Standard deviation measures are used to assess the range of scores within a data set, but are not useful when analyzing data from two data sets. Compiling all data regardless of scale will not allow accurate comparison and analysis of the data. Comparing data from studies with different scales of measurement does not yield meaningful data.

22. When comparing a study with a level of significance of 0.05 with a study having a level of significance of 0.01, the researcher knows that the study with the level of significance of 0.05 is more likely to have a a. correct null hypothesis. b. generalizable finding. c. type I error. d. type II error.

ANS: C There is a greater risk of a type I error with a 0.05 level of significance than with a 0.01 level of significance. A type I error carries a greater risk of rejecting a null hypothesis when it is true, but does not increase the likelihood of a correct null hypothesis. The type I error does not affect the generalizability of the findings. There is a greater risk of a type II error with a 0.01 level of significance than with a 0.05 level of significance.

2. Which statements would the nurse researcher recognize as being true when using descriptive statistics? Select all that apply. a. The researcher might see analysis techniques identified as parametric or nonparametric. b. Descriptive statistics are conducted to examine relationships, make predictions, and determine causality or differences in studies. c. Descriptive statistics allow researchers to organize numerical data in ways that give meaning and facilitate insight. d. Measures of central tendency that are commonly used in statistical analyses are the mode, median, and margin. e. Researchers report descriptive statistics in tables and in the narrative of the results section of their study.

ANS: C, E Descriptive statistics allow researchers to organize numerical data in ways that give meaning and facilitate insight. In any study in which data are numerical, data analysis begins with descriptive statistics. Researchers report descriptive statistics in tables and in the narrative of the results section of their study. Descriptive statistics are conducted to describe the sample and study variables. Analysis techniques identified as parametric or nonparametric are used in inferential statistics. Inferential statistics are conducted to examine relationships, make predictions, and determine causality or differences in studies. Measures of central tendency include the mode, median, and mean.

7. A researcher evaluates the internal consistency (reliability) a newly developed scale used in a pilot study and notes a Cronbach alpha coefficient of space 0.72. The researcher will a. compare the measure with scores from another group of subjects. b. test the scale for validity prior to using it in another study. c. try another measure with better reliability in another pilot study. d. use the scale in the larger study and continue to monitor coefficient results.

ANS: D A Cronbach alpha score of 0.80 to 0.90 indicates that the measure is sufficiently reliable to use in a study, although a value of 0.70 is considered acceptable. The researcher should use the scale with the larger group and monitor this value. It is not necessary, at this point, to compare the measure with scores from another group of subjects. It is not necessary to test the scale for validity prior to using it again. This scale should be used and does not need to be discarded for another scale.

24. In research, the probability that any data score will be within a certain range of a mean value is calculated based on the theory of a. frequency. b. inference. c. levels of significance. d. the normal curve.

ANS: D A normal curve is a theoretical frequency distribution of all possible values in a population, with a 95% probability that any value from that population will fall within 2 standard deviations of the mean. Frequency refers to the number of times a specific value occurs. A statistical inference is made from the study findings obtained from a specific sample and applied to the target population. Levels of significance is a value indicating the chance that values are from different groups when the value of one group is not within the range of values of another group.

25. A researcher plans to apply a one-tailed test of significance when analyzing data from a study. Which is true about using this test? a. The researcher will be unable to predict whether differences are greater than or less than the mean value. b. This is a nondirectional hypothesis, so values will not tend to vary in a specific direction. c. This may increase the possibility of a type I error when evaluating the significance of the findings. d. This will decrease the possibility of a type II error when drawing conclusions about the data.

ANS: D A one-tailed hypothesis means that the data tend to vary in a certain direction. One-tailed statistical tests are uniformly more powerful than two-tailed tests and decrease the possibility of a type II error. A one-tailed hypothesis increases a study's power and improves the ability to predict outcomes. A one-tailed test is a unidirectional hypothesis, with values tending to vary in a specific direction. A one-tailed test does not increase the chance of a type I error.

36. When a data set has a normal distribution curve, which statement is true about the data? a. The mean is the lowest value. b. The median is the highest value. c. The mode is the central value. d. The mode, median, and mean are equal values.

ANS: D In a normal distribution curve, the mode, median, and mean are equal. The other three statements are incorrect.

