Question 1

If a Chi-square analysis yielded a .02 significance level for the null hypothesis,the researcher would conclude that only 2% of the time would he or she find evidence to support the null hypothesis.Since the null hypothesis is not supported,this means there:

Accepted Answer

A significance level of .02 means that there is only a 2% chance of obtaining the observed results if the null hypothesis were true. Therefore, we can reject the null hypothesis and conclude that there is a significant association.

Question 2

What type of analysis includes the examination of frequencies for two nominally scaled variables in a cross-tabulation table to determine whether the variables have a statistically significant nonmonotonic relationship?

Accepted Answer

The examination of frequencies for two nominally scaled variables in a cross-tabulation table to determine whether the variables have a statistically significant nonmonotonic relationship is a classic use case for the chi-square test. The chi-square test compares the observed frequency distribution to the expected frequency distribution and determines whether the differences are statistically significant.

Question 3

With what type of diagram can covariation be examined?

Accepted Answer

Covariation can be examined using a scatter diagram. This type of diagram allows us to visually analyze the relationship between two variables and see if they tend to vary together, which is an indication of covariation. The other types of diagrams listed (Venn, cause and effect, flowchart) are not specifically designed for examining relationships between variables.

Question 4

To reveal the nonmonotonic relationships found to be significant in cross-tabulation tables,researchers often turn to ________,which show the relationships very adequately.

Accepted Answer

Graphical presentations are the best choice to reveal nonmonotonic relationships as they allow researchers to create visual representations of complex relationships that are often difficult to convey through tabular or textual presentations. Graphs, such as scatterplots or line charts, can effectively show the shape and direction of relationships between variables, enabling researchers to make more accurate and meaningful interpretations of their data.

Question 5

If you found a significant correlation of .83 between years of education and hours spent attending San Francisco Giants' baseball games,it would mean that:

Accepted Answer

A correlation coefficient of .83 indicates a strong positive relationship between years of education and hours spent attending San Francisco Giants' baseball games. Therefore, it can be inferred that people with more education spend more time attending Giants' baseball games.

Question 6

________ are the actual cell counts in the cross-tabulation table.

Accepted Answer

Observed frequencies are the actual cell counts in a cross-tabulation table.

Question 7

Any correlation that is ? absolute value of .20 is typically uninteresting to marketing researchers because it:

Accepted Answer

The absolute value of .20 indicates a weak correlation between two variables, which rarely identifies a meaningful association. Therefore, it is uninteresting to marketing researchers.

Question 8

A cross-tabulation table is sometimes referred to as a(n):

Accepted Answer

A cross-tabulation table is commonly denoted as an r x c table, where r represents the number of rows and c represents the number of columns in the table. Therefore, option A is the correct choice. Options B, C, and D are not commonly used to denote cross-tabulation tables.

Question 9

Correlations that fall between the absolute values of ________ generally indicate a"strong"association.

Accepted Answer

According to the common interpretation of correlations, B is the best choice because correlations falling between .80 and .61 indicate a strong association. Correlations in range C are considered moderate and those in range A are considered very strong, so they are not the best choices. The range D is weak so it is not the best choice either.

Question 10

________ indicates not only the degree of association but the direction as well-the sign of the correlation coefficient indicates the direction of the relationship.

Accepted Answer

The Pearson product moment correlation coefficient is the only option given that provides information about both the degree and direction of the relationship between two variables, as indicated by its positive or negative sign. The other correlation coefficients listed provide information about the degree of association but not the direction.

Question 11

The ________ contains the raw numbers determined from the preliminary tabulation.

Accepted Answer

The frequencies table provides the raw numbers from the preliminary tabulation.

Question 12

Losing sight of this step is entirely possible when a statistical analysis program issues a great many correlations often in a layout that is confusing to first-time data analysts:

Accepted Answer

The best choice is to take time to see if a significant correlation exists before reporting it. This is because it is important to ensure that the correlation is relevant to the research objectives and is not just a coincidental finding.

Question 13

Any correlation that falls between the absolute value range of ________ is usually considered indicative of a"weak"association between the variables.

Accepted Answer

The absolute value range of .21 and .40 is relatively low compared to the other options, indicating a weak association between the variables.

Question 14

The degree to which the observed frequencies depart from the expected frequencies is expressed in a single number called the:

Accepted Answer

The measure of how much the observed frequencies deviate from the expected frequencies is measured using the Chi-square test statistic. The other options are not appropriate measures for testing frequencies.

Question 15

Correlation coefficients that fall between the absolute values of 1.00 and .81 are generally considered to be:

Accepted Answer

Correlation coefficients between the absolute values of 1.00 and .81 are considered very strong, indicating a strong linear relationship between two variables.

Question 16

What correlation coefficient measures the linear relationship between two interval- and/or ratio-scaled variables(scale variables)such as those depicted conceptually by scatter diagrams?

Accepted Answer

Pearson product moment correlation measures the linear relationship between two interval- and/or ratio-scaled variables, which is exactly what is being asked for in the question. The other options are used to measure the correlation between different types of variables (e.g. Kendall rank correlation for ordinal variables, Spearman correlation for non-parametric data, and Rank-Biserial correlation for one variable that is dichotomous and the other is continuous).

Question 17

The Chi-square distribution's shape changes depending on:

Accepted Answer

The shape of the chi-square distribution depends on the number of degrees of freedom. Specifically, as the number of degrees of freedom increases, the distribution becomes more symmetrical and bell-shaped.

Question 18

Observed frequencies are compared to ________,which are defined as the theoretical frequencies that are derived from this hypothesis of no association between the two variables.

Accepted Answer

The expected frequencies are defined as the theoretical frequencies that are derived from the hypothesis of no association between the two variables. Therefore, the observed frequencies are compared to the expected frequencies to test whether there is a significant association between the variables.

Question 19

What is used to determine whether a nonmonotonic relationship exists between two nominal-scaled variables?

Accepted Answer

Cross-tabulation is used to analyze the relationship between two nominal-scaled variables, and Chi-square tests are used to determine if there is a significant association or non-monotonic relationship between them. Therefore, choice C, Cross-tabulation and Chi-square tests, is the best option as it addresses both parts of the question.

Question 20

When a researcher uses the Pearson product moment correlation,two highly correlated variables will appear on a scatter diagram as what?

Accepted Answer

When using Pearson product moment correlation, two highly correlated variables will appear on a scatter diagram as a tight ellipse pattern. This pattern indicates a strong positive correlation between the two variables. The ellipse will be elongated and oriented along the line of best fit, with little scatter around the line. The tighter the ellipse, the stronger the correlation between the two variables.

Quiz 14: Making Use of Associations Tests