Question 1

The fourfold point correlation coefficient and Cramér's statistic can range from -1.00 to 1.00.

Accepted Answer

The fourfold point correlation coefficient ranges from -1.00 to 1.00, but Cramér's statistic ranges from 0 to 1.00.

Question 2

Because the chi-square test is typically used to analyze the relationship between two qualitative variables,it cannot be used when one or both variables are quantitative.

Accepted Answer

The chi-square test can be adapted for quantitative variables by categorizing them into discrete groups or bins, allowing the test to analyze the relationship between these categorized variables.

Question 3

Because of sampling error,a chi-square computed from sample data might be less than 0 even when the null hypothesis is true.

Accepted Answer

Chi-square values cannot be negative, so if the computed value is less than 0, there must be an error in the calculation. If the null hypothesis is true, the chi-square value should be greater than or equal to 0. Sampling error may affect the accuracy of the chi-square value, but it should not cause it to be negative.

Question 4

Research has found that Fisher's Exact Test,an alternative method for testing the relationship between two variables in 2 X 2 tables,is less powerful than the chi-square test.

Accepted Answer

Fisher's Exact Test is actually more powerful than the chi-square test in terms of p-values, especially for small sample sizes. However, it can be computationally intensive and may not be feasible for larger sample sizes.

Question 5

For the chi-square goodness-of-fit test,statisticians generally recommend that the lowest expected frequency of any category be somewhere between 5 and 10 if only two categories are involved and about 5 if more than two categories are involved.

Accepted Answer

This is a commonly recommended guideline for the chi-square goodness-of-fit test to ensure that the expected frequencies are not too low, which can lead to inaccurate results.

Question 6

If two variables are unrelated in the population,the population value of chi-square will equal 1.0.

Accepted Answer

The population value of chi-square will not necessarily equal 1.0 if two variables are unrelated. It depends on the degrees of freedom and the significance level chosen for the hypothesis test. If the observed chi-square statistic is close to 1.0, it may suggest that the variables are unrelated, but this is not always the case.

Question 7

The question addressed by the goodness-of-fit test is whether a distribution of frequencies across categories for a variable in a population are distributed in a specified manner.

Accepted Answer

The goodness-of-fit test is used to determine whether the observed distribution of frequencies for a variable in a population matches the expected distribution specified by a hypothesized distribution. Therefore, the statement that the test addresses whether the frequency distribution is distributed in a specified manner is true.

Question 8

Since all discrepancies from the expected frequencies are reflected in the upper tail of the chi-square distribution (as defined by the critical value),the chi-square test is nondirectional.

Accepted Answer

The statement is true. The chi-square test is nondirectional because all discrepancies from the expected frequencies are reflected in the upper tail of the chi-square distribution, regardless of whether the observed values are higher or lower than expected.

Question 9

When a sample is selected so that it consists of a specified number for one of the two variables,the marginal frequency for that variable is ____________________.

Accepted Answer

The answer of When a sample is selected so that...

Question 10

Probably the most common index of the strength of the relationship between two variables in a contingency table is a measure known as the fourfold point correlation coefficient (as it is called when applied to the relationship between variables with two levels each)or Cramér's statistic (as it is called when one or both variables have more than two levels).

Accepted Answer

The statement is true. The fourfold point correlation coefficient or Cramér's statistic is a commonly used index to measure the strength of the relationship between two variables in a contingency table. It is called the fourfold point correlation coefficient when both variables have two levels, and Cramér's statistic when one or both variables have more than two levels.

Question 11

The chi-square test is based on the assumption that the expected frequency for each cell is nonzero.

Accepted Answer

The chi-square test assumes that the expected frequency for each cell is at least 5, not just nonzero.

Question 12

The test of the chi-square statistic applies to the sample as a whole and provides useful information as to which cells are responsible for rejecting the null hypothesis.

Accepted Answer

The chi-square test indicates whether there is a significant association between variables, but it does not specify which cells contribute to the rejection of the null hypothesis.

Question 13

Marginal frequencies are the sums of the frequencies in the corresponding ____________________ or columns.

Accepted Answer

The answer of Marginal frequencies are the sums of the...

Question 14

When both of the variables under study have only two levels,the sampling distribution of the chi-square statistic corresponds more closely to a chi-square distribution than when one or both variables have more than two levels.

Accepted Answer

The chi-square distribution is more closely approximated when the sample size is large and the expected frequencies are sufficiently large, regardless of the number of levels of the variables.

Question 15

There are different chi-square distributions depending on the degrees of freedom associated with them.

Accepted Answer

The chi-square distribution is a family of probability distributions that are dependent on the degrees of freedom (df) associated with the sample. The degrees of freedom allow for the variance of the sample statistic to vary, and so the shape of the distribution changes as the degrees of freedom increase or decrease. Therefore, there are different chi-square distributions depending on the degrees of freedom associated with them.

Question 16

The chi-square statistic is an index that reflects the overall difference between the observed and the expected frequencies.

Accepted Answer

The chi-square statistic measures the difference between the observed and expected frequencies in a categorical data analysis.

Question 17

Although the issue is controversial,statisticians generally recommend the use of the correction for continuity.

Accepted Answer

The answer of Although the issue is controversial,statisticians generally recommend...

Question 18

Yates' correction for continuity involves subtracting .5 from the absolute value of O_j - E_j before these quantities are squared,divided by E_j,and summed across cells.

Accepted Answer

This statement accurately describes Yates' correction for continuity, which adjusts the chi-square statistic for potential small-sample bias. The correction involves subtracting .5 from each absolute deviation between the observed and expected cell frequencies before squaring and dividing by the expected frequency, and then summing these adjusted values across all cells. This adjustment accounts for the fact that the chi-square distribution is discrete and that the calculated test statistic may not exactly represent the true distribution of the test variable.

Question 19

The chi-square test is based on the assumption that the observations are independently sampled from the population of all possible observations.

Accepted Answer

The chi-square test assumes that the observations are independently sampled from the population, which means that the outcome of any observation is not influenced by the outcome of any other observation in the sample. This assumption allows the test to use probabilistic models to compute the likelihood of observing the observed data or more extreme data under the null hypothesis.

Question 20

Conceptually,a large value of V indicates a tendency for particular categories of one variable to be associated with particular categories of the other variable.

Accepted Answer

A large value of V in a contingency table indicates a strong association between the two variables, implying that the distribution of one variable is not independent of the other. This indicates a tendency for certain categories of one variable to be associated with certain categories of the other variable.

Quiz 14: Chi-Square Test