Ch. 13
The variable "number of lifetime hospitalizations" would be measured at which measurement level? Ordinal Ratio Interval Nominal
Ratio Rationale:The number of times a person has been hospitalized is a continuous variable with a rational zero and provides information about the absolute magnitude of the variable. Interval-level measures are continuous but do not have a rational zero. Ordinal measures involve rank ordering an attribute and do not have a rational zero. Nominal measures involve discrete categories—they are not continuous.
The preferred statistical index for estimating the test-retest reliability of a continuous measure is: Cohen's kappa. Pearson's r. the intraclass correlation coefficient (ICC). coefficient alpha.
the intraclass correlation coefficient (ICC). Rationale:When a continuous measure is administered to a sample twice to assess test-retest reliability, the index computed should be the intraclass correlation coefficient. Some researchers use Pearson's r to correlate scores obtained at two points in time, but it is not the preferred index. Coefficient alpha is the index used to estimate internal consistency reliability, not test-retest reliability. Cohen's kappa is often used to estimate interrater reliability, not test-retest reliability.
In sampling distributions of the mean, the standard error of the mean gets smaller (estimates of the population mean get more accurate) as: the value of the mean gets smaller. the sample size gets larger. the number of samples used to construct the sampling distribution gets larger. the sample size gets smaller.
the sample size gets larger. Rationale:The larger the sample size, the more accurate are the sample means as estimates of the population mean. With smaller sample sizes, sample means are less accurate as estimates of the population mean. The value of the mean has no bearing on the magnitude of the standard error. Sampling distributions are not actually constructed; they are theoretical—there are no "samples" for constructing a sampling distribution.
Kathy obtained a score of 110 on a statistics test. Test scores for all students were normally distributed, with a mean of 100 and a standard deviation of 10. Approximately what percentage of students had a score lower than Kathy? Cannot be determined from the information provided 84% 68% 34%
84% Rationale:Kathy scored higher than about 84% of the students (50% had scores below the mean of 100, and 34% scored between the mean and 1 SD above it, i.e., between 100 and 110). Sixty-eight percent of the students scored between 1 SD below and 1 SD above the mean (i.e., between the scores of 90 and 110), but Kathy also scored higher than those who scored below 90. Thirty-four percent of the students scored between the mean and 1 SD above it (i.e., between the scores of 100 and 110), but Kathy's score was also higher than all those below the mean. It is possible to determine the approximate percentage of students that had scores lower than Kathy because the scores were normally distributed.
Which of the following distributions has the most peaks? A normal distribution A bimodal distribution A unimodal distribution An asymmetric distribution
A bimodal distribution Rationale:A bimodal distribution has two peaks (values with high frequencies). Unimodal distributions have only one peak. A normal distribution is unimodal. An asymmetric distribution might have more than one peak, but this is not necessarily the case.
A researcher wants to test the difference between the average weight of a sample of nursing home residents before and after a special nutritional intervention. Which of the following statistical tests should the researcher use? Chi-squared test A paired t-test An independent groups t-test Repeated measures ANOVA
A paired t-test Rationale:Weight is a ratio-level variable for which means can be computed, and the weights of the same people measured twice are being compared, which calls for a paired (dependent groups) t-test. The two sets of weight measurements are not independent because the same people are being measured twice, and so an independent groups t-test is inappropriate. There are only two sets of measurements, and so repeated measures ANOVA is not needed. Weight is a ratio-level variable for which means it can be computed and so the chi-squared test is not appropriate.
A researcher wants to test the differences in average length of stay in hospital for premature infants randomly assigned to four different methods of stimulation. Which of the following statistical tests should the researcher use? Repeated measures ANOVA ANOVA Independent groups t-test Chi-squared test
ANOVA Rationale:Length of stay in hospital is a ratio-level variable for which means it can be computed, and the mean lengths of stay of four different groups of infants are being compared. There is only one measurement (data point) for each infant, and so a repeated measures ANOVA is not appropriate. An independent groups t-test is not appropriate because there are more than two groups being compared. A chi-squared test is not appropriate because the outcome (average length of stay in hospital) is a ratio-level variable, not a nominal one.
