Deck 11: Chi-Square Tests and Strategies When Population Distributions Are Not Normal

Question 1

When carrying out a chi-square test for independence, a good check on your arithmetic in figuring the expected frequencies is to make sure that:

A)the expected frequency of each cell is no larger than the observed frequency
B)the sum of all the expected frequencies times the degrees of freedom equals the sum of all the observed frequencies
C)for each row and column, the sum of the observed frequencies and the sum of the expected frequencies come out to be the same
D)for each row, the sum of all the expected frequencies equals the observed frequencies, minus 1, for each column

Answer 1

for each row and column, the sum of the observed frequencies and the sum of the expected frequencies come out to be the same

Question 2

The main idea of a chi-square test is that you:

A)test the estimated degree of fit (proportion of variance accounted for)of one variable to the other variable
B)compare the population means to see if they vary from each other more than by chance
C)compare population variances, to see if they vary from each other more than by chance
D)test how well the pattern of observed frequencies fits some expected pattern of frequencies

Answer 2

test how well the pattern of observed frequencies fits some expected pattern of frequencies

Question 3

A situation of no relation between variables in a contingency table is known as:

A)dependence
B)reverse relation
C)independence
D)contingent relations

Answer 3

independence

Question 4

A(n)__________ statistic reflects the overall lack of fit between the expected and observed frequencies.

A)nominal variable
B)chi-square
C)expected frequency
D)population

Question 5

A cell's expected frequency is:

A)the number of people in its row divided by the total number of people, multiplied by the number in its column
B)the number of people in its column divided by the total number of people, divided by the row proportion
C)the number of people in the cell's row multiplied by the number of people in the column
D)the number of people in the cell's row divided by the number of people in the column

Question 6

All of the following are steps in figuring the chi-square statistic EXCEPT:

A)determine the actual, observed frequencies in each category or cell
B)divide each squared difference between observed and expected frequencies by the expected frequency for its category or cell
C)figure the overall F ratio by figuring, for each category or cell, the observed minus expected, and squaring this difference
D)determine the expected frequencies in each category or cell

Question 7

In a chi-square test, the variables are:

A)rank-order (ordinal)
B)ratio-scale
C)continuous (quantitative)
D)categorical (nominal)

Question 8

The inventor of the chi-square test was:

A)Karl Pearson
B)W) S. Gossett
C)Ronald Fisher
D)Sir Francis Galton

Question 9

A contingency table is a table in which:

A)the distributions of two nominal variables are laid out so that you have the frequencies of their combinations as well as the totals
B)chi-squares for each category are displayed over each level of the independent variable
C)distributions are translated into t distributions
D)chi-square distributions are translated into F distributions

Question 10

The __________ distribution is always greater than 0 and skewed to the right (most scores clumped on the left, with a tail on the right).

A)Z
B)t
C)χ²
D)F

Question 11

The formula for the chi-squared statistic is:

A)Σ[(O-E)²/E]
B)[Σ(O-E)²]/F
C)O/[Σ(O-E)²]
D)E/[Σ(O-E)²]

Question 12

In a chi-square test, the number of people in a category or cell expected or anticipated if the null hypothesis was true is known as:

A)observed frequency (O)
B)distributed frequency (D)
C)expected frequency (E)
D)attained frequency (A)

Question 13

The exact shape of the chi-square distribution depends on the:

A)ratio
B)underlying normality of the distribution
C)degrees of freedom
D)cutoff score on the distribution of means

Question 14

A __________ is a table in which the distributions of two nominal variables are set up so that you have the frequencies of their combinations, as well as the totals.

A)frequency table
B)contingency table
C)table of distributions
D)nominal variable table

Question 15

In a 3 by 4 contingency table, there are:

A)four levels of each variable
B)two levels of one variable and three levels of the other
C)three levels of one variable and four levels of the other
D)four levels of one variable and five levels of the other

Question 16

In a chi-square test for goodness of fit, the null hypothesis is that:

A)the number of people in one category is no greater than the number of people in the other
B)the variances of the populations of categories are the same
C)the proportion of people over categories breaks down the same for the two populations
D)the means of the two populations of categories are the same

Question 17

The degrees of freedom for the chi-square test for goodness of fit is:

A)the number of categories minus one
B)the mean number of individuals per category, minus the number of categories
C)the mean number of individuals per category, minus one
D)the total number of individuals, minus the number of categories

Question 18

A hypothesis-testing procedure that examines how well an observed frequency distribution of a single nominal variable fits some expected pattern of frequencies is a(n):

A)chi-square test for independence
B)chi-square for goodness of fit
C)observed frequency test
D)multiple correlation

Question 19

When discussing the pattern in a contingency table, the word "independence" means:

