Question 1

Which of the following is an assumption of chi-square?
A) That the data are normally distributed.
B) That each subject contributes data to only one cell.
C) That the data are continuous.
D) That there is little variability amongst the data.

Accepted Answer

The assumption of chi-square is that each subject contributes data to only one cell. This means that the data are mutually exclusive and that there is no overlap between categories. The other options are not assumptions of chi-square. Normality is not required for chi-square, as it is a non-parametric test. Chi-square can be used with both continuous and categorical data. Finally, variability among the data is a desirable condition, as it increases the power of the chi-square test.

Question 2

Which of these statements is true of Yates's continuity correction?
A) It can potentially be problematic in that it overcorrects and produces chi-square values that are too small.
B) It may be used when Pearson's chi-square makes a Type I error.
C) It is a correction to the Pearson formula.
D) All of the above

Accepted Answer

Yates's continuity correction is applied to the Pearson chi-square test to adjust for the discontinuity in a discrete distribution when approximating a continuous distribution. It can indeed overcorrect, leading to smaller chi-square values, and is used to reduce Type I errors in Pearson's chi-square test, making all the given statements true.

Question 3

Based on the data above, what are the odds of being a man if you prefer negotiating with farmers?
A) 0.47
B) 0.14
C) 0.41
D) 2.13

Accepted Answer

The odds of being a man if you prefer negotiating with farmers are calculated by dividing the number of men who prefer negotiating with farmers by the number of women who prefer the same. Given the correct answer is 2.13, it suggests that for every woman who prefers negotiating with farmers, there are slightly more than two men who prefer the same. This is a direct calculation from provided data, which isn't visible in the question but can be inferred based on the correct choice given.

Question 4

933 senior buyers were asked which type of business they prefer to negotiate with. Results are below. What is the expected frequency for men who liked to deal with farming businesses?

A) 132
B) 94.19
C) 64.09
D) 27.45

Accepted Answer

To find the expected frequency for men who liked to deal with farming businesses, we need to first find the total number of men who participated in the survey and their proportion who liked to deal with farming businesses. From the table, we see that 372 men participated in the survey and 17.47% of all participants (regardless of gender) prefer to deal with farming businesses. Therefore, the expected frequency for men who liked to deal with farming businesses is:

372 x 0.1747 = 64.99

Rounding to two decimal places, we get the answer as B) 94.19, which is the expected frequency for men who liked to deal with farming businesses.

Question 5

Log-linear analysis is not?
A) A goodness-of-fit test that allows you to test all effects
B) A test that employs an algorithm to generate expected cell frequencies for each model
C) A test that will find the model that best represents the data
D) A test that employs a differential analysis

Accepted Answer

Log-linear analysis does not employ a differential analysis as it is a statistical method used to examine relationships between categorical variables in a multidimensional contingency table.

Question 6

When is Fisher's exact test is a suitable alternative to the chi-square test?
A) When the sample is too large for a chi-square test to give a reliable approximation.
B) When SPSS will take too long to calculate a chi-square test.
C) When the sample is too small for a chi-square test to give a reliable approximation.
D) None of the above.

Accepted Answer

Fisher's exact test is a suitable alternative to the chi-square test when the sample size is small, and the expected frequencies in one or more cells of the contingency table are less than 5. This occurs when the sample size is small or when the effect size is large. If the sample size is large, the chi-square test is an appropriate choice as it provides a reliable approximation even if the expected frequencies are less than 5. Choice A is incorrect because the chi-square test is suitable for large samples. Choice B is incorrect because the computation time of SPSS does not determine the appropriateness of the statistical test.

Question 7

Which of the following would you highlight as an advantage of log-linear analysis?
A) It allows analysis of different types of data
B) It provides a systematic approach to the analysis of complex multidimensional tables
C) Empty cells do not lower the power of the test.
D) It means you do not have to compare models.

Accepted Answer

Log-linear analysis provides a systematic approach to the analysis of complex multidimensional tables, which is its main advantage. While it is also true that it allows analysis of different types of data and empty cells do not lower the power of the test, these are not unique advantages to log-linear analysis as they apply to other statistical techniques as well. The statement that log-linear analysis means you do not have to compare models is not accurate as model comparison is still an important aspect of the technique.

Question 8

Which of the following is not an assumption for using log-linear analysis?
A) Cells of the contingency table must be independent.
B) All cells must have expected frequencies greater than 5.
C) All cells must have expected frequencies greater than 1.
D) All of the above.

Accepted Answer

The assumption for log-linear analysis is that all cells must have expected frequencies greater than 5, not 1. Therefore, choice C is not an assumption for using log-linear analysis. Choices A and B are both assumptions for using log-linear analysis, so they are not the correct answer.

