Question 1

Cross-tabulation tables allow us to look at two variables simultaneously and are arranged in a row and column format.

Accepted Answer

Cross-tabulation tables allow us to look at two variables simultaneously and are arranged in a row and column format.

Question 2

A correlation coefficient is an index number constrained to fall between the range of -1.0 and +1.0 that communicates both the strength and the direction of association between three or more variables.

Accepted Answer

A correlation coefficient communicates the strength and direction of association between two variables, not three or more.

Question 3

Chi-square analysis always begins with the assumption that no association exists between the two categorical variables under analysis.

Accepted Answer

Chi-square analysis is used to determine whether there is a significant association between two categorical variables. However, before conducting the analysis, the null hypothesis assumes that there is no association between the variables, and the observed frequencies are due to chance.

Question 4

In chi-square, the null hypothesis states that there is no association. When the calculated chi-square value exceeds the critical chi-square table value, the null hypothesis is not supported.

Accepted Answer

This statement is true. In chi-square, the null hypothesis assumes that there is no association between the variables being tested. If the calculated chi-square value exceeds the critical chi-square table value, it means that the observed data significantly deviates from the expected data and the null hypothesis is rejected.

Question 5

When it comes to determining the statistical significance of the correlation coefficient, there are rules of thumb. For example, 0.81 to 1.00 is considered to be "strong."

Accepted Answer

This is true, as a correlation coefficient of 0.81 to 1.00 indicates a strong positive correlation. However, it's worth noting that statistical significance also depends on the sample size and other factors, and the use of rules of thumb isn't always sufficient for determining significance. It's important to conduct appropriate statistical tests to determine if the correlation is statistically significant.

Question 6

To use a correlation, you must first establish that it is statistically significant from one.

Accepted Answer

The answer of To use a correlation, you must first...

Question 7

We would use cross-tabulation if we wanted to visualize the Boolean relationship between two metric-scaled variables.

Accepted Answer

Cross-tabulation is used for analyzing the relationship between two categorical variables. It helps to show the frequency distribution of the variables and how they are related to each other. However, for metric-scaled variables, scatterplots and correlation coefficients are commonly used to visualize the relationship between them.

Question 8

Correlation analysis has the great advantage of relating two variables that are of very different measurements.

Accepted Answer

Correlation analysis can relate variables that are measured on different scales, such as height and weight, income and education level, or temperature and sales.

Question 9

It is more difficult for a chi-square value with high degrees of freedom (i.e., there are more cells) to achieve "significance" than for a chi-square value with fewer degrees of freedom (i.e., there are fewer cells).

Accepted Answer

This statement is true. As the number of cells (degrees of freedom) increases, the expected values for each cell become smaller and more specific, making it harder to achieve significance.

Question 10

The degrees of freedom in chi-square are calculated by multiplying the number of rows minus one, times the number of columns minus one.

Accepted Answer

This is the correct formula for calculating degrees of freedom in a chi-square test.

Question 11

To run chi-square analysis in XL Data Analyst, you should go to the "Relate," then "Crosstabs," select the column variable and the categorical variable(s), then "OK."

Accepted Answer

This is the correct procedure for running a chi-square analysis in XL Data Analyst.

Question 12

Row cell percentage is calculated by dividing a cell frequency by the cell row total.

Accepted Answer

This is correct. To calculate the row cell percentage, you need to divide the frequency of a particular cell by the total for the row that the cell is in.

Question 13

The chi-square analysis would be appropriate to determine if there is an association between the number of dollars spent on books and the number of years of education.

Accepted Answer

The chi-square analysis is used to determine if there is a significant difference between expected and observed frequencies in categorical data. In this case, the variables (dollars spent on books and years of education) are not categorical but continuous, so a different statistical analysis would be needed, such as correlation analysis.

Question 14

Generally speaking, the chi-square value is calculated by dividing the sum of the squared differences between observed and expected frequencies by the expected frequencies.

Accepted Answer

This is the correct formula for calculating the chi-square value.