Which of the following indexes involves a comparison of two risks? Absolute risk The SD Pearson's r Absolute risk reduction
Absolute risk reduction Rationale:The absolute risk reduction (ARR) is the difference between the risk for one group (e.g., an intervention group) and the risk for another (e.g., a control group). Absolute risk is simply the proportion of people in a group who experienced an undesirable outcome; there is no comparison involved. The Pearson correlation coefficient is not an index that describes risk; it summarizes the degree of relationship between two variables. SD is an acronym for standard deviation, an index that describes variability—not risk.
A researcher used ANCOVA to compare the mean depression scores of men and women in two different racial groups (African American and white), holding constant their age. Which variable is the covariate? Age Depression scores Sex Race
Age Rationale:The researcher held constant (covaried) the variable age, which was presumed to be a confounding variable in this example. Both sex and race were independent variables. Depression was the outcome variable.
If the known groups approach were used to validate a new measure through a comparison of the means of two groups, which of the following would be true? The researcher would compare the sensitivity and specificity of the new measure for two known groups. An independent groups t-test would be used to assess construct validity. The researcher would be assessing content validity. A chi-squared test would be used to assess construct validity.
An independent groups t-test would be used to assess construct validity. Rationale:Construct validation, which can involve a known-groups approach, is a hypothesis-testing endeavor for which an independent-groups t-test would be appropriate for continuous scores (means) and two groups. A chi-squared test could be used in a known groups validation but not to compare the mean scores of two groups. The known groups approach to construct validation does not involve the calculation of a measure's sensitivity and specificity. Content validity does not involve a known groups approach.
Which characteristic would be measured at the nominal level? Age Blood type Score on a depression scale Number of pregnancies
Blood type Rationale:A person's blood type would be "measured" by allocating the person to a mutually exclusive blood-type category (A, B, AB, O). The numbers associated with each nominal-level category (e.g., 1 = Type A, 2 = Type B) would have no quantitative meaning. The other attributes would be measured on an interval scale (score on a depression scale) or ratio scale (age and number of pregnancies).
What would be an example of a Type I error? Concluding that there are no posttreatment differences between groups when in fact there are real population differences. Concluding that there are posttreatment differences between groups when in fact real population differences do not exist. Concluding that there are no differences between two groups when in fact population differences do not exist. Concluding that there are differences between groups when in fact real population differences exist.
Concluding that there are posttreatment differences between groups when in fact real population differences do not exist. Rationale:A Type I error occurs when a researcher rejects a null hypothesis (i.e., concludes that group differences exist) when in fact group differences do not exist in the population. Concluding that there are no posttreatment group differences when there are population group differences is a Type II error. The other two options are not errors—the correct conclusions were drawn.
A nurse researcher developed a new self-report scale to measure cigarette consumption and calculated the correlation between scale scores and a gold standard, salivary cotinine levels using Pearson's r. What type of validity is being assessed? Face validity Criterion validity Construct validity Content validity
Criterion validity Rationale: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 cigarette consumption, salivary cotinine levels. Pearson's r is the appropriate statistical test in this situation. Content validity, face validity, and construct validity do not rely on a "gold standard" criterion.
What do correlation coefficients describe? Crosstabulations Direction and strength of relationships between two variables Central tendency of a distribution Variability of a distribution
Direction and strength of relationships between two variables Rationale:Correlation coefficients describe both the strength and the direction of a relationship between two variables, usually ones that are continuous variables. Crosstabulations describe relationships between nominal-level variables. Correlation coefficients do not describe central tendency or variability. Indexes of variability include the range and the standard deviation. Indexes of central tendency describe what is "typical" or average for one variable at a time and include the mean, the mode, and the median.
Which descriptive statistic is the arithmetic average in a distribution of scores? Mean Mode Median Range
Mean Rationale:The mean is the sum of all score values, divided by the total number of scores. The median is the point in a distribution above which and below which 50% of the cases fall. The mode is the value that occurs most frequently in a distribution. The range is an index of variability.
