Deck 15: Chi-Square

Question 1

You want to do a chi-square test but one of the cells in the crosstab has an expected frequency of 0.5. What should you do?

A) Continue with the chi-square test. There is no problem.
B) Divide the value you get for chi-square by 0.5.
C) Do a One-Way ANOVA instead of chi-square
D) Use Recode to collapse one or both of the variables.

Answer 1

Use Recode to collapse one or both of the variables.

Question 2

You are doing a chi-square test and the sample results are consistent with the research hypothesis. On the basis of the following output, what should you do?
Chi-Square Tests
$\begin{array}{|l|r|r|r|}\hline & \text { Value } & \text { df } & \begin{array}{c}\text { Asymp. Sig. } \\\text { (2-sided) }\end{array} \\\hline \text { Pearson Chi-Square } & 13.951^{*} & 6 & .030 \\\text { Likelihood Ratio } & 14.910 & 6 & 021 \\\text { Linear-byLinear } & 7474 & 1 & 006 \\\text { Association } & & & \\\text { N of Valid Cases } & 144 & & \\\hline\end{array}$
a. 5 cells $( 41.7 \% )$ have expected count less than 5 . The minimum expected count is 48 .

A) Stop! There is an expected count problem.
B) The significance level is .021 so you reject the null hypothesis of independence.
C) The significance level is .030 so you reject the null hypothesis of independence.
D) The significance level is .030 so you do not reject the null hypothesis of independence.

Answer 2

Stop! There is an expected count problem.

Question 3

What does a positive residual in a crosstab cell mean?

A) The two variables are negatively associated.
B) There were more cases with that combination of traits than expected.
C) There were fewer cases with that combination of traits than expected.
D) You should not reject the null hypothesis.

Answer 3

There were more cases with that combination of traits than expected.

Question 4

Your research hypothesis is that region and race are related. Based on the following table of residuals, the sample results are consistent with the _____ and you should proceed to _____.
RACE* REGION Crosstabulation
Residual
$\begin{array}{|rr|r|r|r|r|}\hline&&\text { REGION }\\\hline && \text { 1 Northeast } & \text { 2 Midwest } & \text { 3 South } & \text { 4 West } \\\hline \text { RACE } & \text { 1 white } & 6.3 & 26.0 & -32.7 & 4 \\& 2 \text { black } & 4.2 & -23.0 & 45.1 & -26.3 \\& 3 \text { other } & -10.5 & -3.0 & -12.4 & 25.9 \\\hline\end{array}$

A) null hypothesis … Step 3 (check significance level)
B) null hypothesis … Step 4 (state conclusion)
C) research hypothesis … Step 3 (check significance level)
D) research hypothesis … Step 4 (state conclusion)

Question 5

What is the lowest level of measurement that can be used for the two variables in a chi-square analysis?

A) nominal
B) ordinal
C) interval/ratio

Question 6

The text talks about the expected count in a cell of a crosstab. This is the expected count if

A) the row and column variables are independent
B) the row and column variables are significantly related
C) the row and column variables have identical means
D) the row and column variables have identical numbers of valid cases

Question 7

Your crosstab has 4 rows and 4 columns. Chi-square has how many degrees of freedom?

A) 0
B) 4
C) 9
D) 16

Question 8

If religious affiliation and political party affiliation are independent, then

A) The probability of being a Democrat is the same for Protestants, for Catholics, and for Jews.
B) The probability of being Protestant is the same as the probability of being Catholic which is the same as the probability of being Jewish.
C) The probability of being Democrat is the same as the probability of being Independent which is the same as the probability of being Republican.
D) All of the above.

Question 9

Chi-square is _____ measure of association.

A) a nominal
B) an ordinal
C) an interval/ratio
D) not a

Question 10

You gathered your data using a snowball sample which is a non-probability sampling technique. Which of the following inferential procedures may you use to analyze the data?

A) chi-square
B) one-sample t-test
C) both of the above
D) none of the above

Question 11

Your research hypothesis is "In the population, there is a relationship between the driver's sex and the type of vehicle being driven." What type of hypothesis test should be used?

A) paired-samples t test
B) independent samples t test
C) one-way ANOVA
D) two-way ANOVA
E) chi-square

Question 12

Which one of the following messages from SPSS indicates it is OK to use chi-square?

A) 0 cells (.0%) have expected count less than 5. The minimum expected count is 6.32.
B) 4 cells (25.0%) have expected count less than 5. The minimum expected count is 2.36.
C) 8 cells (40.0%) have expected count less than 5. The minimum expected count is 1.14.
D) 4 cells (19.0%) have expected count less than 5. The minimum expected count is 0.91

Question 13

A cell in a crosstab has an observed count of 50 and an expected count of 25. What is the value of the residual?

A) −25
B) 0.5
C) 2
D) 25

Question 14

You want to know if there is a significant difference in the average incomes of persons living in New York, Los Angeles, and Honolulu. Which would be an appropriate procedure to use?

A) Chi-Square Test
B) One Sample T Test
C) One-Way ANOVA
D) Paired-Samples T Test

Question 15

A cell in a crosstab table has an observed count of 15. The row has a total of 30 cases. The column has a total of 20 cases. The table has a total of 100 cases. What is the expected frequency for the cell?

A) 6
B) 20
C) 50
D) 75

Question 16

Your research hypothesis is "In the population, males drive at a faster speed on the interstate than females." What type of hypothesis test should be used?

