Question 1

What terms go only with "test of independence"?
A) empirical data used to determine expected frequencies
B) expected frequencies obtained from theory
C) results somewhat suspect if an expected frequency is small
D) all of the other alternatives are correct.

Accepted Answer

The answer of What terms go only with "test of...

Question 2

The null hypothesis for a test of independence is that the two variables are A) independent B) related C) either independent or related, depending on the size of the $\chi$² value D) either independent or related, depending on the size of the $\chi$² value and the df.

Accepted Answer

The null hypothesis for a test of independence states that there is no association between the two variables, meaning they are independent.

Question 3

The sum of the expected frequencies must be equal to
A) the sum of the observed frequencies
B) the df,
C) (R - 1)(C - 1)
D) none of the other alternatives are correct

Accepted Answer

The sum of the expected frequencies in any statistical analysis must be equal to the sum of the observed frequencies, as they both represent the total counts distributed across different categories or groups in the analysis.

Question 4

In a chi square analysis
A) the sum of the observed frequencies is equal to the sum of the expected frequencies
B) events in one category must be influenced by events in at least one other category
C) both of the descriptive alternatives are correct
D) neither of the descriptive alternatives is correct

Accepted Answer

In a chi-square analysis, the total sum of observed frequencies must equal the total sum of expected frequencies because the expected frequencies are calculated based on the observed data, ensuring that the total number of observations remains constant across the analysis.

Question 5

In a chi square analysis
A) the sum of the observed frequencies is equal to the sum of the expected frequencies
B) observations in one category must be independent of observations in the other categories
C) both of the descriptive alternatives are correct
D) neither of the descriptive alternatives is correct

Accepted Answer

Both A and B are correct. In a chi-square analysis, the total observed frequencies must equal the total expected frequencies for the calculation to be valid. Additionally, observations must be independent across categories to meet the assumptions of the chi-square test.

Question 6

The sum of the expected frequencies is greater than the sum of the observed frequencies when A) a test of independence rejects H₀ B) a goodness-of-fit test rejects H₀ C) both of the descriptive alternatives are correct D) neither of the descriptive alternatives is correct

Accepted Answer

The sum of expected frequencies is always equal to the sum of observed frequencies in both tests of independence and goodness-of-fit tests. The tests compare observed frequencies to expected frequencies to see if there are significant differences, but the sums of both sets of frequencies must be equal for the comparisons to be valid.

Question 7

In a correctly worked chi square problem, the relationship between the sum of the observed frequencies (a) and the sum of the expected frequencies (b) is that
A) a > b
B) a < b
C) a $\neq$ b
D) none of the other alternatives are correct.

Accepted Answer

In a chi-square test, the sum of the observed frequencies is always equal to the sum of the expected frequencies, so none of the other alternatives are correct.

Question 8

In a correctly worked chi square problem, the sum of the expected frequencies is greater than the sum of the observed frequencies
A) for goodness-of-fit problems that produce a significant chi square value
B) for tests of independence that produce a significant chi square value
C) for goodness-of-fit problems and for tests of independence, regardless of the chi square value
D) under no conditions.

Accepted Answer

In a correctly worked chi square problem, the sum of the expected frequencies must equal the sum of the observed frequencies. This is because expected frequencies are calculated based on the total sample size, which is the same for both observed and expected frequencies.

Question 9

In a correctly worked chi square problem, the sum of the expected frequencies is greater than the sum of the observed frequencies
A) never
B) when the calculated chi square is significant
C) when the calculated chi square is not significant
D) for goodness-of-fit tests.

Accepted Answer

In a correctly worked chi square problem, the sum of the expected frequencies always equals the sum of the observed frequencies. This is because expected frequencies are calculated based on the total sample size, which is derived from the observed frequencies.

Question 10

Theoretical frequencies in a test of independence are obtained
A) by assuming the categories of events are independent
B) from predictions based on a theory
C) by assuming the categories of events are related in some way
D) in the same way as in tests of goodness of fit.

