Deck 14: Chi Square Tests

Question 1

The characteristic that distinguishes chi square from other inferential statistics is that null hypothesis statistical testing is not used.

Answer 1

False

Question 2

The person who published the first article on chi square was Ronald A. Fisher.

Answer 2

False

Question 3

Chi square test probabilities come from the normal distribution.

Answer 3

False

Question 4

The chi square distribution is a histogram with the number of rectangles equal to the degrees of freedom.

Question 5

To get a chi square value, expected values are subtracted from observed values.

Question 6

To find expected values for a chi square goodness of fit test, multiply margin totals.

Question 7

A rejected null hypothesis in a chi square goodness of fit test of means that the theory is adequate.

Question 8

The effect size index your text described for chi square was d.

Question 9

For a 3 x 3 chi square test of independence, the number of degrees of freedom is 4.

Question 10

The characteristic that distinguishes chi square from other inferential statistics is the kind of data analyzed.

Question 11

The person who published the first article on chi square was William S. Gosset.

Question 12

Chi square test probabilities come from the t distribution.

Question 13

The chi square distribution is a normal distribution.

Question 14

To get a chi square value, observed values are subtracted from expected values.

Question 15

To find expected values for a chi square test of independence, multiply margin totals.

Question 16

For a chi square test of goodness of fit, the null hypothesis is that the data fit the theory.

Question 17

A rejected null hypothesis in a chi square test of independence means that the two variables are related.

Question 18

The effect size index your text described for chi square was phi (?).

Question 19

For a 2 x 3 chi square test of independence, the number of degrees of freedom is 2.

Question 20

The characteristic that distinguishes chi square from other inferential statistics is that there is no null hypothesis.

Question 21

The person who published the first article on chi square was Francis Galton.

Question 22

Chi square test probabilities come from the F distribution.

Question 23

To get a chi square value, a numerator is divided by an expected value.

Question 24

Expected values for a chi square goodness of fit test are based on a theory rather than on observations.

Question 25

For a chi square test of goodness of fit, the null hypothesis is that the data do not fit the theory.

Question 26

The effect size index your text described for chi square was f.

Question 27

For a 2 x 4 chi square test of independence, the number of degrees of freedom is 3.

Question 28

Data Set 14-1: With tomatoes, the color of the fruit and the height of the plant are genetically determined (with red dominant over yellow, and tall dominant over short). Suppose for a few minutes, that you are a geneticist during the 1920s or 1930s when these facts are unknown. If the above theory is true, a particular set of crossings will result in a 9:3:3:1 ratio, with nine tall reds to three short reds to three tall yellows to one short yellow.

-The investigation in Data Set 14-1 is one

A) of independence
B) of goodness of fit
C) that could be either
D) that will require combining categories due to the two 3's and a 1.

Question 29

Data Set 14-1: With tomatoes, the color of the fruit and the height of the plant are genetically determined (with red dominant over yellow, and tall dominant over short). Suppose for a few minutes, that you are a geneticist during the 1920s or 1930s when these facts are unknown. If the above theory is true, a particular set of crossings will result in a 9:3:3:1 ratio, with nine tall reds to three short reds to three tall yellows to one short yellow.

-Suppose data were gathered for Data Set 14-1 and the null hypothesis was rejected. You can conclude that

A) the theory should be scrapped and another explanation sought
B) the data support the theory
C) more information is necessary before a decision can be made, namely

Question 30

Data Set 14-2: A college student was interested in the relationship between handedness and academic ability. She classified her sample two ways: left- or right-handed and top or bottom half of the class.

-The study described in Data Set 14-2 is one of

A) independence
B) goodness of fit
C) could be either

Question 31

Data Set 14-2: A college student was interested in the relationship between handedness and academic ability. She classified her sample two ways: left- or right-handed and top or bottom half of the class.

-Which conclusion is correct if the null hypothesis is rejected for Data Set 14-2?

A) the data are most likely invalid because there were probably more right- than left-handed students
B) handedness and academic ability are not related to each other
C) handedness and academic ability are related to each other
D) none of the other alternatives are correct

Question 32

Data Set 14-3: Each of the following represent data for a chi square test of independence. $\begin{array}{llllllllll}\mathrm{W} & \mathrm{X} & \mathrm{Y} & \mathrm{Z}\\1 \quad 29 & 1\quad 4 & 1 \quad 12 \quad 10 & 16 \quad18 \quad 27\\29 \quad 30 & 4 \quad 10 & 10 \quad 16 \quad21 & 39 \quad 42 \quad 50\\&&9\quad 13 \quad 18&\end{array}$

-Refer to Data Set 14-3. Degrees of freedom are equal to 2 for

A) W
B) X
C) Y
D) Z.

