Deck 19: Chi-Square

Question 1

When our emphasis is on sorting outcomes into categories of data, we are concerned with

A) frequency data.
B) categorical data.
C) bean counting.
D) both a and b

Answer 1

both a and b

Question 2

The most common level of α when running a goodness-of-fit chi-square is

A) .05
B) .01
C) .05/ c
D) .95

Answer 2

.05

Question 3

An example of data that would be analyzed with a chi-square is

A) the mean scores received by men and women on a computer science lab report.
B) the average number of meals eaten by cats and dogs.
C) the numbers of Republican and Democrats who voted for and against stricter drunk-driving laws.
D) the deviations from the median shown in the visual acuity levels of children and adults.

Answer 3

the numbers of Republican and Democrats who voted for and against stricter drunk-driving laws.

Question 4

A goodness-of-fit test is

A) only used when we want to test the hypothesis that the categories are equally represented.
B) used when we want to test the hypothesis that some categories are more frequent that others.
C) used to test the null hypothesis that the data are distributed in a way that would be predicted by a theory.
D) probably the most common statistical test we have.

Question 5

The chi-square distribution is

A) a sampling distribution.
B) the distribution against which we evaluate chi-square values.
C) a distribution whose shape varies with the number of degrees of freedom.
D) all of the above

Question 6

A significant result with a goodness-of-fit test might suggest to us that

A) observations are not distributed in line with the null hypothesis.
B) the category means are different.
C) some assumption was likely to have been violated.
D) we have a very flat distribution.

Question 7

Which of the following is the formula for a standard chi-square test?

A)
B)
C)
D) none of the above

Question 8

The chi-square test is used when we have

A) measurement data.
B) ratio data.
C) interval data.
D) categorical data.

Question 9

You should be careful about using a chi-square test when

A) the expected frequencies are quite small.
B) the obtained frequencies are quite small.
C) the expected frequencies are different across the categories.
D) both a and c

Question 10

When using the chi-square tables, we reject the null hypothesis when

A) chi-square is larger than the tabled value.
B) chi-square is smaller than the tabled value.
C) chi-square is far from the tabled value in either direction.
D) It depends.

Question 11

The critical value of χ²

A) decreases as we increase the degrees of freedom.
B) increases as we increase the degrees of freedom.
C) increases as we increase the number of observations ( N ).
D) varies only as a function of α, not as a function of the degrees of freedom.

Question 12

When we sort subjects only into those who improved their performance over time, worsened their performance over time, and stayed the same, we have

A) a one-way classification.
B) a two-way classification.
C) a contingency table.
D) a set of ordered data.

Question 13

The null hypothesis for the previous example which used a chi-square is

A) men and women do not differ on computer science lab report scores.
B) cats and dogs eat the same number of meals.
C) political affiliation and voting behavior on drunk driving are independent variables.
D) children and adults do not show different deviations in visual acuity.

Question 14

With categorical data, the primary piece of data is

A) a measurement.
B) a cell frequency.
C) a mean.
D) both b and c

Question 15

The denominator in chi-square is there to

A) keep the resulting answer in perspective relative to the total frequency.
B) keep the result in perspective relative to the size of the expected frequency.
C) keep people honest.
D) control the probability of a Type II error.

Question 16

For a goodness-of-fit chi-square test, the degrees of freedom are equal to

A) N - 1, where N is the number of observations.
B) C - 1, where C is the number of categories.
C) NC - 1.
D) ( N - 1)( C - 1).

Question 17

A goodness-of-fit test is used with

A) a contingency table.
B) normally distributed variables.
C) a one-way categorization.
D) a test of linearity.

Question 18

A typical null hypothesis with a goodness-of-fit test as presented in the text might be

A) the hypothesis that the means increase evenly across categories.
B) the hypothesis that the representation in each category is equal.
C) the hypothesis that subjects are normally distributed.
D) the hypothesis that the expected values are uniformly large.

Question 19

The multicategory goodness-of-fit case for chi-square is

A) a simple extension of the two-category case.
B) a way of comparing more that two categories.
C) a common situation.
D) all of the above

Question 20

If we run a chi-square test on a one-way classification, a significant result tells us that

A) science has triumphed over evil.
B) the categories are evenly represented in the data.
C) the frequencies differ by category.
D) we have made an error.

Question 21

The chi-square test can run into trouble if

A) the observations are not independent.
B) the expected frequencies are too low.
C) the total number of subjects is very small.
D) all of the above

Question 22

For the next several questions, assume that we had the following contingency table:

With a two-way contingency table the degrees of freedom are

A) RC - 1.
B) C - 1.
C) RC .
D) ( R - 1)( C - 1).

Question 23

We can only use a chi-square test with frequency data if

A) the observations are independent.
B) the observations are sorted into categories.
C) the sample size is not very small.
D) all of these apply

Question 24

The text mentions a correction for continuity and suggests that

A) you always use it with a 2 × 2 table.
B) you always use it with any contingency table.
C) it is not needed.
D) you only use it with a goodness-of-fit test.

