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

Accepted Answer

For a chi-square test for independence, each row and column in the contingency table should add up to the same total (the total number of individuals in the sample). This means that the sum of the observed and expected frequencies for each row and column should also be equal. Therefore, option C is the correct choice. The other options do not provide a good check on the arithmetic involved in calculating expected frequencies.

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

Accepted Answer

The main idea of a chi-square test is to 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

Accepted Answer

When there is no relation between the variables presented in a contingency table, they are considered independent. Therefore, choice C is the best answer. Choices A, B, and D suggest some form of relationship between the variables, which is not the case with 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

Accepted Answer

The chi-square statistic measures the overall lack of fit between the expected and observed frequencies in a contingency table.

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

Accepted Answer

The expected frequency of a cell in a contingency table is calculated by taking the product of the total number of observations in the cell's row and column, then dividing by the grand total of all observations. This is accurately described in option A.

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

Accepted Answer

Option C is incorrect because it describes the computation of the F ratio, which is not part of the chi-square calculation. Steps A, B, and D are all part of the process of calculating the chi-square statistic.

Question 7

In a chi-square test, the variables are:
A)rank-order (ordinal)
B)ratio-scale
C)continuous (quantitative)
D)categorical (nominal)

Accepted Answer

In a chi-square test, the variables are categorical, meaning they are nominal or ordinal. Therefore, option D - categorical (nominal) is the best choice. The other options are not relevant in the context of a chi-square test.

Question 8

The inventor of the chi-square test was:
A)Karl Pearson
B)W) S. Gossett
C)Ronald Fisher
D)Sir Francis Galton

Accepted Answer

Karl Pearson is credited with the development of the chi-square test, a statistical method used to determine the goodness of fit between observed and expected frequencies in one or more categories.

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

Accepted Answer

A contingency table displays the frequencies of combinations of two nominal variables, along with their totals. It allows for the analysis of the relationship between the two variables. Chi-squares and t-distributions are often used in the analysis of contingency tables, but they are not part of the table itself. F-distributions are not typically used in this context.

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

Accepted Answer

The correct distribution is the Chi-square (χ^2) distribution, which is always greater than 0 and skewed to the right. This is because it is based on squared values, making negative values impossible, and it tends to have a shape where most of the data is clumped to the left with a long tail stretching to the right.

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]

Accepted Answer

The chi-squared statistic is calculated using the formula Σ[(O-E)²/E], where O represents the observed frequency and E represents the expected frequency.

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)

Accepted Answer

The expected frequency (E) represents the number of people in a category or cell that would be anticipated or expected if the null hypothesis was true. It is used to calculate the chi-square statistic and compare it to a critical value to determine if the null hypothesis should be rejected or not.

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

Accepted Answer

The exact shape of the chi-square distribution is determined by the degrees of freedom.

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

Accepted Answer

A contingency table, also known as a cross-tabulation or crosstab, is a table that shows the distribution of two categorical variables and their possible combinations. The frequencies of each combination are displayed in the body of the table, and the totals are given along the margins. The advantage of a contingency table is that it allows us to examine possible relationships between the variables and identify any patterns or associations.

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

Accepted Answer

In a contingency table, rows represent one variable while columns represent the other. Therefore, there are three levels of one variable (represented by the rows) and four levels of the other variable (represented by the columns).

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

Accepted Answer

The null hypothesis in a chi-square test for goodness of fit is that the proportion of people over categories breaks down the same for the two populations. This means that there is no difference in the distribution of the categories between the two populations being compared.

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

Accepted Answer

The degrees of freedom for the chi-square test for goodness of fit is calculated as the number of categories minus one. This is because one category's frequency can be determined if the frequencies of all the other categories and the total frequency are known.

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

Accepted Answer

A chi-square test for goodness of fit is specifically designed to compare observed frequencies to expected frequencies for a single nominal variable. The other options listed are not relevant to this type of analysis.

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

Accepted Answer

Independence in a contingency table means that there is no relationship between the variables. This means that knowing the value of one variable does not provide any information about the value of the other variable. Option (A) suggests that there is a relationship between the two variables; option (B) suggests that the variables should not be compared, which is not related to independence; option (C) is incorrect as the formula for expected frequencies incorporates the assumption of independence, and thus larger observed frequencies do not necessarily imply lack of independence.

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

Accepted Answer

The values in a chi-square distribution can be quite large and do not have any upper limit. They are not normally distributed and can be skewed either positively or negatively depending on the degrees of freedom. They are always greater than 0 as they represent the sum of squared deviations from the expected values.

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

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:

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

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

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

A cell's expected frequency is:

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

In a chi-square test, the variables are:

The inventor of the chi-square test was:

A contingency table is a table in which:

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

The formula for the chi-squared statistic is:

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:

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

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.

In a 3 by 4 contingency table, there are:

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

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

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) :

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

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