Question 33

Data Set 14-3: Each of the following represent data for a chi square test of independence. $\begin{array}{llllllllll}\mathrm{W} & \mathrm{X} & \mathrm{Y} & \mathrm{Z}\\1 \quad 29 & 1\quad 4 & 1 \quad 12 \quad 10 & 16 \quad18 \quad 27\\29 \quad 30 & 4 \quad 10 & 10 \quad 16 \quad21 & 39 \quad 42 \quad 50\\&&9\quad 13 \quad 18&\end{array}$

-In Data Set 14-3, the problem with the smallest expected frequency cell is

A) W
B) X
C) Y
D) all of the other alternatives are correct have one cell that is equally small.

Question 34

Data Set 14-3: Each of the following represent data for a chi square test of independence. $\begin{array}{llllllllll}\mathrm{W} & \mathrm{X} & \mathrm{Y} & \mathrm{Z}\\1 \quad 29 & 1\quad 4 & 1 \quad 12 \quad 10 & 16 \quad18 \quad 27\\29 \quad 30 & 4 \quad 10 & 10 \quad 16 \quad21 & 39 \quad 42 \quad 50\\&&9\quad 13 \quad 18&\end{array}$

-In Data Set 14-3, the short-cut method can be used on

A) W
B) X
C) Y
D) Z
E) A and b

Question 35

Data Set 14-4:Each of the following represent data for a chi square test of independence. $\begin{array}{rlllllllll}\mathrm{W} & \mathrm{X} & \mathrm{Y} & \mathrm{Z}\\3 \quad 1 & 15 \quad 45 & 10 \quad 20 \quad 30 & 15 \quad 18 \quad 24 \\25 \quad 2 & 40 \quad 10 & 30 \quad 20 \quad 10 & 21 \quad 35 \quad 40 \\25 \quad 3 & \quad & \quad \quad & 18 \quad 20 \quad 25\end{array}$


-Refer to Data Set 14-4. Degrees of freedom equal 4 for

A) W
B) X
C) Y
D) Z
E) and .

Question 36

Data Set 14-4:Each of the following represent data for a chi square test of independence. $\begin{array}{rlllllllll}\mathrm{W} & \mathrm{X} & \mathrm{Y} & \mathrm{Z}\\3 \quad 1 & 15 \quad 45 & 10 \quad 20 \quad 30 & 15 \quad 18 \quad 24 \\25 \quad 2 & 40 \quad 10 & 30 \quad 20 \quad 10 & 21 \quad 35 \quad 40 \\25 \quad 3 & \quad & \quad \quad & 18 \quad 20 \quad 25\end{array}$


-In Data Set 14-4, the cell with the smallest expected frequency is in

A) W
B) X
C) Y
D) Z.

Question 37

Data Set 14-4:Each of the following represent data for a chi square test of independence. $\begin{array}{rlllllllll}\mathrm{W} & \mathrm{X} & \mathrm{Y} & \mathrm{Z}\\3 \quad 1 & 15 \quad 45 & 10 \quad 20 \quad 30 & 15 \quad 18 \quad 24 \\25 \quad 2 & 40 \quad 10 & 30 \quad 20 \quad 10 & 21 \quad 35 \quad 40 \\25 \quad 3 & \quad & \quad \quad & 18 \quad 20 \quad 25\end{array}$


-In Data Set 14-4, the short-cut method can be used on

A) W
B) X
C) Y
D) all of the other alternatives are correct.

Question 38

The chi square chapter has in common with the previous chapters that

A) it is about hypothesis testing
B) population variances must be equal
C) both of the descriptive alternatives are correct
D) neither of the descriptive alternatives is correct

Question 39

Chi square has in common with the techniques in previous chapters

A) population scores are assumed to be normally distributed
B) a null hypothesis is tested
C) both of the descriptive alternatives are correct
D) neither of the descriptive alternatives is correct.

Question 40

The data analyzed with a chi square has ________ in common with data analyzed by the techniques in previous chapters.

A) populations are normally distributed
B) variances of the population are equal
C) both of the descriptive alternatives are correct
D) neither of the descriptive alternatives is correct.

Question 41

Which of the following is not true of a chi square test?

A) Its nature is additive.
B) It can detect that two variables are related to each other.
C) The populations are assumed to be normally distributed.
D) The dependent variable is frequencies.

