Deck 11: CHI-Squared Tests of Fit

Question 1

Parametric tests work by assuming ______.

A) that a meaningful statistic can be set and then testing a parameter again that statistic
B) that a meaningful parameter can be set and then testing a sample against that parameter
C) that a parameter can be used to reasonably summarize data and then measuring that parameter
D) none of these

Answer 1

B

Question 2

A non-parametric test ______.

A) makes fewer assumptions about the parameters it measures
B) does not assume that a meaningful parameter exists
C) does not make assumptions about scale of measurement
D) none of these

Answer 2

B

Question 3

Because they do not rely upon means and standard deviations, non-parametric tests can often be conducted when the scale of measurement of the outcome variable is ______.

A) nominal or ordinal
B) ordinal or interval
C) interval or ratio
D) ratio only

Answer 3

A

Question 4

Non-parametric tests examine the ______ of a(n) ______ .

A) goodness, independence
B) independence, goodness
C) fit, model
D) model, fit

Question 5

A goodness of fit test is used when we want to see how likely data is given a model of likely ______.

A) counts of a single nominal variable
B) interactions between two nominal variables
C) values for a parameter
D) none of these

Question 6

Which of these is a research question describing a goodness of fit test?

A) Is this preference for our product likely given a population mean of 8?
B) Are there differences in preferences for our product between groups?
C) Between our three products, is one chosen more often by men?
D) When sampling each of our products, which is most often chosen as best?

Question 7

Which of these is a research question describing a test of independence?

A) Is this preference for our product likely given a population mean of 8?
B) Are there differences in preferences for our product between groups?
C) Between our three products, is one chosen more often by men?
D) When sampling each of our products, which is most often chosen as best?

Question 8

Which of these is a valid null hypothesis for a χ² goodness of fit test?

A) Product preferences are independent of gender.
B) Product preferences are not independence of gender.
C) There is no difference between observed and expected frequencies of product preference.
D) There is a difference between observed and expected frequencies of product preference.

Question 9

Which of these is a valid alternative hypothesis for a χ² test of independence?

A) Product preferences are independent of gender.
B) Product preferences are not independence of gender.
C) There is no difference between observed and expected frequencies of product preference.
D) There is a difference between observed and expected frequencies of product preference.

Question 10

The shape of the χ² distribution is dependent on ______.

A) between-groups degrees of freedom
B) within-groups degrees of freedom
C) total degrees of freedom
D) none of these

Question 11

Degrees of freedom for a χ² test are dependent upon the number of ______.

A) subjects
B) categories
C) types
D) none of these

Question 12

When $\alpha$ = .05 at 6 degrees of freedom, the critical χ² is ______.

A) 12.592
B) 24.725
C) 11.070
D) none of these

Question 13

In a goodness of fit test, when $\alpha$ = .05 and k = 9, degrees of freedom are ______.

A) 5
B) 9
C) 8
D) none of these

Question 14

In a test of independence, when $\alpha$ = .01, k₁ = 7 and k₂ = 4, degrees of freedom are ______.

A) 6
B) 3
C) 27
D) 18

Question 15

In a goodness of fit test, when $\alpha$ = .01 and n = 20, the critical χ² is ______.

A) 52.191
B) 50.892
C) 31.410
D) none of these

Question 16

In a goodness of fit test, when k = 5 and $\alpha$ = .05, the critical χ² is ______.

A) 9.488
B) 11.070
C) 24.725
D) none of these

Question 17

In a test of independence, when $\alpha$ = .01 and k₁ = 5, the critical χ² is ______.

A) 21.666
B) 24.725
C) 9.488
D) none of these

Question 18

In a test of independence, when $\alpha$ = .05, k₁ = 6 and k₂ = 3, the critical χ² is ______.

A) 28.869
B) 12.592
C) 18.307
D) 7.815

Question 19

The χ² statistic examines ______.

A) the difference between observed and expected counts as a proportion of expected counts
B) the squared difference between observed and expected counts as a proportion of expected counts
C) the difference between observed and expected counts as a proportion of observed counts
D) the squared difference between observed and expected counts as a proportion of observed counts

Question 20

In a goodness-of-fit test, when n = 30 and k = 3, what do we expect to occur in each cell?

A) 3
B) 30
C) 10
D) 90

Question 21

A ______ table is used to illustrate the counts at each intersection of two variables in a test of independence.

A) contingency
B) cross
C) computational
D) none of these

Question 22

In a test of independence, a unique effect created by a particular combination of levels in two variables is called a(n) ______.

A) interaction
B) blend
C) combination
D) none of these

Question 23

χ² tests are sensitive to small cell sizes. You should try to have a sufficient sample size to have at least ______ observed or expected cases in every cell.