A)the distribution of one variable varies over different levels of the other
B)the variables in the table should not be compared
C)the observed frequencies are larger than the expected frequencies
D)there is no relationship between the variables

Question 20

The values in a chi-square distribution are always greater than 0 and:

A)are normally distributed
B)less than 1
C)can be quite large
D)are negatively skewed

Question 21

The effect-size measure for a chi-square test for independence used with a contingency table that is larger than 2 by 2 is known as:

A)Pearson's chi
B)Gosset's phi
C)Cohen's d
D)Cramer's phi

Question 22

According to Cohen's conventions for the phi coefficient, a large effect size is:

A) .10
B) .15
C) .40
D) .50

Question 23

In a chi-square test for independence, the null hypothesis is that:

A)the two population variances are independent
B)the two variables are independent in the population
C)the means of the populations are not equal
D)the means of the populations are equal

Question 24

The approximate power for the chi-square test for independence in a study with a predicated medium effect size and sample size of 100 (df total = 3)would be:

A) .12
B) .77
C) .21
D) .71

Question 25

Which of the following would NOT be allowed in an ordinary application of the chi-square tests?

A)Participants' preference for studying sitting or lying down are assessed as sophomores and then again as seniors.
B)Tall and short people are compared on their religious affiliation.
C)The number of people of different ethnicities working in a particular company is compared to the proportions of those ethnicities in the general public.
D)The number of successes of an advertisement is compared for three different groups of consumers to see if the number of successes is equal for the three groups.

Question 26

A __________ is a measure of association between two dichotomous nominal variables.

A)chi-square statistic
B)phi coefficient
C)zeta coefficient
D)Z score

Question 27

In a study with 100 people, an analysis results in a χ² value of 3.15. What is the phi coefficient?

A) .02
B) .32
C) .18
D) 1.8

Question 28

In a study with a 3 by 2 design, phi and Cramer's phi:

A)are equivalent
B)are equivalent if phi is divided by 2
C)are unrelated
D)are the inverse of one another

Question 29

In a study with a 4 by 4 design and a large effect size, Cramer's phi would be approximately:

A) .29
B) .35
C) .50
D) .06

Question 30

Which of the following research questions cannot be answered using a chi-square analysis?

A)Does the percentage of students at Greenwood College who prefer decaffeinated coffee differ from the percentage preferring regular coffee?
B)Do light-haired people prefer small dogs to large or mid-sized dogs?
C)Do children change their preferences for sugar cereals after viewing a healthy eating ad campaign?
D)Do more first-year students than second-year college students use the library as their primary study location?

Question 31

For the following question(s): In a developing country, 100 people were randomly surveyed about their socioeconomic class and religious affiliation. Here are the results and an excerpt from the results section of this fictional study:
Of the total population, what percentage was comprised of agnostics, atheists, and others?

A)(12 + 13 + 22)= 47%
B)(4 + 6 + 18)= 28%
C)(8 + 7 + 4)= 19%
D)(12 + 22 + 22)= 56%

Question 32

The degrees of freedom for the chi-square test for independence is:

A)the number of categories minus one
B)the number of columns minus one, times the number of rows minus one
C)the total number of category levels minus one
D)the number of people minus the number of cells

Question 33

The phi coefficient is:

A)always less than 0
B)equal to the square root of χ²/N
C)always greater than 1
D)equal to the square root of χ²/ N-1

Question 34

The formula for Cramer's phi statistic is:

A)the square root of [χ²/N (df smaller)]
B)the square root of [χ²/N (df larger)]
C)df smaller multiplied by N-1
D)χ²/ df smaller

Question 35

"(N_Columns -1)(N_Rows -1)" is the formula for the degrees of freedom for:

A)the chi-square test for goodness of fit
B)the chi-square test for independence
C)the within-group estimate of a two-way analysis of variance
D)all of the above

Question 36

The approximate total number of participants needed for 80% power with a 3 by 3 (df = 4)contingency table at the .05 level if you expect a medium effect would be:

A)48
B)133
C)1,194
D)121

Question 37

All of the following are true about the phi coefficient EXCEPT:

A)it is very closely related to the correlation coefficient
B)it is the same as the correlation coefficient squared (r²)
C)it is the Greek letter "φ"
D)it is equal to the square root of χ²/N

Question 38

In a chi-square test of independence, the term "expected frequency" generally refers to:

A)the distribution of people over categories on the measured variables under the assumption of equal numbers of people in all cells
B)the expected distribution of people over categories on one variable if the distribution of people over categories on the other variable is completely unrelated to it
C)the spread of the independent variable to see if it is a truly independent variable
D)the population's distribution of the scores on the dependent variable

Question 39

What percentage of the middle class was Catholic?

A)7)5/34 = 22%
B)5/100 = 5%
C)5/34 = 15%
D)7)5/100 = 8%

Question 40

What is the approximate total number of participants needed for 80% power for the chi-square test of independence (.05 significance level, total df = 2)with a predicted large effect size?