Which of the following distributions of normally distributed scores is most heterogeneous? Mean = 100, range = 12 Mean = 100, SD = 10 Mean = 100, mode = 100 Mean = 100, SD = 5
Mean = 100, SD = 10 Rationale:There is more variability of scores in the distribution in which the standard deviation (SD) is 10 than in the others. The range of scores in this distribution would be about 60—from -3 SD below the mean (i.e., 70) to +3 SD above it (i.e., 130). In the options where the range = 12 and the SD = 5, the distributions are more homogeneous. In the option that specified that the mode = 100, there is no information about variability.
Which index of central tendency is often used when variables are severely skewed? Mode Median Mean Range
Median Rationale:For variables that are skewed, the median provides a better indicator of what is "typical" than other indexes of central tendency. When a distribution is skewed, the mean tends to be biased in the direction of the skew. The mode is an unstable indicator and is rarely the best index of central tendency. The range is not an index of central tendency; it is an index of variability.
Logistic regression yields which of the following? F ratios An R2 CIs around the means Odds ratios
Odds ratios Rationale:In logistic regression, the outcome variable is dichotomous (e.g., compliant vs. noncompliant), and the results show the factor by which the odds change (e.g., the odds of compliance) for a unit change in each predictor. Logistic regression does not yield F ratio statistics or an R2. Logistic regression does yield confidence interval information—but around odds ratio (OR) values, not means.
Which of the following tests is not used to test differences between groups of people? t-Test ANOVA Chi-squared test Pearson's r
Pearson's r Rationale:Pearson's r is used to test whether the correlation between two continuous variables is significantly different from zero—group differences are not being tested. A t-test is used to test differences in two group means, and ANOVAs are used to test differences in three or more group means. The chi-squared test can be used to test differences in proportions between two or more groups.
In hypothesis testing, what is the actual procedure? Proving that the null hypothesis is incorrect Acceptance of the null hypothesis if data indicate it is probably wrong. Rejection of the null hypothesis if study data indicate that it is probably wrong Proving that the research hypothesis is correct
Rejection of the null hypothesis if study data indicate that it is probably wrong Rationale:Study data are used to determine whether a null hypothesis has a high probability of being incorrect. If data indicate the null hypothesis is probably wrong, it should be rejected, not accepted. It cannot be proved that a null hypothesis is or is not correct without obtaining data from the entire population.
A researcher wants to test differences in average heart rates in a group of premature infants at 2, 4, 6, and 10 hours after birth. Which of the following statistical tests should the researcher use? Paired t-test ANOVA Chi-squared test Repeated measures ANOVA
Repeated measures ANOVA Rationale:Mean heart rates for the same infants measured at four points in time are being compared, and so an repeated measures ANOVA is appropriate. There are four different measurements, and therefore, the two-measurement paired t-test is not appropriate. It would also not be appropriate to use regular ANOVA because the groups being compared are not independent—they are the same infants measured at four points over time. The dependent variable is a ratio-level variable and so a chi-squared test is not appropriate.
Which of the following is included in the steps of statistical hypothesis testing? Determining the sample size Interpreting the results Developing the research hypothesis Setting a level of significance
Setting a level of significance Rationale:The researcher must choose a criterion for accepting or rejecting a null hypothesis. This level is typically .05, but sometimes .01 is the criterion. Interpretation takes place after the hypothesis testing has yielded statistical results. Development of the hypotheses precedes hypothesis testing and does not occur as part of it. When hypothesis testing is underway, the sample size has already been determined—the sample has been selected and the data from that sample have been collected.
Multiple regression could be used to test which of the following? The effect of age and smoking status on patients' heart rates and blood pressure readings The effect of age and preoperative stress on presence versus absence of surgical complications The effect of age and preoperative stress levels on patients' heart rate The effect of preoperative stress levels on patients' heart rate
The effect of age and preoperative stress levels on patients' heart rate Rationale:In this situation, there are two independent variables (age and stress) and an outcome variable measured on a ratio scale (heart rate), and so multiple regression would be appropriate. In the situation of the effect of age and smoking on heart rate and blood pressure, there are two independent variables (age and stress) and multiple dependent variables (heart rate and two blood pressure readings). This is not a situation for multiple regression. In the situation of the effect of age and stress on the presence/absence of surgical complications, there are two independent variables (age and stress), but the dependent variable (complication status) is a nominal-level variable. Logistic regression analysis would likely be used. In this situation of the effect of stress on heart rate, there is only one independent variable (stress level) and one dependent variable (heart rate). A Pearson's r would likely be used.