A) 3
B) 5
C) 10
D) 15

Question 24

If $\chi$ ²(3) = 8.1, then you should ______.

A) Reject the null
B) Retain the null
C) Retain the alternative
D) Reject the alternative

Question 25

In a test of independence, if $\chi$ ² = 9.0, k₁ = 3 and k₂ = 3, you should ______.

A) Reject the null
B) Retain the null
C) Retain the alternative
D) Reject the alternative

Question 26

If $\chi$ ² = 2, n = 10 and k = 4, what is the value of Cramer's V?

A) 0.26
B) 0.07
C) 2
D) none of these

Question 27

If $\chi$ ² = 4, n = 20, k₁ = 5 and k₂ = 7, what is the value of Cramer's V?

A) 0.05
B) 0.26
C) 5
D) none of these

Question 28

Which of the following is considered a "strong" Cramer's V?

A) .2
B) .8
C) -.8
D) none of these

Question 29

When a χ² is statistically significant, for supplemental analyses, we ______.

A) calculate Cramer's V
B) calculate Cohen's d
C) calculate a phi coefficient
D) none of these

Question 30

A Cramer's V calculated on a 2 × 2 contingency table is also called a ______.

A) Cohen's d
B) phi coefficient
C) eta-squared
D) none of these

Question 31

With one degree of freedom, the χ² distribution looks similar to a normal distribution.

Question 32

In a χ² goodness of fit test, the expected values are always equal.

Question 33

Non-parametric tests are used when we cannot make assumptions about parameters.

Question 34

With a non-parametric test, we examine how particular data fit a particular model.

Question 35

In a goodness of fit test, we test a model assuming that two variables are independent from one another.

Question 36

χ² tests are always non-directional.

Question 37

Counts occurring at all possible combinations of two variables can be expressed using a contingency table.

Question 38

The following is a valid null hypothesis: There is a difference between observed and expected frequencies of gum preference.

Question 39

The following is a valid alternative hypothesis: : Gum preference is not independent of gender.

Question 40

All χ² distributions are similar to the normal distribution.

Question 41

The region of rejection in χ² is always in the left tail.

Question 42

When conducting a goodness-of-fit test on data with 6 groups, there are 5 degrees of freedom.

Question 43

When conducting a goodness-of-fit test on data with 7 groups, the critical value is 12.592.

Question 44

When conducting a χ² test of independence with 8 groups in the first variable and 5 groups in the second variable, there are 28 degrees of freedom.

Question 45

When conducting a χ² test of independence when k₁ = 3 and k₂ = 4, the critical value is 21.026.

Question 46

χ² is calculated as the sum of all squared differences between observed and expected counts, divided by observed counts.

Question 47

Because χ² is sensitive to small cell counts, you should always collect a large enough sample so that observed and expected cell sizes are all above 5.

Question 48

If $\chi$ ²(2) = +1.133, the null should be rejected.

Question 49

If $\chi$ ² = 20 and k = 12, the null should be retained.

Question 50

Cramer's V can be interpreted as the difference between cells in standard deviation units.

Question 51

When is a non-parametric test more appropriate than a parametric test?

Question 52

How do you determine the expected model for a goodness-of-fit test? Provide an example.

Question 53

When is a χ² test of independence used? Provide an example of significant interaction in a business context.

Question 54

Cramer's V is not easily interpretable on its own. But under what conditions is it more useful?

Question 55

You run a small business with four employees: Susan, Jimmy, Albert, and Camilla. Because you need three employees at work at any given time, only one employee ever has the day off. Unfortunately, everyone always wants Saturday off. One of your employees has confronted you and said that you favour some employees over others in providing Saturdays off. To investigate this, you pulled up a list of who has recently had Saturdays off each week. Over the past 24 weeks, Jimmy has had 10 Saturdays off, Susan has had 2 Saturdays off, Albert has had 12 Saturdays off, and Camilla has had 16 Saturdays off.
1) What is the research question?
2) What are the hypotheses?
3) What are the degrees of freedom?
4) What is the critical value for this test?
5) State the formal results of the test.
6) Should you compute a measure of the overall effect size? How do you know? If so, calculate this effect size.
7) State all appropriate conclusions.

Question 56

You run a small business with three retail clothing outlets. At each outlet, you sell three types of products: budget items, mid-range, and high fashion. You have decided to investigate if sales of these types differ by store. To do this, you retrieved a list of sales at all three stores and created a dataset also recording which store sold which item. Conduct a test of independence to investigate this. The contingency table from your records appears below.
1) What is the research question?
2) What are the hypotheses?
3) What are the degrees of freedom?
4) What is the critical value for this test?
5) State the formal results of the test.
6) Should you compute a measure of the overall effect size? How do you know? If so, calculate this effect size.
7) State all appropriate conclusions.