Deck 10: The Chi-Square Test and Measures of Association

Question 1

Chi-square distributions that are positively skewed have a research hypothesis that is

A)a one-tailed test.
B)negatively distributed.
C)analogous to the null hypothesis.
D)empirically predetermined.

Answer 1

a one-tailed test.

Question 2

The obtained chi-square statistic summarizes the difference between ______ and ______ in a bivariate table.

A)f ₒ;f ₑ
B)y;Y
C)µ₁;µ₂
D)t;Z

Answer 2

f ₒ;f ₑ

Question 3

The idea that two variables are unrelated in the population is referred to as statistical

A)independence.
B)significance.
C)inference.
D)dependence.

Answer 3

independence.

Question 4

The sampling distribution of chi-square sampling can be best described as

A)a square.
B)negatively skewed.
C)flat.
D)a family of distributions.

Question 5

Chi-square is a useful test for determining ______ significance but not for determining ______ significance.

A)substantive;statistical
B)statistical;substantive
C)observed;expected
D)expected;observed

Question 6

What is the null hypothesis for a chi-square test?

A)Two variables are related in the sample.
B)Two variables are related in the population.
C)Two variables are unrelated in the sample.
D)Two variables are unrelated in the population.

Question 7

Which of the following affects the shape of a chi-square distribution?

A)The number of variables being analyzed
B)The level of measurement of the variable
C)The degrees of freedom
D)The t statistic

Question 8

A PRE of ______ indicates that the two variables are not associated.

A)0
B)-.5
C).5
D)±1

Question 9

A measure of association reflects the strength of a relationship and often the ______ of the relationship.

A)determination
B)stability
C)direction
D)definition

Question 10

Which of the following illustrates a limitation of the chi-square test?

A)It is not based on theory.
B)It does not tell us about statistical significance.
C)It can be used for nominal order data only.
D)It is sensitive to sample size.

Question 11

Which of the following is an assumption required by the chi-square test?

A)A normally distributed population
B)Random sampling
C)Standard deviation equal to 1.0
D)No extreme or outlying observations

Question 12

According to the concept of ______,two variables are associated when information about one can help us improve our prediction of the other.

A)measure of association
B)proportional reduction of error
C)Pearson's correlation coefficient
D)Cramer's V

Question 13

A ______ is an inferential statistical technique designed to test for significant relationships between two variables organized in a bivariate table.

A)cross-tabulation
B)bivariate tabulation
C)chi-square test
D)comparison test

Question 14

Those frequencies that are expected in a bivariate table if the two variables were statistically independent are called ______ frequencies.

A)observed
B)ordered
C)statistical
D)expected

Question 15

Gamma is a useful indicator for ______ variables.

A)unusual
B)dichotomous
C)nominal
D)insignificant

Question 16

A measure of association whose value may vary depending on which variable is considered the independent variable and which the dependent variable is called a(n)

A)symmetrical measure.
B)asymmetrical measure.
C)interdependent associate.
D)dependent associate.

Question 17

Lambda is a measure of association suitable for ______ variables.

A)nominal
B)ordinal
C)interval-ratio
D)subversive

Question 18

In a bivariate table,two variables are said to be statistically independent when,within each category of the independent variable,the percentage distributions of the dependent variable are

A)identical.
B)unequal.
C)descending.
D)ascending.

Question 19

Which of the following values could NOT be a chi-square statistic?

A)57.45
B)57
C).45
D)-57.4

Question 20

The number of degrees of freedom for a chi-square test is calculated as

A)n-1.
B)n+1.
C)(rows-1)(columns+1).
D)(rows-1)(columns-1).

Question 21

SELECT ALL THAT APPLY.Measures of association

A)reflect the strength of the relationship between variables.
B)sometimes reflect direction of the relationship between variables.
C)indicate the usefulness of predicting the dependent variable from the independent variable.
D)are based on the concept of the proportional reduction of error (PRE).

Question 22

Suppose you obtain a chi-square statistic of 67.81.Are your results statistically significant if the critical value obtained from the distribution of chi-square is 3.84 with an alpha level of .05?

Question 23

The number of degrees of freedom in a cross-tabulation data with three rows and four columns is 12.