A)26
B)39
C)107
D)1,194

Question 41

For the following question(s): A study reported; "A chi-square test for independence was conducted to explore the relationship between whether a person had or had not sought psychological counseling and the person's profession (lawyer, car dealer, college professor, high school teacher, and postal worker). A significant relationship was found, X²(4, N = 100)= 12.33, p < .05." Here are the results:
What percentage of postal workers had NOT sought counseling?

A)5/34 = 15%
B)5/100 = 5%
C)5/9 = 56%
D)5/14 = 36%

Question 42

If one were to carry out a square-root transformation on the following data (16, 64, 1089, 484), the resulting dataset will comprise which group of numbers?

A)2, 4, 8, 33
B)1, 1, 1, 1
C)4, 8, 33, 22
D)4, 8, 22, 33

Question 43

For the following question(s): A study reported; "A chi-square test for independence was conducted to explore the relationship between whether a person had or had not sought psychological counseling and the person's profession (lawyer, car dealer, college professor, high school teacher, and postal worker). A significant relationship was found, X²(4, N = 100)= 12.33, p < .05." Here are the results:
What percentage of college professors had sought counseling?

A)22/66 = 33%
B)22/29 = 76%
C)19/66 = 29%
D)19/29 = 66%

Question 44

In a square-root transformation:

A)high numbers become very low and low numbers become very high
B)moderate numbers remain unchanged, but low numbers become slightly higher
C)low numbers become much lower and high numbers remain basically unchanged
D)moderate numbers become slightly lower and high numbers become much lower

Question 45

One finding of this study was that:

A)being poor caused people to be Catholic
B)poor people tended to be Protestant, Catholic, or other, while middle-class people were most likely to be Protestant
C)poor people valued religion more than middle-class people
D)being Catholic caused people to be poor

Question 46

What percentage of people were protestant in this study?

A)22
B)17
C)31
D)4

Question 47

Assumptions for statistical procedures are about:

A)populations
B)samples
C)inferences
D)hypotheses

Question 48

What is an important point to consider for any data transformation procedure:

A)one must perform the transformation on all the scores on a given variable
B)no matter what transformation is used, the order of the scores always stays the same
C)the transformed version of a set of scores may meet the normality assumption
D)all of the above

Question 49

A population is usually NOT normally distributed if:

A)a small sample drawn from the population is positively skewed
B)two variables are measured at the same time
C)a scale or index is used for the measured variable
D)there is a strong ceiling or floor effect

Question 50

A widely used procedure when the sample scores do not appear to come from a normal population is to:

A)duplicate scores that will make the sample more normal
B)sample only members of the population who will make the samples normal
C)transform the scores
D)normalize the scores by deleting the individuals that make the distribution non-normal

Question 51

In general, the t test and the analysis of variance are:

A)dependent on five basic assumptions
B)free of assumptions
C)sensitive to violations of assumptions
D)adequate if there are not large violations of assumptions

Question 52

When the normal-curve assumption is strongly violated, the ordinary t test:

A)resembles an analysis of variance
B)is conducted using Z scores instead of t scores
C)gives an incorrect result
D)is adequate

Question 53

In addition to inventing the chi-square test, Kari Pearson also invented the method of computing correlation used today and coined the terms(s):

A)histogram
B)skew
C)spurious correlation
D)all of the above

Question 54

The phi coefficient for this study is:

A) .03
B) .35
C)1.11
D) .11

Question 55

A sample that comes from a normally distributed population:

A)might have more members than the population
B)is often approximately normally distributed
C)is always normally distributed
D)is almost always curvilinear

Question 56

All of the following are valid conclusions from the study EXCEPT:

A)approximately 55% of lawyers sought counseling
B)car dealers comprised 23% of the entire sample
C)a majority of postal workers sought counseling
D)a majority of high school teachers sought counseling

Question 57

A mathematical procedure (such as taking the square root)applied to each score in a sample, usually done to make the sample distribution closer to normal, is known as a:

A)procedural transliteration
B)data transformation
C)data manipulation logarithm
D)normality inducer

Question 58

All of the following are true about the inventor of the chi-square test EXCEPT:

A)his name was Karl Pearson
B)he also invented the method of figuring correlation used today
C)he stole most of his ideas (or "borrowed heavily")from other statisticians
D)he also did work in the now-discredited field of eugenics

Question 59

One finding of this study was that:

A)high school teachers tended to seek counseling less than the other professions studied
B)car dealers sought counseling less than other professions in the study
C)car dealers and college professors had the most stressful jobs, since they had had to seek counseling more than people in other professions.
D)car dealers were about evenly split on those who had and those who had not sought counseling

Question 60

When conducting a statistical test, a single outlier can:

A)make the test more robust to violations of the assumption of normality
B)reduce the sample's variance, making significant results easier to achieve
C)lead to a significant result when the other numbers, considered without the outlier, would not have led to a significant result
D)improve the reliability of the statistical procedure

Question 61

In research articles, data transformations are usually mentioned in the:

A)discussion section
B)introduction
C)reference section
D)results section

Question 62

Which of the following are the correct scores if 1, 4, 25, and 81 are transformed using the rank-order method?