A) one-sample t test
B) paired-samples t test
C) independent samples t test
D) two-way ANOVA
E) chi-square

Question 17

You are doing a chi-square test and the sample results are consistent with the research hypothesis. On the basis of the following output, what should you do?
Chi-Square Tests
$\begin{array}{|l|r|r|r|}\hline &{\text { Value }} & \text { df } & {\begin{array}{c}\text { Asymp. Sig. } \\\text { (2-sided) }\end{array}} \\\hline \text { Pearson Chi-Square } & 13.266^{a} & 6 & 039 \\\text { Likelihood Ratio } & 13.442 & 6 & 037 \\\text { Linear-by-Linear } & 1.015 & 1 & .314 \\\text { Association } & & & \\\text { N of Valid Cases } & 342& & \\\hline\end{array}$
a. 1 cells $( 8.3 \% )$ have expected count less than 5 . The minimum expected count is $4.57$ .

A) Stop! There is an expected count problem.
B) The significance level is .039 so you reject the null hypothesis of independence.
C) The significance level is .039 so you do not reject the null hypothesis of independence.
D) The significance level is .314 so you do not reject the null hypothesis of independence.

Question 18

Your research hypothesis is "In the population, the effect of type of vehicle being driven on average speed differs by driver's sex." What type of hypothesis test should be used?

A) one-sample t test
B) independent samples t test
C) one-way ANOVA
D) two-way ANOVA
E) chi-square

Question 19

Chi-square indicates

A) the direction of an association
B) the strength of an association
C) both "a" and "b"
D) none of the above

Question 20

Which religious group is most over-represented in the South?
RELIGION * REGION Crosstabulation
Residual
RELIGION
$\begin{array}{|l|l|r|r|r|r|}\hline & \text { 1 Northeast } & \text { 2 Midwest } & \text { 3 South } & \text { 4 West } \\\hline \text { RELIGION 1 Protestant } & -45.4 & -4.3 & 84.9 & -35.2 \\\text { 2 Catholic } & 44.9 & 1.3 & -42.9 & -3.3 \\\text { 3 Jewish } & 5.1 & .4 & -4.7 & -.8 \\\text { 4 other } & -.2 & -3.5 & -4.3 & 8.0 \\\text { 5 none } & -4.4 & 6.1 & -32.9 & 31.3 \\\hline\end{array}$

A) Protestants
B) Catholics
C) Jews
D) persons belonging to other religions

Question 21

Answer the questions that follow this SPSS output:

Your research hypothesis is "In the population, SEX and strength of religious affiliation (RELINTEN) are related."

A) What is your null hypothesis?
B) Are your sample results consistent with the null hypothesis or the research hypothesis? (null / research)
C) What is the probability of getting the sample results you got if the null hypothesis is true? (If this step in hypothesis testing can be skipped, write the word "SKIP".)
D) What is your conclusion? (In other words, do you "reject" or "not reject" the null hypothesis based on these results?)
E) Are your results statistically significant? (yes / no)

Question 22

You want to know if there is a significant relationship between race and academic major. Which would be an appropriate procedure to use?

A) Chi-Square Test
B) One Sample T Test
C) One-Way ANOVA
D) Paired-Samples T Test

Question 23

Your research hypothesis is "In the population, there is a difference in the average speed of persons driving sports cars, minivans, motorcycles, and sedans." What type of hypothesis test should be used?

A) paired-samples t test
B) independent samples t test
C) one-way ANOVA
D) two-way ANOVA
E) chi-square

Question 24

A statistical guideline that is widely accepted is not to use chi-square if even one cell has an expected count of _____ or if more than _____ of the cells have expected counts of less than 5.

Question 25

Your research hypothesis is "In the population, persons drive at an average speed that is greater than 70 mph." What type of hypothesis test should be used?

A) one-sample t test
B) independent samples t test
C) one-way ANOVA
D) two-way ANOVA
E) chi-square

Question 26

Variables included in a chi-square hypothesis test can have which levels of measurement?

Question 27

What kinds of questions can you answer using a chi-square hypothesis test?

Question 28

Your research hypothesis is "In the population, the average SAT score of persons the second time they take the test is higher than the average of those same persons the first time they took the test." What type of hypothesis test should be used?

A) one-sample t test
B) paired-samples t test
C) independent samples t test
D) two-way ANOVA
E) chi-square

Question 29

What should you do next if chi-square is significant?

Question 30

Answer the question that follows this SPSS output:

You want to do a chi-square test but the crosstab has an expected count problem. How could you transform one or both of the variables to remedy the problem?

Question 31

Here is a bivariate table with observed counts and expected counts. What is the value of chi-square for this table?



chi-square = __________

Question 32

Fill in the expected frequencies for each of the cells in the following table.

Question 33

What does a positive cell residual tell you? A negative cell residual? A zero cell residual?

Question 34

What expected counts would indicate that the value of chi-square may be unstable because the cases are too thinly spread across the crosstab?

Question 35

Answer the questions that follow this SPSS output:

Your research hypothesis is "In the population, whether or not a person would allow an atheist to teach college (COLATH) and strength of religious affiliation (RELINTEN) are related."

A) What is your null hypothesis?
B) Are your sample results consistent with the null hypothesis or the research hypothesis? (null / research)
C) What is the probability of getting the sample results you got if the null hypothesis is true? (If this step in hypothesis testing can be skipped, write the word "SKIP".)
D) What is your conclusion? (In other words, do you "reject" or "not reject" the null hypothesis based on these results?)
E) Are your results statistically significant? (yes / no)

Question 36

For each of the following, calculate the cell residual:

Question 37

What does it mean if two variables are independent? If two variables are related?

Question 38

What can you do if the expected cell frequencies are too small for a chi-square hypothesis test?

Question 39

You are doing a chi-square problem. Your row variable has two categories. Your column variable has seven categories. How many degrees of freedom will your chi-square have?
__________ degrees of freedom