Accepted Answer

Theoretical frequencies in a test of independence are calculated under the assumption that the categories of events are independent, which is the null hypothesis in such tests.

Question 11

To find expected frequencies in a test of independence,
A) use theoretical frequencies
B) add marginal totals to each other and divide by N
C) subtract marginal totals from each other and divide by N
D) multiply marginal totals by each other and divide by N.

Accepted Answer

To find expected frequencies in a test of independence, you multiply the marginal totals (the totals for each row and column) by each other and then divide by the total number of observations (N). This method is used in chi-square tests for independence to determine what the frequency of observations would be if the variables were independent.

Question 12

To find expected frequencies in a test of independence,
A) begin by assuming that the categories are independent
B) use predictions based on a theory
C) begin by assuming that the categories of events are related in some way
D) none of the other alternatives are correct.

Accepted Answer

To find expected frequencies in a test of independence, such as the chi-square test, you begin by assuming that the categories are independent. This assumption allows you to calculate expected frequencies under the null hypothesis that there is no association between the categories.

Question 13

A friend brings you data that can be used to establish the independence of two variables. You run an analysis on the data and find a chi square value larger than the tabled value. Your analysis shows that the two variables
A) are independent
B) are not independent
C) either of the descriptive alternatives, depending on a third factor, namely ___________.

Accepted Answer

A chi square value larger than the tabled value indicates that there is a significant association between the two variables, meaning they are not independent.

Question 14

A friend brings you data that can be used to establish the independence of two variables. You run an analysis on the data and find a chi square value smaller than the tabled value. Your analysis supports the idea that the two variables
A) are independent
B) are not independent
C) either of the descriptive alternatives are correct, depending whether the calculated value is significantly smaller than the tabled value.

Accepted Answer

When the chi-square value is smaller than the critical value from the chi-square distribution table, it indicates that there is not enough evidence to reject the null hypothesis of independence between the variables.

Question 15

An investigator was interested in the relationship between color preference and number of siblings. A test of independence produced a $\chi$² that allowed the null hypothesis to be rejected. The proper conclusion is A) there is a relationship between color preference and number of siblings B) there is no relationship between color preferences and number of siblings C) either of the descriptive alternatives, depending on the size of the $\chi$²

Accepted Answer

When a test of independence allows for the rejection of the null hypothesis, it indicates that there is a statistically significant relationship between the variables being tested. In this case, it suggests a relationship between color preference and the number of siblings.

Question 16

In a $\chi$² test of independence between age and personality type, the null hypothesis was rejected. The proper conclusion is A) age and personality are independent of each other B) age and personality are related to each other C) age and personality are measured on different scales and cannot be related with statistics D) a test of goodness of fit is proper for this problem.

Accepted Answer

Rejecting the null hypothesis in a test of independence indicates that there is a significant relationship between the variables, in this case, age and personality.

Question 17

In a $\chi$²test of independence between gender and kinds of phobias, the null hypothesis was rejected. The proper conclusion is that A) gender and phobias are independent of each other B) gender and phobias are related to each other C) knowing a person's phobia gives you no clue to his or her gender D) none of the descriptive alternatives are correct.

Accepted Answer

Rejecting the null hypothesis in a test of independence means that there is a significant relationship between the variables being tested. In this case, it indicates that gender and kinds of phobias are related to each other.

Question 18

In the short cut method of calculating $\chi$²; A) the marginal totals are not used B) the observed frequencies are multiplied by the expected frequencies C) the expected frequencies are not calculated directly D) all of the descriptive alternatives are correct.

Accepted Answer

In the shortcut method, expected frequencies are not calculated directly; instead, a formula involving observed frequencies and marginal totals is used to simplify the calculation.

Question 19

For a 2 x2 test of independence, is the effect size index, and is a medium value. A) $\theta$(theta) 0.50 B) $\theta$ (theta) 0.30 C) $\phi$(phi) 0.50 D) $\phi$ (phi) 0.30.

Accepted Answer

For a 2x2 test of independence, the effect size index is phi (φ), and a medium value for phi is considered to be 0.30.