Question 25

For the next several questions, assume that we had the following contingency table:

Which of the following are the cell totals?

A) 25, 36, 61, 21
B) 25, 12, 36, 9
C) 61, 21, 37, 45
D) 82

Question 26

If we want to use the chi-square test to test the difference between means we should

A) convert the means to standard scores.
B) convert the means to totals.
C) run a different test instead.
D) be sure the means are not too small.

Question 27

In a Chi-square, k refers to the number of categories.

Question 28

If we want to test proportions, one wrong way to do so is to

A) put the proportions themselves directly into the chi-square formula.
B) convert proportions to frequencies.
C) take the difference in proportions and turn it into a z score.
D) You can't do any of these things.

Question 29

The difference between the chi-square test for a 2 × 2 table and one for a larger table is

A) we must use a different formula.
B) a 2 × 2 is a goodness-of-fit chi-square.
C) you can't handle a contingency table larger than a 2 × 3.
D) There is no difference other than the number of cells we include.

Question 30

A contingency table involves

A) one category of classification.
B) more than one variable on which subjects are classified.
C) no more than two levels of classification.
D) a substantially different computational approach.

Question 31

For the next several questions, assume that we had the following contingency table:

Which of the following are marginal totals?

A) 25 and 36
B) 12 and 36
C) 25, 9, and 82
D) 61 and 21

Question 32

If we want to use the chi-square test to test the difference between two proportions, we should

A) convert the proportions to means.
B) convert the proportions to frequencies.
C) run a z test.
D) either b or c

Question 33

The correction for continuity is known as

A) Fisher's correction.
B) Pearson's correction.
C) Howell's correction.
D) Yates' correction.

Question 34

Chi-square is used to analyze continuous data.

Question 35

For the next several questions, assume that we had the following contingency table:

In the contingency table shown above, the degrees of freedom would equal

A) 1.
B) 2.
C) 3.
D) 4.

Question 36

With several categories in a goodness-of-fit test, a significant result means

A) the categories increase in frequency from left to right.
B) the categories decrease in frequency from left to right.
C) the categories are equally frequent.
D) The test doesn't pay any attention to which category is larger than which other categories.

Question 37

In a chi-square test the expected frequency is

A) the frequency you would expect if the null hypothesis were false.
B) the frequency you actually obtained.
C) the frequency you would expect if the null hypothesis were true.
D) Expected frequency has nothing to do with the null hypothesis.

Question 38

Expected frequencies are the expected value for the number of observations in a cell if the alternative hypothesis is true.

Question 39

A Goodness-of-fit test compares the observed number of frequencies with predicted frequencies.

Question 40

For the next several questions, assume that we had the following contingency table:

In the table above, the expected frequency in the Male/Disagree cell is closest to

A) 11.
B) 5.
C) 28.
D) 9.

Question 41

In a Chi-square including two variables, one with 4 categories, and the other with 3 categories, the df = 6.

Question 42

Indicate whether or not the following Chi-square statistics are significant:
a. χ ² = 2.75; k =2
b. χ ² = 11.00; k =5
c. χ ² = 12.40; df = 6

Question 43

A researcher wants to be sure that her random assignment to groups has been working. She wants to be sure that socio-economic status and treatment group are independent. Ideally, given her particular sample, there would be an equal number of people in each category. Calculate the marginal totals and the expected frequencies for each cell.

Question 44

Assuming the student body in the previous example is 30% male and 70% female,
a. What are the expected values
b. Calculate and interpret Chi-square

Question 45

Calculate and interpret Chi-square for the previous example.

Question 46

In order for a Chi-square test to be valid, a general rule of thumb is that every cell have expected frequencies greater than or equal to 10.

Question 47

A political science student did a survey to see if the political affiliation of voters was related to whether or not they would consider voting for a progressive candidate in the upcoming gubernatorial race. How would you calculate the marginals and expected frequencies for each cell.

Question 48

A professor believes that a greater proportion of females than males have enrolled in her class. Assuming an equal number of males and females in the student body, calculate Chi-square, and evaluate her hypothesis based on the following data.

Question 49

If a Chi-square is conducted based on data from 30 people who are categorized into one of 4 possible categories, the df = 26.

Question 50

A social worker has been asked to testify before her state legislature about the impact of long-term foster care on child outcomes and government spending. She knows that 60% of children who remained in the foster care system without being adopted ended up in prison. The figure for foster care children who were eventually adopted was 25%. These data were based on 500 children who remained in foster care and 800 children who were eventually adopted. Create the appropriate contingency table.

Question 51

It is appropriate to use Chi-square when data from the same subject are in multiple cells.

Question 52

Calculate and interpret Chi-square based on the contingency table you created.

Question 53

In a contingency table, the expected frequency of any given cell is represented by this formula:

Question 54

Calculate and interpret the z score based on the proportion of youth who end up in prison using the data from the previous example.

Question 55

Based on the previous example:
a. What are the df?
b. Calculate and interpret Chi-square.

Question 56

A marginal total is the sum of the level of one variable across all of the levels of the other variable.