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Unit 10: Test of Association - Practice Quiz

DEMGN832 — Research Methodology 60 Questions
0 Correct 0 Wrong 60 Left
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1 What does a correlation coefficient primarily measure?

Correlation coefficient Easy
A. The strength and direction of a relationship
B. The total number of observations
C. The difference between two sample means
D. The frequency of the largest value

2 What is the usual range of a correlation coefficient?

Correlation coefficient Easy
A. to
B. to
C. to
D. to

3 What does a correlation coefficient of generally indicate?

Correlation coefficient Easy
A. A strong relationship that must be nonlinear and causal
B. No linear correlation
C. Perfect positive correlation
D. Perfect negative correlation

4 Which value indicates the strongest negative correlation?

Correlation coefficient Easy
A.
B.
C.
D.

5 Spearman rank correlation is mainly used with which type of data?

Spearman rank correlation Easy
A. Unordered nominal data
B. Data divided into many unrelated experimental groups
C. Ranked or ordinal data
D. Only continuous ratio data

6 Which symbol commonly represents Spearman's rank correlation coefficient?

Spearman rank correlation Easy
A.
B.
C.
D.

7 In the Spearman rank formula, what does represent?

Spearman rank correlation Easy
A. The difference between the original values and their sample mean
B. The total number of ranks
C. The mean of all ranks
D. The difference between paired ranks

8 If two sets of ranks are exactly the same, what is Spearman's rank correlation?

Spearman rank correlation Easy
A.
B.
C.
D.

9 Karl Pearson's correlation coefficient measures which kind of relationship?

Karl's Pearson correlation Easy
A. A linear relationship
B. A change in frequencies
C. Any relationship between several nominal categories
D. A difference in medians

10 Which symbol is commonly used for Karl Pearson's sample correlation coefficient?

Karl's Pearson correlation Easy
A.
B.
C.
D.

11 If Karl Pearson's correlation coefficient is , what does it indicate?

Karl's Pearson correlation Easy
A. A perfect relationship proving that one variable causes the other
B. A positive linear relationship
C. A negative linear relationship
D. No linear relationship

12 Which type of graph is commonly used to view a relationship before calculating Pearson's correlation?

Karl's Pearson correlation Easy
A. Scatter plot
B. Frequency polygon
C. Pie chart
D. A detailed organizational flowchart with several decision branches

13 Which test is commonly used to examine association between two nominal variables?

Test of association between nominal data Easy
A. Pearson correlation test
B. One-way analysis of variance
C. Paired-samples test
D. Chi-square test of independence

14 How are data commonly arranged when testing association between two nominal variables?

Test of association between nominal data Easy
A. In a stem-and-leaf plot
B. In a time-series graph showing repeated measurements over many years
C. In a contingency table
D. In a scatter plot

15 Which pair consists of nominal variables?

Test of association between nominal data Easy
A. Age and monthly income
B. Temperature and examination score
C. Height and body weight
D. Blood group and eye color

16 What is the null hypothesis in a test of association between two nominal variables?

Test of association between nominal data Easy
A. The variables are perfectly related
B. The category means are equal
C. The first variable directly causes every change observed in the second variable
D. The variables are independent

17 What does the chi-square statistic compare?

Chi-square test Easy
A. Observed and expected frequencies
B. Two sample means
C. Two correlation coefficients
D. The largest and smallest measurements

18 Which expression is the formula for the chi-square statistic?

Chi-square test Easy
A.
B.
C.
D.

19 For a contingency table with rows and columns, what are the degrees of freedom?

Chi-square test Easy
A.
B.
C.
D.

20 If the -value from a chi-square test is less than the chosen significance level, what is the usual decision?

Chi-square test Easy
A. Reject the null hypothesis
B. Conclude that the variables have exactly the same numerical mean
C. Accept every alternative claim
D. Increase the observed frequencies

21 A study reports a correlation coefficient of between daily screen time and examination scores. Which interpretation is most appropriate?

Correlation coefficient Medium
A. A weak positive linear association
B. A strong causal effect of screen time on scores that applies equally to every student
C. No meaningful linear association
D. A strong negative linear association

22 If the correlation between study time and test score is , what percentage of the variation in test scores is explained by their linear relationship with study time?