Question 42

Chi square and ANOVA have in common the requirement(s) that

A) population scores must be normally distributed
B) observations or scores must be independent of each other
C) both of the descriptive alternatives are correct
D) neither of the descriptive alternatives is correct.

Question 43

A difference between the F and t distributions and the chi square distribution is that chi square

A) doesn't require assumptions about $\sigma$
B) doesn't require random assignment
C) both of the descriptive alternatives are correct
D) neither of the descriptive alternatives is correct

Question 44

A difference between using the F and t distributions and the chi square distribution is that the chi square distribution

A) doesn't require assumptions about $\sigma$
B) doesn't require that the populations be normally distributed
C) both of the descriptive alternatives are correct
D) neither of the descriptive alternatives is correct

Question 45

A difference between using the F and t distributions and the chi square distribution is that the chi square distribution

A) doesn't require random assignment
B) doesn't require that the populations be normally distributed
C) both of the descriptive alternatives are correct
D) neither of the descriptive alternatives is correct

Question 46

The way in which the data analyzed with chi square differ from those analyzed with ANOVA is that chi square data are

A) normally distributed
B) not normally distributed
C) not random samples
D) frequency counts.

Question 47

The chi square test was invented about

A) 1800
B) 1850
C) 1900
D) 1950.

Question 48

Chi square was named and invented by Karl Pearson, the same person who

A) invented the t distribution
B) invented the F ratio
C) invented the correlation coefficient
D) none of the other alternatives are correct

Question 49

The person who developed $\chi$ ² was

A) Ronald A. Fisher
B) William S. Gosset
C) Karl Pearson
D) Helen Walker.

Question 50

The other statistic that Karl Pearson is responsible for, besides chi square, is

A) ANOVA
B) t test
C) correlation coefficient
D) confidence intervals.

Question 51

Chi square was named by the person who invented it, the same person who

A) invented the t distribution
B) invented the F ratio
C) invented the correlation coefficient
D) none of the descriptive alternatives are correct.

Question 52

Here is a question from the footnotes of the chapter. The journal was started in 1901 to publish articles that combined and .

A) Psychological Review, psychology and biology
B) Psychological Review, psychology and sociology
C) Biometrika, biology and mathematics
D) Biometrika, biology and psychology.

Question 53

According to the figure in your book showing the shape of the chi square distribution, chi square becomes more

A) positively skewed as df becomes larger
B) negatively skewed as df becomes smaller
C) normal as df becomes larger
D) none of the other alternatives are correct

Question 54

If you compare chi square curves for skewness, as degrees of freedom increase, the curves are

A) positively skewed but becoming less so
B) positively skewed and becoming more so
C) negatively skewed but becoming less so
D) negatively skewed and becoming more so.

Question 55

The chi square distribution is

A) one curve
B) a family of curves
C) a family of symmetrical curves
D) a family of symmetrical, rectangular curves.

Question 56

The chi square distributions in the table of your text are ________________ distributions.

A) theoretical
B) empirical
C) a combination of theoretical and empirical
D) neither theoretical or empirical.

Question 57

Suppose you had on a single graph three chi square distributions with degrees of freedom of 1, 5 and 10. Choose a point on the X-axis and draw a vertical line. The distribution that would have the most area to the right of the vertical line would be the one with

A) 1 df
B) 5 df
C) 10 df
D) none of the other alternatives are correct the areas would all be equal.

Question 58

The shape of the theoretical $\chi$ ² distribution is determined by

A) the number of observations
B) the size of the expected frequency of events
C) the number of categories of events
D) all of the other alternatives are correct

Question 59

The $\chi$ ² distributions in the table of your text are

A) empirical distributions
B) theoretical distributions
C) based on a combination of empirical and theoretical facts
D) none of the other alternatives are correct

Question 60

The term "contingency table"goes with

A) all $\chi$ ² tests
B) tests of independence only
C) tests of goodness of fit only
D) $\chi$ ²problems in which df > 1.

Question 61

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.

Question 62

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.

Question 63

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

Question 64

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

Question 65

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

Question 66

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

Question 67

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.

Question 68

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.

Question 69

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.

Question 70

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.

Question 71

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.

Question 72

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.

Question 73

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 ___________.

Question 74

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.

Question 75

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

Question 76

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.

Question 77

In a $\chi$ ² test 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.

Question 78

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.

Question 79

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.

Question 80

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

A) subjects
B) categories
C) both subjects and categories.