Question 1

A correlation matrix can quickly give the researcher an overview of the direction, strength and statistical significance of each paired relationship.

Accepted Answer

A correlation matrix displays the correlation coefficients between pairs of variables and can help researchers quickly understand the direction, strength and statistical significance of each relationship.

Question 2

To compute the Chi-square value for the contingency table, the researcher must first identify an expected distribution for that table.

Accepted Answer

The chi-square test compares the observed counts in a contingency table to the expected counts, which are based on a null hypothesis of no association between the variables being examined. Therefore, the researcher must first identify an expected distribution for that table.

Question 3

To calculate the expected frequencies for the cells in a cross tabulation, the actual observed numbers of respondents in each individual cell is required.

Accepted Answer

The expected frequencies can be calculated using formulas that take into account the total number of respondents and the proportions in each group, without needing to know the actual observed numbers in each cell.

Question 4

The Chi-square test analyses the significance of the data in an R x C contingency table, in which R stands for row and C stands for column.

Accepted Answer

The statement is true.

Question 5

All of the following statistical tests can be used to test for associations between variables, except:

Accepted Answer

ANOVA is not used to test for associations between variables, but rather to test for differences between groups. The other three options (Spearman's rank correlation, regression analysis, and Chi-square test) are all used to test for associations between variables.

Question 6

Which type of statistical test is appropriate for testing whether or not there is an association between two ordinal variables?

Accepted Answer

Spearman's rank correlation is a non-parametric test used to measure the strength and direction of association between two ordinal variables. It is appropriate when the data are not normally distributed and there is no assumption of a linear relationship between the variables.

Question 7

A researcher would like to test whether or not gender (that is, male or female) is related to brand awareness (that is, aware or unaware). Which of the following statistical tests would you suggest?

Accepted Answer

A chi-square test is appropriate for testing the relationship between two categorical variables, in this case gender (male or female) and brand awareness (aware or unaware). The other options are not appropriate for this type of analysis.

Question 8

One of the simplest techniques for describing sets of relationships between two interval variables is the cross-tabulation.

Accepted Answer

Cross-tabulation is a technique for describing the relationship between two categorical variables, not interval variables.

Question 9

All of the following statements about the Correlation Coefficient are true, except:

Accepted Answer

The correlation coefficient provides direction and strength of the association between two variables, as well as statistical significance of the association. However, it does not provide the variance in associations. The coefficient of determination (R-squared) provides information about the variance in associations.

Question 10

In regression analysis, the error of a predicted score is found by subtracting the predicted value of Y from the actual value of Y.

Accepted Answer

This statement is correct. The error or residual is calculated as the difference between the actual value of Y and the predicted value of Y.

Question 11

An F-test can be applied to a regression to determine the residual error.

Accepted Answer

An F-test can be applied to a regression to test the overall significance of the regression model, but it does not directly determine the residual error. The residual error can be obtained by calculating the difference between the observed values and the predicted values of the dependent variable in the regression model.

Question 12

A Spearman's rank-order correlation coefficient examines the relationship between two ordinal variables.

Accepted Answer

A Spearman's rank-order correlation coefficient measures the monotonic relationship between two ordinal variables, which means that as one variable increases, the other variable either increases or decreases consistently.

Question 13

If there is no relationship between two variables, then the Pearson's correlation coefficient between them will be:

Accepted Answer

If there is no relationship between two variables, then Pearson's correlation coefficient will be zero. A correlation coefficient of +1 indicates a perfect positive linear relationship, while a correlation coefficient of -1 indicates a perfect negative linear relationship. A correlation coefficient of +0.50 indicates a positive linear relationship, but it is not perfect. Therefore, the best choice is D, which represents no relationship at all.

Question 14

When testing for association between two variables, it is possible that they can be statistically significant but not appear to be meaningfully associated.

Accepted Answer

Statistical significance only measures the likelihood of obtaining an association by chance, not the strength or direction of the association. A statistically significant association may still have a weak or non-existent effect size, making it less meaningful in practical terms.

Question 15

Bivariate linear regression investigates the relationship between a dependent variable and two independent variables.

Accepted Answer

Bivariate linear regression investigates the relationship between a dependent variable and only one independent variable. Multiple linear regression investigates the relationship between a dependent variable and two or more independent variables.

Question 16

The Chi-square test tests the goodness of fit of the observed distribution with the expected distribution.

Accepted Answer

The Chi-square test is used to test the goodness of fit of the observed distribution with the expected distribution.

Question 17

To use the Chi-square test, both variables in a 2 x 2 contingency table must be measured on a ratio or interval scale.

Accepted Answer

The Chi-square test can be used with categorical or nominal data, which is not measured on a ratio or interval scale.

Question 18

The appropriate statistical test to use to calculate the association between two nominal variables is:

Accepted Answer

The appropriate statistical test to use to calculate the association between two nominal variables is the Chi-square test. Chi-square test is used to determine if there is a significant association or relationship between two categorical variables (nominal or ordinal) in a contingency table. The test involves comparing the observed frequencies in each category with the expected frequencies based on the assumption of independence between the two variables. Therefore, the best choice in this scenario is the Chi-square test.

Question 19

The least-squares regression line minimises the sum of the squared deviations of the actual values from the predicted values in the regression line.

Accepted Answer

This is the definition of the least-squares regression line.

Question 20

A researcher would like to predict sales volume against advertising dollar expenditure. Which of the following statistical tests would you suggest?

Accepted Answer

Regression analysis is the best choice as it allows the researcher to create a regression equation to predict sales volume based on the amount of money spent on advertising. The relationship between the two variables can be analyzed along with statistical significance and the strength of the relationship.

Quiz 14: Bivariate Statistical Analysis: Tests of Association