Question 1

The chi-square test for goodness of fit evaluates the distribution for one variable,and the test for independence evaluates the relationship between two variables.

Accepted Answer

The statement is true. The chi-square test for goodness of fit is used to determine whether the observed frequency distribution of a variable fits a theoretical distribution. The chi-square test for independence is used to determine whether two variables are independent or related to each other.

Question 2

The expected frequencies for a chi-square test are always whole numbers (no fractions or decimals).

Accepted Answer

The expected frequencies for a chi-square test can be fractions or decimals as they are calculated based on probabilities and sample sizes. The observed frequencies, however, must always be whole numbers as they represent actual counts.

Question 3

For a fixed level of significance,the critical value for chi-square increases as the degrees of freedom increase.

Accepted Answer

This is true. As the degrees of freedom increase, the chi-square distribution becomes less skewed and more normal-like, which leads to larger critical values to achieve the same level of significance.

Question 4

For the chi-square test for goodness of fit,the researcher must select a sample with an equal number of individuals in each category.

Accepted Answer

The chi-square test for goodness of fit does not require an equal number of individuals in each category; it compares the observed frequencies in each category with the expected frequencies, which are based on a theoretical distribution.

Question 5

The observed frequencies for a chi-square test can be fractions or decimal values.

Accepted Answer

The observed frequencies for a chi-square test must be whole numbers, as they represent the actual counts of individuals or events in the sample. Fractions or decimal values would not make sense in this context. However, expected frequencies may be fractions or decimals in some cases.

Question 6

A chi-square test should not be used if any expected frequency is less than five.

Accepted Answer

This is a commonly accepted guideline for the use of chi-square tests. If any expected frequency is less than five, the validity of the test can be questioned and alternative statistical tests may be more appropriate.

Question 7

The phi-coefficient is used to evaluate effect size for the chi-square test for independence,provided the test has df > 1.

Accepted Answer

The phi-coefficient is specifically used for evaluating effect size in a 2x2 contingency table (which has df = 1), not for chi-square tests with degrees of freedom greater than 1.

Question 8

Cramér's V is used to evaluate effect size for the chi-square test for independence whenever the test has df = 1.

Accepted Answer

Cramér's V can be used to evaluate the effect size for the chi-square test for independence regardless of the degrees of freedom (df), not only when df = 1. It is suitable for any contingency table size.

Question 9

For the expected frequencies in a chi-square test for independence,the proportions for any row are the same as the proportions in every other row.

Accepted Answer

In a chi-square test for independence, the expected frequencies are calculated under the assumption that the variables are independent, meaning the proportion of categories in one variable should be consistent across the levels of the other variable, resulting in the same proportions across rows when comparing expected frequencies.

Question 10

If other factors are held constant,increasing the sample size for a chi-square test for independence will increase the likelihood of rejecting the null hypothesis.

Accepted Answer

Increasing the sample size for a chi-square test for independence will increase the power of the test, which means it will be more likely to detect a true relationship or association between the two categorical variables being tested. This, in turn, increases the likelihood of rejecting the null hypothesis.

Question 11

The phi-coefficient is used to evaluate effect size for a chi-square test for goodness of fit provided there are only two categories.

Accepted Answer

The phi-coefficient is used to measure the association between two binary variables, not for evaluating effect size in a chi-square test for goodness of fit. For goodness of fit, effect size might be assessed using other measures like Cramer's V when dealing with categorical data in more than two categories.

Question 12

For a chi-square test for independence,the expected frequencies for any row are the same as the expected frequencies in every other row.

Accepted Answer

The expected frequencies for each row are calculated separately based on the row total and the overall total, and thus can be different from the expected frequencies in other rows. However, the expected frequencies for each column are the same as the expected frequencies in every other column.

Question 13

The chi-square test for independence is similar to a correlation because it evaluates the relationship between two variables.

Accepted Answer

Both the chi-square test for independence and correlation evaluate the relationship between two variables, but they differ in the type of variables they can handle and the nature of the relationship they examine. The chi-square test for independence is used to determine whether there is a significant association between two categorical variables, while correlation is used to measure the strength and direction of the linear relationship between two continuous variables.

Question 14

In general,a large value for chi-square indicates a good fit between the sample data and the null hypothesis.

Accepted Answer

A large value for chi-square indicates a poor fit between the sample data and the null hypothesis, suggesting that the null hypothesis should be rejected in favor of an alternative hypothesis.

Question 15

The data for a chi-square test for independence can be viewed either as representing one sample with two measurements for each participant or as two (or more)separate samples.

Accepted Answer

The data for a chi-square test for independence can be viewed as representing two (or more) separate samples, each with one measurement for each participant.

Question 16

For a fixed level of significance,the critical value for chi-square decreases as the size of the sample increases.

Accepted Answer

The critical value for chi-square is determined by the level of significance (alpha) and the degrees of freedom, not the sample size. As the degrees of freedom increase, which can happen with larger sample sizes, the critical value can change, but not necessarily decrease.

Question 17

The chi-square test for independence is similar to an independent-measures t test because it can be used to evaluate the difference between two populations or two treatment conditions.

Accepted Answer

The answer of The chi-square test for independence is similar...

Question 18

The chi-square test for independence uses the same formula as the chi-square statistic for the goodness-of-fit test.

Accepted Answer

Both the chi-square test for independence and the chi-square goodness-of-fit test calculate the chi-square statistic using the formula that involves summing the squared difference between observed and expected frequencies, divided by the expected frequencies. The difference lies in the application and interpretation of the test, not in the calculation of the chi-square statistic itself.

Question 19

Although the outcome for a chi-square test for independence is influenced by sample size,measures of effect size such as the phi-coefficient or Cramér's V are not.

Accepted Answer

Measures of effect size like the phi-coefficient or Cramér's V are designed to provide information about the strength of the association independent of sample size, thus they are not influenced by the size of the sample.

Question 20

A chi-square test for independence produces a chi-square statistic with df = 2.The data for this research study form a 2×2 matrix with four separate categories.

Accepted Answer

If the chi-square statistic has df = 2, it means that the data form a contingency table with at least three categories in at least one of the variables. Therefore, the data for this research study cannot form a 2×2 matrix with only four separate categories.

Quiz 15: The Chi-Square Statistic: Tests for Goodness of Fit and Independence