Question 15

There is no connection between scatter diagrams and correlation coefficients.

Accepted Answer

Scatter diagrams are used to visually analyze the relationship between two variables while correlation coefficients are used to measure the strength and direction of the relationship between two variables numerically. Therefore, there is a connection between scatter diagrams and correlation coefficients.

Question 16

Covariation is defined as the amount of change in one variable systematically associated with a change in another variable.

Accepted Answer

Covariation is indeed defined as the amount of change in one variable systematically associated with a change in another variable.

Question 17

When we present findings on cross-tabulations with chi-square analysis, graphical presentations such as bar or stacked bar charts are often useful.

Accepted Answer

Bar or stacked bar charts are common graphical presentations used to display cross-tabulations with chi-square analysis. They provide a visual representation of the relationship between two categorical variables and can help to highlight any significant differences or associations.

Question 18

With the information used to construct a cross-tabulation table, a column percentages table can also be constructed, but a row percentages table cannot.

Accepted Answer

With the same information used to construct a cross-tabulation table, both column percentages and row percentages tables can be constructed.

Question 19

If we determine a precise linear relationship between two variables, then by knowing the value of one variable we should be able to predict the other variable.

Accepted Answer

This statement is true. A linear relationship between two variables means that as the value of one variable changes, the value of the other variable changes proportionally. Therefore, if we know the value of one variable, we can use the linear equation to predict the value of the other variable.

Question 20

If you plotted data between two variables and the points all fell precisely in a straight line that was sloping upward to the right, your correlation coefficient would be equal to +1.0.

Accepted Answer

This statement is true. A correlation coefficient of +1.0 indicates a perfect positive correlation, which means that there is a perfect linear relationship between the two variables and all points fall on a straight line sloping upward to the right.

Quiz 13: Relationships Between Variables

Cross-tabulation tables allow us to look at two variables simultaneously and are arranged in a row and column format.

A correlation coefficient is an index number constrained to fall between the range of -1.0 and +1.0 that communicates both the strength and the direction of association between three or more variables.

Chi-square analysis always begins with the assumption that no association exists between the two categorical variables under analysis.

In chi-square, the null hypothesis states that there is no association. When the calculated chi-square value exceeds the critical chi-square table value, the null hypothesis is not supported.

When it comes to determining the statistical significance of the correlation coefficient, there are rules of thumb. For example, 0.81 to 1.00 is considered to be "strong."

To use a correlation, you must first establish that it is statistically significant from one.

We would use cross-tabulation if we wanted to visualize the Boolean relationship between two metric-scaled variables.

Correlation analysis has the great advantage of relating two variables that are of very different measurements.

It is more difficult for a chi-square value with high degrees of freedom (i.e., there are more cells) to achieve "significance" than for a chi-square value with fewer degrees of freedom (i.e., there are fewer cells).

The degrees of freedom in chi-square are calculated by multiplying the number of rows minus one, times the number of columns minus one.

To run chi-square analysis in XL Data Analyst, you should go to the "Relate," then "Crosstabs," select the column variable and the categorical variable(s), then "OK."

Row cell percentage is calculated by dividing a cell frequency by the cell row total.

The chi-square analysis would be appropriate to determine if there is an association between the number of dollars spent on books and the number of years of education.

Generally speaking, the chi-square value is calculated by dividing the sum of the squared differences between observed and expected frequencies by the expected frequencies.

There is no connection between scatter diagrams and correlation coefficients.

Covariation is defined as the amount of change in one variable systematically associated with a change in another variable.

When we present findings on cross-tabulations with chi-square analysis, graphical presentations such as bar or stacked bar charts are often useful.

With the information used to construct a cross-tabulation table, a column percentages table can also be constructed, but a row percentages table cannot.

If we determine a precise linear relationship between two variables, then by knowing the value of one variable we should be able to predict the other variable.

If you plotted data between two variables and the points all fell precisely in a straight line that was sloping upward to the right, your correlation coefficient would be equal to +1.0.