A)1, 2, 5, 9
B)1, 4, 25, 81
C)4, 4, 25, 25
D)1, 2, 3, 4

Question 63

The result of using a parametric test with data transformed into ranks:

A)will be just as accurate as either the ordinary parametric test or the rank-order test
B)will be slightly less accurate as either the ordinary parametric test or the rank-order test
C)will require a smaller sample size to derive an accurate result
D)will require a larger sample size to derive an accurate result

Question 64

Of the following rank-order tests, which applies to the same kind of research situation as a t test for independent means?

A)Wilcoxon signed-rank test
B)Wilcoxon rank-sum test
C)Kendall's tau
D)Spearman's rho

Question 65

Some statisticians have shown that instead of using the special procedures in rank-order tests, you get about the same results if you transform scores into ranks and then:

A)figure a Spearman Z
B)find the mean of the scores' inverses
C)apply all the usual arithmetic for calculating an ordinary parametric test, such as a t test
D)apply all the usual arithmetic for calculating a typical nonparametric test, such as a Wilcoxon signed-rank test

Question 66

Which of the following is an appropriate type of data transformation procedure for a set of scores in the behavioral and social sciences?

A)Square-root transformation
B)Log transformation
C)Arcsine transformation
D)Any of the above

Question 67

"A chi-square test for independence indicated that males and females were not evenly distributed across the categories [χ² (3, N = 234)= 56.79, p = .04]." What is the chi-square value in this study?

A)3
B)234
C)56.79
D).04

Question 68

Which of the following is a positive feature of rank-order tests?

A)Rank-order methods have not been developed for many complex situations.
B)The simple logic of rank-order tests breaks down if there are many ties in ranks.
C)Rank-order methods distort the original data, losing information.
D)You can use rank-order methods regardless of the shape of the distributions of the original scores.

Question 69

When you are using ranked data, the population distribution tends to be ___________ in shape. (Hint: there are equal numbers-one-of each rank.)

A)bimodal
B)multimodal
C)hexagonal
D)rectangular

Question 70

What is a potential disadvantage of using a data transformation procedure?

A)Transformations may come closer to the true meaning of the underlying measurement
B)Transformations may not work because there may not be a reasonable transformation that makes the scores normal or have equal variance in all groups
C)Transformations may distort scores in ways that lose the original meaning
D)Both B and C

Question 71

In research articles, chi-square tests usually include the frequencies in each category or cell as well as:

A)the degrees of freedom and significance level
B)the number of participants
C)the sample's chi-square value
D)all of the above

Question 72

Hypothesis-testing procedures based on ranks are also called:

A)nonparametric tests
B)parametric tests
C)distribution-free tests
D)both A and C

Question 73

A results section noted, "Comparisons of desire to swim and parental expectations were made using Wilcoxon rank-sum test." What type of test was used?

A)rank-order test
B)analysis of variance
C)parametric test
D)t test for independent means

Question 74

Which of the following are the correct scores if 4, 25, 25, and 100 were transformed using the rank-order method?

A)2, 5, 5, 10
B)1, 2.5, 2.5, 4
C)1, 2, 3, 4
D)1)5, 2, 3.5, 4

Question 75

Which of the following is a nonparametric test?

A)Analysis of variance
B)t test for dependent means
C)Chi-square
D)t test for independent means

Question 76

A log transformation has the same type of effect as a square-root transformation, but the effect is stronger, so it is more suitable for distributions that are:

A)normally distributed
B)very strongly skewed to the left
C)very strongly skewed to the right
D)bimodal in their distribution

Question 77

Because the distribution of rank-order scores is known exactly rather than estimated, rank-order tests:

A)do not require estimating any parameters
B)are used in most real studies
C)are almost always preferred over square-root transformations
D)require drawing additional samples

Question 78

In a situation with three groups, you would normally do a one-way analysis of variance. If you were to use a rank-order method, however, you would use the:

A)Wilcoxon signed-rank test
B)Wilcoxon rank-sum test
C)Kendall's tau
D)Kruskal-Wallis H test

Question 79

The chi-square test was invented by __________.

Question 80

The sample scores for a procedure that is "distribution-free" would probably be transformed using the:

A)reflection transformation
B)antilog transformation
C)rank-order method
D)inverse transformation