MODULE 9.1: Tests for Independence

Question 1

Q: What distribution does the test statistic follow when testing if population correlation coefficient equals zero for normally distributed variables?

Answer 1

A: The test statistic follows a t-distribution. n-1 df

The t-distribution is used because the sample correlation coefficient 𝑟
is an estimate of the population correlation coefficient 𝜌 and the variability of this estimate is captured by the t-distribution when the sample size is finite.

Question 2

Q: How are the degrees of freedom calculated in a contingency table with r rows and c columns?

Answer 2

A: df = (r - 1) × (c - 1)

Question 3

Q: What is the Pearson correlation coefficient used to measure?

Answer 3

A: The Pearson correlation coefficient measures the linear relationship between two variables.

Question 4

Q: What type of test is the Spearman rank correlation test?

Answer 4

A: The Spearman rank correlation test is a nonparametric test.

Question 5

Q: When testing independence in a contingency table, when do we reject the null hypothesis?

Answer 5

A: We reject the null hypothesis when the test statistic exceeds the critical value.

Question 6

Q: For a Spearman rank correlation test with n > 30, what distribution does the test statistic follow?

Answer 6

A: The test statistic follows a t-distribution.

Question 7

Q: What is the null hypothesis when testing independence in a contingency table?

Answer 7

A: H₀: The two characteristics are independent of each other.

Question 8

Q: What type of test is used to compare actual table values to expected values in a contingency table?

Answer 8

A: A chi-square test is used.

Question 9

Q: Is the chi-square test for independence one-tailed or two-tailed?

Answer 9

A: It is one-tailed (only positive values).

Question 10

Q: What does a sample correlation coefficient that is different from zero indicate about the population correlation coefficient?

Answer 10

A: It suggests that the population correlation coefficient might not be zero, but statistical testing is needed to confirm this at a given significance level.

Question 11

Q: What is the null hypothesis for testing if the population correlation coefficient equals zero?

Answer 11

:ρ=0 (The population correlation coefficient is zero, indicating no linear relationship

Question 12

Q: What is a contingency table?

Answer 12

A: A table used to display the frequency distribution of two categorical variables, showing how they relate to each other.

Question 13

Q: What is the test of independence based on contingency table data?

Answer 13

A: A Chi-Square Test is used to determine if two categorical variables are independent.

Question 14

Q: What is the null hypothesis for a Chi-Square Test of Independence?

Q: What is the alternative hypothesis for a Chi-Square Test of Independence?

Answer 14

: The two variables are independent.

: The two variables are not independent.

Question 15

Q: What is the significance level for rejecting the null hypothesis in a Chi-Square Test?

Answer 15

A: Compare the computed test statistic to the critical value at the chosen significance level (e.g., 5%). If the test statistic exceeds the critical value, reject the null hypothesis.

Question 16

Q: In the contingency table example, what is the calculated Chi-Square statistic?

Answer 16

A: The calculated Chi-Square statistic is 27.43, which is compared to the critical value to determine whether to reject the null hypothesis.

Question 17

A test of independence based on contingency table data uses a(n)

Answer 17

chi-square statistic. A test for independence based on contingency table data uses a chi-square statistic.

Question 18

A researcher wants to test whether the weekly returns on two stocks are correlated. The test statistic for the appropriate test follows a:

Answer 18

t-distribution with n − 2 degrees of freedom.

Question 19

For a test of independence based on contingency table data, the test statistic is calculated as the:

Answer 19

sum of squared differences between each table cell’s actual value and its expected value, if the two characteristics are independent.

Question 20

A researcher wants to test a hypothesis that two variables have a population correlation coefficient equal to zero. For a sample size of 30, the appropriate df for the test would be

Answer 20

28

The test statistic for a hypothesis test concerning population correlation follows a t-distribution with n − 2 degrees of freedom. For a sample size of 30 and a significance level of 5%, the sample statistic must be greater than 2.048 or less than −2.048 to reject the hypothesis that the population correlation equals zero.