Correlation coefficient Medium
A.
B.
C.
D. , because the square root of the correlation gives the explained percentage

23 The correlation between and is . New variables are defined as and . What is the correlation between and ?

Correlation coefficient Medium
A.
B.
C.
D.

24 The covariance between two variables is , and their standard deviations are and . What is their correlation coefficient?

Correlation coefficient Medium
A.
B.
C.
D.

25 For six paired observations with no tied ranks, the sum of squared rank differences is . What is Spearman's rank correlation coefficient?

Spearman rank correlation Medium
A.
B.
C.
D.

26 Three observations are tied and would occupy rank positions , , and . Which rank should be assigned to each tied observation?

Spearman rank correlation Medium
A.
B. Ranks , , and assigned in an arbitrary order based on their original positions
C.
D.

27 The rankings of eight employees on productivity are exactly the reverse of their rankings on absenteeism. What is Spearman's rank correlation?

Spearman rank correlation Medium
A.
B.
C.
D.

28 Five participants have ranks on variable and ranks on variable . Assuming no ties, what is Spearman's rank correlation?

Spearman rank correlation Medium
A.
B.
C.
D.

29 For the paired data and , what is Karl's Pearson correlation coefficient?

Karl's Pearson correlation Medium
A.
B.
C.
D.

30 A dataset has a Pearson correlation of . One extreme bivariate outlier is then removed. Which statement is correct?

Karl's Pearson correlation Medium
A. The correlation must become positive
B. The correlation may change substantially
C. The correlation must become zero
D. The correlation remains unchanged because Pearson's coefficient is completely resistant to extreme observations

31 For five observations, , , , , and . What is Karl's Pearson correlation coefficient?

Karl's Pearson correlation Medium
A.
B.
C.
D.

32 The Pearson correlation between and is . If and , what is the regression coefficient of on ?

Karl's Pearson correlation Medium
A.
B.
C.
D.

33 A researcher cross-classifies employees by department and preferred training method. What is the null hypothesis for a test of association?

Test of association between nominal data Medium
A. Every training method has the same total frequency
B. Department causes training preference
C. All departments have equal sample sizes
D. Department and training preference are independent

34 For a contingency table, the chi-square statistic is and the sample size is . What is the phi coefficient?

Test of association between nominal data Medium
A.
B.
C.
D.

35 A contingency table produces from observations. What is Cramer's ?

Test of association between nominal data Medium
A.
B.
C.
D.

36 A very large sample produces a statistically significant association between two nominal variables, but Cramer's is . What is the best conclusion?

Test of association between nominal data Medium
A. The variables are perfectly associated
B. The variables have a strong association
C. The association must be strong because statistical significance always guarantees a large and practically important effect
D. Association exists, but it may be weak

37 In a contingency table, a row total is , a column total is , and the grand total is . What is the expected frequency for their intersecting cell under independence?

Chi-square test Medium
A.
B.
C.
D.

38 What are the degrees of freedom for a chi-square test of independence using a contingency table?

Chi-square test Medium
A.
B.
C.
D.

39 A table has observed frequencies . Using the Pearson chi-square formula without a continuity correction, what is the test statistic?

Chi-square test Medium
A.
B.
C.
D.

40 A chi-square test of independence gives at the significance level. Which decision is appropriate?

Chi-square test Medium
A. Reject association; evidence of independence
B. Accept the null hypothesis as certainly true because the test statistic is smaller than the significance level
C. Retain independence; no evidence of association
D. Reject independence; evidence of association

41 A dataset has a Pearson correlation of between variables and . Which transformation would necessarily leave the correlation unchanged?

Correlation coefficient Hard
A. Replacing with and with
B. Replacing with and with
C. Replacing with and with
D. Replacing with and with

42 For a sample of , the observed Pearson correlation is . Using , which conclusion is most appropriate for a two-sided test of ?

Correlation coefficient Hard
A. Reject at because with degrees of freedom
B. Fail to reject at because with degrees of freedom
C. Reject at because with degrees of freedom
D. Reject at because with degrees of freedom

43 A scatterplot shows a strong U-shaped relationship between and , with nearly symmetric observations around the minimum. Which result is most plausible?

Correlation coefficient Hard
A. A large negative Pearson correlation
B. A large positive Pearson correlation
C. A Pearson correlation equal to the coefficient of determination
D. A Pearson correlation close to zero

44 Two variables have covariance , standard deviations and , and sample means that are otherwise irrelevant. What is their correlation coefficient, and what does it imply?