Question 24

A gamma of -1.0 indicates a perfect,negative association between the variables.

Question 25

The larger the chi-square statistic,the smaller the p value.

Question 26

Below are hypothetical data on the relationship between sex and marital satisfaction.Calculate the expected frequencies,or the frequencies we would expect to observe if there were no relationship between sex and marital satisfaction.

Question 27

SELECT ALL THAT APPLY.Chi-square test

A)requires no assumptions about the shape of the population distribution.
B)can be applied to only nominal data.
C)can be applied to nominal or ordinal data.
D)is also referred to as the goodness-of-fit test.

Question 28

Lambda is an appropriate measure of association if the percentage difference is very small (usually less than 5%).

Question 29

The stronger the relationship between the variables,the larger will be the reduction in the number of errors of prediction.

Question 30

Below are hypothetical data on the relationship between sex and marital satisfaction.Calculate the number of degrees of freedom associated with the chi-square test for these data.

Question 31

Gamma and Kendall's tau-b are measures of association which are suitable for nominal variables.

Question 32

When two variables are not associated,they are said to be statistically dependent.

Question 33

SELECT ALL THAT APPLY.PRE measures of association

A)can range from 0.0 to 1.0.
B)of zero indicate that the two variables have a perfect relationship.
C)of one indicate that the two variables have a perfect relationship.
D)reflect the strength of the association between the two variables.

Question 34

SELECT ALL THAT APPLY.The main properties of the chi-square distribution are that

A)the distributions are positively skewed.
B)chi-square values are always positive.
C)a chi-square of zero means that the variables are completely independent and the observed frequencies in every cell are equal to the corresponding expected frequencies.
D)as number of degrees of freedom decreases,the chi-square distribution becomes more symmetrical.

Question 35

The following data on social class and the value placed on thinking for oneself were obtained from the General Social Survey.Calculate and compare the appropriate percentages for the data in this table.

Question 36

SELECT ALL THAT APPLY.Cramer's V

A)is a measure of association that can be used for nominal variables.
B)can take both positive and negative values
C)is a non-directional measure.
D)uses PRE framework.

Question 37

SELECT ALL THAT APPLY.In chi-square test,

A)reducing the observed frequencies by half will cut down the calculated chi-square by exactly half.
B)doubling the observed frequencies will cut down the calculated chi-square by exactly half.
C)a relatively strong association between the variables may significant when the sample size is small.
D)the sample size is inversely proportional to the size of the calculated chi-square.

Question 38

SELECT ALL THAT APPLY.The expected frequency

A) is denoted by fo.
B) is evaluated using the formula (column marginal) (row marginal)/N.
C) is the frequency in a bivariate table if the variables were statistically independent.
D) is the most important element in using the Chi-square test.

Question 39

SELECT ALL THAT APPLY.The degree of freedom in a bivariate table

A)is the number of cells in the table for which the expected frequencies are free to vary.
B)is the product of the number of rows and columns.
C)compensates the distortion of a bivariate table if one cell is over or undersampled.
D)with two rows and two columns is 4

Question 40

Lambda may range in values from 0.0 to ±1.

Question 41

What interpretation do we get if Kendall's Tau-b reaches a value of 1?

Question 42

In order to determine the statistical significance of the chi-square statistic,you need to know the number of cells in the table for which the expected frequencies are free to vary given that the marginal totals are already set.What is the statistical name for this quantity and how is it calculated?

Question 43

Imagine you were examining whether the relationship between race and length of work is statistically significant.How would you state your research hypothesis?

Question 44

Briefly describe the primary difference between symmetrical and asymmetrical measures of association.

Question 45

Suppose you obtain a chi-square statistic of 3.86.Are your results statistically significant if the critical value obtained from the distribution of chi-square is 6.63 with an alpha level of .01?

Question 46

The following data on social class and the value placed on thinking for oneself were obtained from the General Social Survey.Calculate the expected frequencies for each cell.

Question 47

Apply the five-step model of a chi-square test to a specific example.

Question 48

Which variable is the independent variable in the table below?

Question 49

A researcher is examining the relationship between job security and job satisfaction.Use the data below to calculate the value of gamma.

Question 50

Why is it sometimes important to condition one's result by another variable?