What is a researcher's "level of significance" for a statistical test? The measurement level of key variables The level that a researcher accepts as the risk of committing a Type I error The level of clinical importance of a finding The level that a researcher accepts as the probability of committing a Type II error
The level that a researcher accepts as the risk of committing a Type I error Rationale:A researcher establishes a level of significance for a statistical test that sets the risk of committing a Type I error. If the criterion for a significance level of .05, the researcher accepts a risk that 5 times out of 100 a Type I error will be committed. Significance here is used in its statistical sense, not in the sense of clinical importance. The measurement level of a variable has no bearing on the significance level of a statistical test. The significance level is not a criterion for the researcher's risk of committing a Type II error.
Consider the following scores: 10, 20, 20, 30, 40, 50, 60. Which index of central tendency would have a value of 30? The mode The median The mean, the mode, and the median The mean
The median Rationale:In this example, the median is equal to 30—it is the value above which and below which 50% of the cases fall. The mode in this example is 20 (there are two values of 20), and the mean is 32.9 (230 ÷ 7 = 7.2).
Which of the following statements is true? A nonsignificant result means that the null hypothesis is true. The minimal accepted level of significance for most research is .05. Lowering the risk of a Type I error also lowers the risk of a Type II error. The risk of making a Type I error is greater with a .01 level of significance than with a .05 level.
The minimal accepted level of significance for most research is .05. Rationale:By convention, the probability of a Type I error that is greater than 5 out of 100 (e.g., .07) is considered too great a risk to be acceptable. A .01 level of significance (1 out of 100 chance of error) is more stringent than a .05 level (5 out of 100 chance), i.e., the risk is lower. A nonsignificant result means that no conclusion can be reached about the tenability of the null hypothesis. Lowering the risk of committing a Type I error actually increases the risk of a Type II error, all else equal.
A team of nurse researchers found that the scores on a health-related quality of life scale in their study were distributed from 30 to 70. Which of the following statements is true? The scores were normally distributed. The mean for this distribution was 50. The SD in this distribution was 10. The range for this distribution was 40.
The range for this distribution was 40. Rationale:The range is the highest score minus the lowest score in a distribution. In this example, 70 minus 30 equals 40. There is no way to tell, from the information provided, what the standard deviation for the distribution is, what the mean is, or whether or not the scores are normally distributed.
The 95% confidence interval around a sample mean of 50 is 45, 55. Which of the following statements is true? The lower limit of the 95% CI is 50. The point estimate for the population mean is variable. The population mean is 50. There is less than a 5% chance that the population mean is 60.
There is less than a 5% chance that the population mean is 60. Rationale:There is a 95% probability that the true population mean lies between 45 and 55, so there is less than a 5% chance that the population mean is really 60. The lower limit of the 95% CI is 45, not 50. The value of 50 is the point estimate of the population mean. There is no way to know the true population mean. The point estimate for the population mean is 50, and the interval estimate is between 45 and 55.
What is the purpose of multiple regression? To predict values of one variable based on values of a second variable To predict a nominal-level dependent variable on the basis of two or more predictor variables To predict a continuous dependent variable on the basis of two or more independent variables To predict values of covariates
To predict a continuous dependent variable on the basis of two or more independent variables Rationale:Multiple regression is a method of predicting a continuous dependent variable on the basis of two or more independent (predictor) variables—not just one predictor. Multiple regression is not used to predict covariates—variables in a multiple regression analysis are not called covariates, although multiple regression can be used to control confounding variables. It is logistic regression, not multiple regression, that is used to predict a nominal-level variable on the basis of two or more predictors.
Which of the following is true? In multiple regression, the outcome variable can be dichotomous. Values of R are never negative. The value of R is the same as the value of the F statistic in multiple regression. R2 indicates the proportion of variance in the independent variables explained by the outcome variable.