Question 20

The effect size index,$\phi$, varies depending on the number of
A) subjects
B) categories
C) both subjects and categories.

Accepted Answer

The answer of The effect size index,$\phi$, varies depending on...

Quiz 14: Chi Square Tests

What terms go only with "test of independence"?

The null hypothesis for a test of independence is that the two variables are

The sum of the expected frequencies must be equal to

In a chi square analysis

In a chi square analysis

The sum of the expected frequencies is greater than the sum of the observed frequencies when

In a correctly worked chi square problem, the relationship between the sum of the observed frequencies (a) and the sum of the expected frequencies (b) is that

In a correctly worked chi square problem, the sum of the expected frequencies is greater than the sum of the observed frequencies

In a correctly worked chi square problem, the sum of the expected frequencies is greater than the sum of the observed frequencies

Theoretical frequencies in a test of independence are obtained

To find expected frequencies in a test of independence,

To find expected frequencies in a test of independence,

A friend brings you data that can be used to establish the independence of two variables. You run an analysis on the data and find a chi square value larger than the tabled value. Your analysis shows that the two variables

A friend brings you data that can be used to establish the independence of two variables. You run an analysis on the data and find a chi square value smaller than the tabled value. Your analysis supports the idea that the two variables

An investigator was interested in the relationship between color preference and number of siblings. A test of independence produced a $\chi$ ² that allowed the null hypothesis to be rejected. The proper conclusion is

In a $\chi$ ² test of independence between age and personality type, the null hypothesis was rejected. The proper conclusion is

In a $\chi$ ²test of independence between gender and kinds of phobias, the null hypothesis was rejected. The proper conclusion is that

In the short cut method of calculating $\chi$ ²;

For a 2 x2 test of independence, is the effect size index, and is a medium value.

The effect size index, $\phi$ , varies depending on the number of

Quiz 14: Chi Square Tests

What terms go only with "test of independence"?

The null hypothesis for a test of independence is that the two variables are

The sum of the expected frequencies must be equal to

In a chi square analysis

In a chi square analysis

The sum of the expected frequencies is greater than the sum of the observed frequencies when

In a correctly worked chi square problem, the relationship between the sum of the observed frequencies (a) and the sum of the expected frequencies (b) is that

In a correctly worked chi square problem, the sum of the expected frequencies is greater than the sum of the observed frequencies

In a correctly worked chi square problem, the sum of the expected frequencies is greater than the sum of the observed frequencies

Theoretical frequencies in a test of independence are obtained

To find expected frequencies in a test of independence,

To find expected frequencies in a test of independence,

A friend brings you data that can be used to establish the independence of two variables. You run an analysis on the data and find a chi square value larger than the tabled value. Your analysis shows that the two variables

A friend brings you data that can be used to establish the independence of two variables. You run an analysis on the data and find a chi square value smaller than the tabled value. Your analysis supports the idea that the two variables

An investigator was interested in the relationship between color preference and number of siblings. A test of independence produced a χ\chiχ 2 that allowed the null hypothesis to be rejected. The proper conclusion is

In a χ\chiχ 2 test of independence between age and personality type, the null hypothesis was rejected. The proper conclusion is

In a χ\chiχ 2 test of independence between gender and kinds of phobias, the null hypothesis was rejected. The proper conclusion is that

In the short cut method of calculating χ\chiχ 2;

For a 2 x2 test of independence, is the effect size index, and is a medium value.

The effect size index, ϕ\phiϕ , varies depending on the number of

An investigator was interested in the relationship between color preference and number of siblings. A test of independence produced a $\chi$ ² that allowed the null hypothesis to be rejected. The proper conclusion is

In a $\chi$ ² test of independence between age and personality type, the null hypothesis was rejected. The proper conclusion is

In a $\chi$ ²test of independence between gender and kinds of phobias, the null hypothesis was rejected. The proper conclusion is that

In the short cut method of calculating $\chi$ ²;

The effect size index, $\phi$ , varies depending on the number of