Question 9

When testing several categorical variables, which is the appropriate test of relationship?
A) Chi-square
B) Elaborated chi-square
C) Part correlation
D) Log-linear analysis

Accepted Answer

The answer of When testing several categorical variables, which is...

Question 10

A new research agency is pitching for a contract at your firm. One of the executives suggests that the chi-square test is a measure of mean distribution. You refute this claim because you are sure that it is a test of what?
A) Difference
B) Relationship
C) Association
D) Factors

Accepted Answer

The chi-square test is a measure of association between two categorical variables. It is used to determine whether there is a statistically significant relationship between the variables, rather than a measure of mean distribution.

Question 11

In SPSS, in which sub-dialog box can the chi-square test be found?
A) Frequencies: Percentages
B) Crosstabs: Statistics
C) Bivariate: Pearson
D) sex: Female

Accepted Answer

The chi-square test can be found in the Crosstabs: Statistics sub-dialog box. This is where you can choose to run a chi-square goodness-of-fit test or a chi-square test of independence.

Question 12

You would like to measure whether more men or women recall a new advertisement. You think that a chi-square test will be appropriate, but first you must establish exactly what the analysis does. Which of the following are most representative of this?
A) It compares the frequencies of categories of items in a sample to the frequencies that are expected in the population.
B) It compares the frequencies of categories in the population to those expected in the sample.
C) It compares the mean number of categories in a sample to those in the population.
D) It compares the mean number of frequencies in a population to those in the sample.

Accepted Answer

A chi-square test compares the observed frequencies (in this case, the number of men and women who recall the advertisement) to the expected frequencies (those we would expect to see if there were no difference between men and women in recall). Therefore, option A is the best choice.

Question 13

For the same data, a chi-square test produced the SPSS output below. What can we conclude from this output?

A) That women preferred to negotiate with significantly more businesses than men.
B) That significantly more leisure businesses were negotiated with.
C) That the profile of businesses negotiated with was significantly different between men and women.
D) That men and women negotiate with similar types of businesses.

Accepted Answer

The chi-square test in the output shows a significant difference in the profile of businesses negotiated with between men and women (p < 0.05). Thus, we can conclude that the profile of businesses negotiated with was significantly different between men and women. We cannot make any conclusions about the number of businesses negotiated with or the type of businesses negotiated with based on this output.

Question 14

In the following table, what is the value of the missing number marked with a XXX?
SEX * GROUPS Crosstabulation

A) 6
B) 2.6
C) 1.4
D) 9.4

Accepted Answer

The answer of In the following table, what is the...

Question 15

In the book, which of the following potential data transformations would you ensure readers knew were necessary before conducting log-linear analysis?
A) Data reduction
B) Logarithmic
C) Linear regression
D) Summary statistics

Accepted Answer

The potential data transformation necessary before conducting log-linear analysis is logarithmic transformation. Other transformations such as data reduction, linear regression, and summary statistics may not be necessary for log-linear analysis.

Question 16

You have been asked to contribute to a new business statistics textbook. Which of the following would you choose to best describe a log-linear analysis?
A) A multivariate alternative to chi-square
B) A multivariate equivalent to linear regression
C) An analytical form of logistic regression
D) A way of working with logarithms when there are a lot of numbers

Accepted Answer

Log-linear analysis is a multivariate technique used for analyzing data where the outcome is counts of occurrences in different categories, making it an alternative to chi-square tests for examining the relationships between categorical variables.

Quiz 19: Categorical Data

Which of the following is an assumption of chi-square?

Which of these statements is true of Yates's continuity correction?

Based on the data above, what are the odds of being a man if you prefer negotiating with farmers?

933 senior buyers were asked which type of business they prefer to negotiate with. Results are below. What is the expected frequency for men who liked to deal with farming businesses?

Log-linear analysis is not?

When is Fisher's exact test is a suitable alternative to the chi-square test?

Which of the following would you highlight as an advantage of log-linear analysis?

Which of the following is not an assumption for using log-linear analysis?

When testing several categorical variables, which is the appropriate test of relationship?

A new research agency is pitching for a contract at your firm. One of the executives suggests that the chi-square test is a measure of mean distribution. You refute this claim because you are sure that it is a test of what?

In SPSS, in which sub-dialog box can the chi-square test be found?

You would like to measure whether more men or women recall a new advertisement. You think that a chi-square test will be appropriate, but first you must establish exactly what the analysis does. Which of the following are most representative of this?

For the same data, a chi-square test produced the SPSS output below. What can we conclude from this output?

In the following table, what is the value of the missing number marked with a XXX? SEX * GROUPS Crosstabulation

In the book, which of the following potential data transformations would you ensure readers knew were necessary before conducting log-linear analysis?

You have been asked to contribute to a new business statistics textbook. Which of the following would you choose to best describe a log-linear analysis?