Applied Statistics From Bivariate Through Multivariate Techniques 2nd Edition Warner - Test Bank

Chapter 3: Statistical Significance Testing Multiple Choice 1. Of the following, which is not an issue in null hypothesis significance testing logic: a. disconfirmatory evidence b. convenience sampling c. the likelihood the null hypothesis is correct d. probability of obtaining a value larger than observed Ans: c 2. Failing to reject the null hypothesis when it is true is: a. a Type I error b. a Type II error c. a correct decision d. an incorrect decision Ans: c 3. Which value is used to determine the nominal confidence level: a. α b. β c. μ d. σ Ans: a 4. Which value is used to determine statistical power: a. α b. β c. μ d. σ Ans: b 5 A researcher assumes the average depression score among college students is 44 on a scale from 0 to 100. In his convenience sample, he believes the average depression score is 58. The estimated average in his sample is the researcher’s: a. null hypothesis b. research hypothesis c. population mean d. sample standard deviation Ans: b 6. A researcher assumes the average depression score among college students is 44 on a scale from 0 to 100. In his convenience sample, he believes the average depression score is 58. This is a: a. cutoff value b. non-directional test c. one-tailed test d. two-tailed test Ans: c 7 According to the American Psychological Association, the best way to represent significance levels in tables is by: a. exclamation points b. superscripted letters c. highlighting the significant values d. asterisks Ans: d 8. Which is not an assumption of null hypothesis significance testing: a. random sampling b. dependent observations c. representative sample d. quantitative measurements Ans: b 9. Which is a possible reason a test result could be statistically nonsignificant: a. detectable relationship b. reliable and valid measure c. adequate statistical power d. small effect size Ans: d 10.What would be a possible reason a test result could be stastistically significant with no true effect: a. there is no relationship between the independent and dependent variables b. the measures are unreliable c. experimenter expectancies d. adequate sample size Ans: c 11. Cohen’s d is: a. a measure of effect size b. a test to determine significance c. an estimate of the standard error d. the difference between the hypothesized mean and the actual mean Ans: a 12. Statistical power is the probability of: a. obtaining a test statistic large enough to reject H0 when H0 is true. b. obtaining a test statistic large enough to reject H0 when H0 is false. c. obtaining a test statistic to accept H0 when it is true. d. rejecting a test statistic Ans: b 13. Statistical power is not dependent upon the: a. sample size b. effect size c. population mean d. nominal alpha level Ans: c 14. The advantage of using Cohen’s d is that it provides a difference in group means based on the: a. standard deviation of the scores. b. units of measurement for the scores. c. variance of the scores. d. outliers of the scores. Ans: a 15. Rejecting the alternate hypothesis when it is true is: a. Type I error b. Type II error c. a correct decision d. an incorrect decision Ans: b True/False 1 An educated guess the researcher makes about the population mean is a test hypothesis. Ans: False 2. A researcher commits a Type II error by rejecting the null hypothesis when the null hypothesis is actually true. Ans: False 3. It is okay to change the nominal alpha level after the calculations are completed. Ans: False 4. It is inappropriate to interpret a nonsignificant result as “acceptance” of the null hypothesis. Ans: True Short Answer 1.Failing to reject the null hypothesis when it is false is called a _________. Ans: Type II error 2. The probability of rejecting the null hypothesis when it is true is_______. Ans: alpha (α) 3. A self-rated health scale has a known mean of 5 and a known standard deviation of 1.6. In a sample of 24 adults, the mean is 6.7 and the standard deviation is 0.8. What is the 95% confidence interval of the population mean? Ans: {4.36, 5.64} 4. A self-rated health scale has a known mean of 5 and a known standard deviation of 1.6. The researcher believes self-rated health is lower in his sample. In his sample of 24 adults, the mean is 6.7 and the standard deviation is 0.8. Should the researcher reject the null hypothesis? Ans: No, the researcher should not reject the null hypothesis. 5. When would you use a t test instead of a z test? Ans: When the population standard variance is unknown . Essay 1. Define the purpose of null hypothesis significance testing. Ans: Assume a value for the population mean. Evaluate the sample mean. Determine if the sample mean would occur by chance alone. If the sample mean is unlikely to occur, reject the assumed value of the population mean. 2. List ways to limit the risk of a Type I error. Ans: Use random and representative samples, do not change α and β after analyses, limit the number of significance tests, use Bonferroni-adjusted alphas for multiple comparisons, and replicate the outcome in a new sample. Chapter 7: Bivariate Pearson Correlation Multiple Choice 1. Pearson’s correlation r of a bivariate data set is similar to the z-score in a univariate data set in that: a. both are unitless or standardized indexes which allow comparison of variables with different scales. b. like z, r can range from +∞ to -∞. c. r is also normally distributed with most values occurring between +2 and -2 standard deviations. d. lower scores have