32. Assuming a normal distribution, what range of numbers would include two thirds of the scores if they ranged from 50 to 99, M = 75, and SD = 5? Between a. 55 and 95 b. 65 and 85 c. 68 and 82 d. 70 and 80

ANS: D In the normal curve, 68% of scores will be within 1 standard deviation above or below the mean. In the example, two thirds of scores (66%) fall between 70 and 80. The mean = 75 and the SD = 5 for this sample. It follows that scores will fall between 1 standard deviation below (75 - 5 = 70) and 1 standard deviation above the mean (75 + 5 = 80). The other three statements are incorrect.

1. Which situation will involve the use of inferential statistics? a. A comparison of independent variables in a quasi-experimental study b. A discussion about demographic data c. An analysis of demographic variables of the target population d. An examination of the differences between control and experimental group scores

ANS: D Inferential statistics are designed to address objectives, questions, and hypotheses in studies to allow inference from the study sample to the target population. These statistics are used to identify relationships, examine predictions, and determine group differences. Descriptive statistics are used as summary statistics to organize data and are used to describe the sample or key variables.

5. It is important to know the demographic variables among study subjects to a. calculate central tendency and standard deviation of study scores. b. ensure that control and experimental subjects are different. c. ensure that outcomes are not caused by independent variables. d. understand how well the sample represents the target population.

ANS: D One goal of analyzing demographic variables in a study to make sure that the sample population is representative oNf the target population so that findings may be generalized to the larger population. Demographic variables are not used to calculate central tendency and standard deviation of study results. Researchers evaluate demographic variables in experimental studies to ensure that the groups are similar so that outcomes can be related to the independent variables and not to population differences.

59. What is true about the Chi-square test of independence? a. Chi-square test of independence results are important calculations in most studies. b. In a relatively small sample size, the Chi-square test of independence can reduce the chance of a type II error. c. The Chi-square test of indeUpenSdenNce isTa powOerful test used to examine differences in studies with two subjects. d. The Chi-square test of independence is used to determine whether two variables are related or independent.

ANS: D The Chi-square test of independence determines whether two variables are independent or related. This test is relatively unimportant in most studies and is not a powerful test. Large sample sizes are necessary to reduce the chance of a type II error.

37. Which describes the mode of a data set? a. The appropriate measure of central tendency for interval data b. The appropriate measure of central tendency for ordinal data c. The exact center of scores for nominal data d. The score value occurring with greatest frequency

ANS: D The mode represents the score that occurs with greatest frequency in a data set. The mode is the appropriate measure of central tendency for nominal data, not for interval or ordinal data.

44. Which is true about the measure of a data set's range? a. It is an average score. b. It is calculated using central scores. c. It is determined only for interval-level data. d. It is sensitive to outliers in a data set.

ANS: D The range represents the difference between the lowest score and the highest score and is sensitive to any outliers that may occur far from the scores clustered in the middle. It is determined using any type of data, not just interval-level data.

34. A researcher will present demographic data about ethnicity, gender, and diagnoses about a study population using which method? a. Continuous frequency distribution b. Grouped frequency distribution c. Percentage frequency distribution d. Ungrouped frequency distribution

ANS: D Ungrouped frequency distribution tables are used to present categorical data, such as demographic data, when categories are discrete. Continuous data are presented using grouped data tables. Ungrouped frequency distribution tables are used to present categorical data, such as demographic data, when categories are discrete. A percentage distribution indicates the percentage of subjects who fall into a category and is often used when comparing scores from findings with other data samples.

6. What statement is accurate about decision theory in understanding the statistical analysis process? a. The level of significance falls within a range based on the degrees of significance. b. It assumes that the groups in a study used to test a hypothesis are components of different populations relative to the variables under study. c. It is used to explain the extent of a relationship, the probability that an event will occur in each situation, or that an event can be accurately predicted. d. It requires that the cutoff point selected for a study be absolute.

ASN: D Decision theory requires that the cutoff point selected for a study be absolute. Absolute means that even if the value obtained is only a fraction above the cutoff point, the samples are considered to be from the same population, and no meaning can be attributed to the difference. The level of significance is dichotomous, meaning that the difference is significant or not significant; there are no "degrees" of significance. Decision theory also assumes that all of the groups in a study used to test a particular hypothesis are components of the same population relative to the variables under study. Probability theory is used to explain the extent of a relationship, the probability that an event will occur in a given situation, or that an event can be accurately predicted.