Back to Subject

Unit 10: Test of Association - Practice Quiz

DEMGN832 — Research Methodology 60 Questions
0 Correct 0 Wrong 60 Left
0/60

1 What does a correlation coefficient primarily measure?

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

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. Perfect negative correlation
B. No linear correlation
C. A strong relationship that must be nonlinear and causal
D. Perfect positive 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. Ranked or ordinal data
B. Only continuous ratio data
C. Unordered nominal data
D. Data divided into many unrelated experimental groups

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 mean of all ranks
B. The difference between the original values and their sample mean
C. The difference between paired ranks
D. The total number of 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. Any relationship between several nominal categories
B. A linear relationship
C. A difference in medians
D. A change in frequencies

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 negative linear relationship
B. A perfect relationship proving that one variable causes the other
C. A positive 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. A detailed organizational flowchart with several decision branches
B. Scatter plot
C. Frequency polygon
D. Pie chart

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

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

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

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

15 Which pair consists of nominal variables?

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

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 independent
B. The variables are perfectly related
C. The first variable directly causes every change observed in the second variable
D. The category means are equal

17 What does the chi-square statistic compare?

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

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. Conclude that the variables have exactly the same numerical mean
B. Accept every alternative claim
C. Increase the observed frequencies
D. Reject the null hypothesis

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 strong negative 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 weak positive 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. , because the square root of the correlation gives the explained percentage
D.

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. Ranks , , and assigned in an arbitrary order based on their original positions
B.
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 zero
B. The correlation must become positive
C. The correlation remains unchanged because Pearson's coefficient is completely resistant to extreme observations
D. The correlation may change substantially

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. Department and training preference are independent
B. All departments have equal sample sizes
C. Department causes training preference
D. Every training method has the same total frequency

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 association must be strong because statistical significance always guarantees a large and practically important effect
C. Association exists, but it may be weak
D. The variables have a strong association

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

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 close to zero
D. A Pearson correlation equal to the coefficient of determination

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 moderate positive linear association
B. , indicating a strong positive linear association
C. , indicating a very strong positive 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 decrease toward
B. The correlation cannot change because correlation is standardized
C. The correlation must increase toward
D. The correlation may change substantially in magnitude or sign

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

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

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

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

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

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 its negative
B. It becomes zero
C. It remains unchanged
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 variables must be measured in identical units
C. The relationship should be approximately linear without extreme influence
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 in the linear model
C. Study time explains of score variation
D. The causal effect of study time is score units

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. Changing the units of both variables by positive factors
B. Adding a constant to
C. Multiplying by a negative constant
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. A contingency-table test of independence
B. Pearson correlation of the category labels
C. A paired-samples test of category means
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 chi-square statistic must be larger than its critical value
B. The variables are certainly causally independent
C. The sample contains no sampling variability
D. There is no evidence of association represented by the odds ratio

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. The association remains significant in every population
B. Smoking status is proven to cause the disease
C. Disease status is proven to cause smoking
D. Smoking status and disease status are statistically associated

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.
Previous MCQ
Unit 9
Next MCQ
Unit 11