Values of R are never negative. Rationale:Values of R range from .00 to 1.00, indicating strength but not the direction of relationships. The value of R and the value of F would virtually never be the same. R2 indicates the proportion of variance in the outcome variable explained by the independent variables, not vice versa. If the dependent variable is dichotomous and there are multiple predictors, the appropriate analysis would be logistic regression.
The relationship between diastolic and systolic blood pressure would be described as: a positive relationship. a nonrelationship. a perfect relationship. a negative relationship.
a positive relationship. Rationale:As values for diastolic blood pressure increase, values for systolic blood pressure also tend to increase. There is a modest, positive relationship between diastolic and systolic blood pressure measurements. The relationship between the two blood pressure readings is not perfect; if it were perfect, it would be necessary to measure only one or the other. As values for diastolic pressure increase, values for systolic blood pressure do not tend to decrease, as would be the case with a negative relationship.
A sample is to a population as: a statistic is to a parameter. a crosstabs table is to a correlation matrix. nominal measurement is to ratio measurement. a skewed distribution is to a normal distribution.
a statistic is to a parameter. Rationale:A descriptive index (e.g., a percentage) from a sample is a statistic, whereas a descriptive index calculated from population data is a parameter. A similar analogy cannot be made between nominal and ratio measurement, crosstabs tables and correlation matrixes, or skewed and normal distributions.
A sampling distribution of the mean is: based on data values from a study sample. a theoretical, not an actual, distribution. created with the means from 5,000 samples. based on data values from a population.
a theoretical, not an actual, distribution. Rationale:No one actually constructs a sampling distribution of the mean; it is a theoretical distribution for a (hypothetical) infinite number of sample means and is used as a basis for inferential statistics. A sampling distribution is not based on actual data values from a sample or a population.
The relationship between nurses' gender and their specialty area could be described by using a: frequency distribution. correlation coefficient. correlation matrix. crosstabs table.
crosstabs table. Rationale:A crosstabs table is a two-dimensional frequency distribution that can be used to describe relationships between two nominal-level variables, such as gender and nurses' specialty area. A correlation coefficient describes relationships between two continuous variables—i.e., those measured on an interval or ratio scale. A frequency distribution is used to describe the distribution of a single variable. A correlation matrix presents correlations for multiple variables (three or more) measured on an interval or ratio scale—which is not the case in this example.
Which of the following is an effect size index? F t χ2 d
d Rationale:The d index is used to summarize the magnitude of an effect (e.g., of an intervention) in situations in which two group means are being compared. t is the statistic used to test the significance of difference of two groups means; it is not an effect size index. F is the statistic used to test the significance of difference of 3+ group means in an ANOVA context; it is not an effect size index. χ2 is the statistic used to test the significance of differences in proportions between groups; it is not an effect size index.
Power, the ability of a statistical test to detect true relationships: is considered adequate if it as least .50. reduces the risk of a Type I error. is greater when sample size increases. is reduced when sample size increases.
is greater when sample size increases. Rationale:The larger the sample, the greater the power of the statistical test, and the lower the risk of committing a Type II error. The most efficient way to increase power is to increase sample size. Type I errors are not a function of power. By convention, power is considered adequate if it is at least .80.
The distribution for the variable "Number of days hospitalized" in a large general hospital would most likely be: symmetrically distributed. normally distributed. negatively skewed. positively skewed.
positively skewed. Rationale:Most patients would be released within a few days of admission, and declining numbers would be released at longer intervals; the tail would point to the right. A negative skew would occur if most patients had extremely long hospital stays and smaller numbers were released at shorter intervals. It seems most plausible that the number of days hospitalized would be skewed rather than symmetrically (or normally) distributed.
Which correlation coefficient describes the strongest relationship? r = .63 r = -.72 r = .48 r = .00
r = -.72 Rationale:Even though -.72 is a negative correlation coefficient, it has the largest absolute value of the four options and therefore indicates the strongest relationship. A correlation of .63 describes the second strongest relationship and .48 is the third strongest. A correlation of .00 describes the total absence of a relationship between two variables.