Correlation coefficient Hard
A. , indicating a strong positive linear association
B. , indicating a very strong positive association
C. , indicating a moderate positive linear association
D. , indicating a very strong positive association

45 A single observation is found to have an unusually large value of both and , far outside the remaining cloud of points. Which effect is most likely if this point is removed?

Correlation coefficient Hard
A. The correlation must increase toward
B. The correlation must decrease toward
C. The correlation may change substantially in magnitude or sign
D. The correlation cannot change because correlation is standardized

46 For six paired observations with no tied ranks, the differences between the two ranks are . What is Spearman's rank correlation?

Spearman rank correlation Hard
A.
B.
C.
D.

47 When tied values occur in either variable, which procedure is generally appropriate for computing Spearman's rank correlation?

Spearman rank correlation Hard
A. Assign the smallest rank to every tied observation
B. Assign the largest rank to every tied observation
C. Assign midranks and compute Pearson correlation on the ranks
D. Delete all observations involved in any tie

48 A researcher obtains between disease severity categories and treatment burden scores. Which interpretation is most defensible?

Spearman rank correlation Hard
A. The ranking of one variable is strongly consistent with the ranking of the other
B. The two variables have identical measurement units
C. The treatment burden causes disease severity to increase
D. The two variables have an exact linear relationship

49 Which pattern can produce a high Spearman correlation but a substantially lower Pearson correlation?

Spearman rank correlation Hard
A. A monotonic but strongly curved relationship
B. Two independent variables with equal sample means
C. Two variables measured in different physical units
D. A perfectly linear relationship with constant variance

50 If every rank in one variable is reversed while the ranks in the other variable remain unchanged, what happens to Spearman's correlation?

Spearman rank correlation Hard
A. It becomes zero
B. It remains unchanged
C. It becomes its negative
D. It becomes equal to Pearson's original correlation

51 For paired data, holds exactly for every observation, and is not constant. What are the Pearson correlation and coefficient of determination?

Karl's Pearson correlation Hard
A. and
B. and
C. and
D. and

52 Which condition is most directly violated when Pearson correlation is used to summarize a relationship containing a severe nonlinear curve and influential outliers?

Karl's Pearson correlation Hard
A. The sample size must equal the population size
B. The relationship should be approximately linear without extreme influence
C. The variables must be measured in identical units
D. Both variables must have a population mean of zero

53 A study reports between study time and examination score. Which statement is mathematically correct but does not imply causation?

Karl's Pearson correlation Hard
A. Examination score explains of study-time variation
B. Study time explains of score variation
C. The causal effect of study time is score units
D. Study time explains of score variation in the linear model

54 If the covariance between and is positive, which change can make Pearson's correlation negative without changing the observations' paired ordering?

Karl's Pearson correlation Hard
A. Multiplying by a negative constant
B. Adding a constant to
C. Changing the units of both variables by positive factors
D. Multiplying by a positive constant

55 A nominal variable has categories with no intrinsic order. Which analysis is most appropriate for testing its association with another nominal variable?

Test of association between nominal data Hard
A. Pearson correlation of the category labels
B. A paired-samples test of category means
C. A contingency-table test of independence
D. Spearman correlation of arbitrarily assigned ranks

56 In a table, the odds ratio is but the sample size is very large. What is the correct interpretation?

Test of association between nominal data Hard
A. The sample contains no sampling variability
B. There is no evidence of association represented by the odds ratio
C. The variables are certainly causally independent
D. The chi-square statistic must be larger than its critical value

57 A significant association between smoking status and disease status is found in an observational study. Which conclusion is justified?

Test of association between nominal data Hard
A. Smoking status is proven to cause the disease
B. Smoking status and disease status are statistically associated
C. Disease status is proven to cause smoking
D. The association remains significant in every population

58 A contingency table has row totals and , column totals , , and , and grand total . What is the expected count for the cell in the first row and second column?

Chi-square test Hard
A.
B.
C.
D.

59 For a contingency table, what are the degrees of freedom for the chi-square test of independence?

Chi-square test Hard
A.
B.
C.
D.

60 In a table, the observed counts are in row order. What is the Pearson chi-square statistic for testing independence?

Chi-square test Hard
A.
B.
C.
D.
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