negative values (-) and higher scores have positive values (+). Ans: a 2. A positive correlation between two variables, X and Y, indicates that: a. as scores on X increase, scores on Y decrease b. as scores on X increase, scores on Y increase c. as scores on X decrease, score on Y increase d. no relationship between X and Y Ans: b 3. Which of the following correlations rxy represents the strongest possible relationship between X and Y: a. +0.50 b. +3.00 c. +.70 d. -.80 Ans: d 4. Which is not an assumption for Pearson’s r: a. aach score on X should be independent of other X scores b. scores on X and Y are quantitative. c. scores on X and Y are uniformly distributed d. scores on Y should be linearly related to scores on X Ans: c 5. The shape of a bivariate normal distribution is: a. a triangle b. a circle c. a rectangle d. an oval Ans: d 6. Which of the following is not true regarding preliminary data screening in correlation analysis: a. an extreme outlier can actually reduce the magnitude of r. b. an extreme outlier can actually increase the magnitude of r. c. curvilinear relationships almost always increase the magnitude of r. d. a lack of homogeneity of variance across X and Y can significantly reduce the magnitude of r. Ans: c 7. Which of the following is the formula to calculate Pearson’s r: a. ∑ (Yij - Mi)2 b. ∑ (zx * zy) / N c. (N - μ) / σ d. Cov (X,Y) Ans: b 8. Pearson’s r can also be considered as: a. a measure of how much values differ in a sample b. the size of a typical value c. the number of independent pieces of information d. a unit-free measure of covariance Ans: d 9. The null hypothesis that tests a lack of a linear relationship is: a. H0 : ρxy = 0 b. H0 : ρxy ≠ 1 c. H0 : rxy = 0 d. H0 : rxy ≠ 1 Ans: a 10. Which is true of the sampling distributions for r: a. when the population correlation ρxy = 0, the sample distribution is positively skewed. b. when the population correlation ρxy nears 1, the sample distribution is negatively skewed. c. the sampling distribution is normally distributed ranging from -∞ to +∞. d. as the sample size increases, the distribution becomes normal across all values of ρxy. Ans: b 11. The test statistic for the null hypothesis in bivariate correlation is: a. F = r2 / (1 - r2) b. t = ρxy / SEr c. t = (r - ρ0) / SEr d. q = (Ma - Mb) / √ (MSwithin / n) Ans: c 12. Which is not a problem when comparing correlations involving different populations or different variables: a. restricted range of X or Y scores in either group. b. differences in reliability of measures between comparison groups. c. the covariances between X and Y may be different in comparison groups. d. variables may have different levels of homogeneity between comparison groups. Ans: c 13. Which is true regarding the reporting of correlations in research journals: a. researchers tend to run too few correlations thereby under-evaluating their data. b. cross-validation procedures tend to inflate the risk of Type I errors. c. use of a Bonferroni correction reduces the values of r thereby masking the true value. d. researchers should use theory or previous research to determine which correlations to analyze. Ans. :d 14. Data points in bivariate correlation are concordant if: a. both zx and zy are positive or both are negative. b. zx is positive and zy is negative. c. zx is negative and zy is positive. d. zx and zy have no correlation. Ans.:a 15. A spurious correlation can be a result of: a. a mediating effect where X causes Z and Z causes Y. b. an interaction effect where the correlation of X and Y differ on categorical levels of X. c. random variations between X and Y. d. restricted range where X and/or Y have limited variability. Ans. :b True/False 1. The sign of r provides information about the strength of the relationship between X and Y. Ans: False 2. Pearson’s r is unit-free. Ans: True 3. It is appropriate to make a causal inference based on Pearson’s r alone. Ans: False 4. The standard error for Fisher Z depends on ρ and N. Ans: False 5. Restricting the range of potential answers limits the external validity of the study. Ans: True Short Answer 1. If X and Y are both categorical, Pearson’s r is called ________. Ans: a phi coefficient 2. What is meant by the fact that correlation is a symmetric index between X and Y? Ans: The correlation of X with Y is the same as the correlation of Y with X. 3. What is meant by “regression toward the mean” for correlations less than 1.0? Ans: The predicted score zy on the dependent variable is closer to the mean than the score of the zx independent variable. 4. Explain how effect size is determined in bivariate correlation. Ans: Effect size is the proportion of variance in Y that can be predicted from X which is calculated as rxy2. Essay 1. What happens to rxy when there is a curvilinear relationship and how can you remedy the problem? Ans: X and Y may be very strongly related if a curvilinear relationship exists but rxy will be small because correlation only measures linear relationship strength. One solution is to transform X or Y via a log or square root transformation. Better sampling techniques may also help if X and Y are truly correlated in the population. 2. If a significant correlation does not imply causation, what does it imply? Ans: Many reasons exist for the correlation of X and Y: 1) X may actually cause Y, 2) Y may cause X, 3) X may cause Z which in turn causes Y, 4) X may be confounded with Z which is related to Y, 5) X and Y may measure the same construct, and 6) X and Y may be correlated due to sampling error.