Quiz 6
can contain fractions or decimal values
The expected frequencies ______.
distributions
The null hypothesis for the Kruskal-Wallis H test specifies the equality of the various population
there is no relationship between the two variables
The null hypothesis for the chi-square test for independence states that ____.
N (N + 1) / 2
The sum of the ranks from 1 to N is equal to:
The Mann Whitney test
The symbol U represents
Chi-square
The test that assesses whether the observed frequencies differ significantly from expected frequencies is called
between groups
The tie is "critical" for the U or H test if it occurs
expected frequencies should be five or more
The valid use of chi square requires that all
less than zero
The value of chi square never can be
data collected when there are two independent variables
A CONTINGENCY TABLE displays
data collected when there are two independent variables.
A CONTINGENCY TABLE displays
the rank-sum test
A researcher who wishes to test the difference between the locations of two independent samples by using a nonparametric test should use:
12
A sample of 100 people is classified by gender (male/female) and by whether or not they are registered voters. The sample consists of 80 females and 20 males, and has a total of 60 registered voters. If these data were used for a chi-square test for independence, the expected frequencies should have ____ males who are registered voters.
between plus and minus ranks
A tie is "critical" for the T test if it occurs
both of the above
As compared with the corresponding parametric test, a nonparametric test generally:
small and unequal
Beware of unequal variances when sample sizes are
null hypotheses for specific population characteristics
Designating the U, T, and H tests as "nonparametric tests" refers to the notion that these tests aren't based on
Squared ranks
Fundamentally, KWANOVA is based on the sum of
3.0
If Bill is ranked highest, and Mary, Richard, and Joan are all tied for second, what ranks should be assigned to Mary, Richard, and Joan?
one less than the total number of categories
In the one-way test, degrees of freedom for chi square equals
in the vicinity of its critical value
Refer to more advanced books for a possible adjustment if there is at least one "critical" tie and the observed value of U, T, or H is
the sum of the expected frequencies for those who prefer Pepsi the sum of the observed frequencies for those who prefer Pepsi N / 2 ***All of the above***
Refer to the two-variable chi-square study shown below. The entries in the table represent observed frequencies. Men Women Prefer Coke 8 2 Prefer Pepsi 4 6 In this example, the sum of the expected frequencies for those who prefer Coke is equal to:
sample sizes are small
Replace the t test for two independent samples with the Mann-Whitney U test whenever the assumptions of the t test appear to be violated and
nondirectional
Since all discrepancies between observed and expected frequencies are squared, the chi-square test is
a large proportion of the cases are tied
Statistical procedures that deal with ordinal statistics are generally not valid when:
2
THE FOLLOWING QUESTION REFERS TO THE TABLE BELOW SHOWING THE OBSERVED FREQUENCIES WITH WHICH SAMPLES OF MALE AND FEMALE COLLEGE STUDENTS DESCRIBE THEIR POLITICAL PREFERENCE AS EITHER LIBERAL OR CONSERVATIVE. CONSERVATIVE LIBERAL TOTAL MALES 30 70 100 FEMALES 20 80 100 TOTAL 50 150 200 If a seperate column were available for those students who describe themselves as "neither liberal nor conservative," the number of degrees of freedom would equal
For analyzing data from two or more independent samples of subjects
The Kruskal-Wallis one-way analysis of variance is used
by combining the scores of all groups and rank ordering the entire set
The Kruskal-Wallis test begins by _____.
t-test for independent samples
The MANN-WHITNEY U test is equivalent to the
The t test's assumptions of normality and equal variances are untenable
The MANN-WHITNEY U test is used in place of the t-test when
the dependent sample t-test
The Wilcoxon T test is the non-parametric equilavent to
Rank-ordered difference scores
The Wilcoxon t test is based on
from a repeated-measures study
The Wilcoxon test is used with data _____.
Tukey's HSD; mean ranks
The appropriate post hoc test to be used with the KWANOVA is _____ which is applied to _____.
the number of categories increases
The critical value of the chi-square statistic for a one-way test increases as:
(r-1)(c-1)
The degrees of freedom for a two-way X^2 are:
the two samples are combined and the individuals in the total group are ranked
To compute the value for the Mann-Whitney U
Two-variable chi square
To test the significance of the relationship between two variables when data are in the form of frequencies, which of the following should be used?
The chi-square statistic can never be negative
What does it mean to obtain a negative value for the chi-square statistic?
The observed frequencies are different than the expected frequencies
When X^2 (observed) exceeds X^2 (critical) one can conclude
1 and 3
When applying Yate's CORRECTION FOR CONTINUITY the strategy is to 1. Subtract .5 from O when O>E 2. Add .5 to O when O>E 3. Add .5 to O when O<E 4. Subtract .5 from O when O<E
The smaller sum of the signed ranks is compared to the critical value of T
When assessing the Wilcoxon T
Positive difference scores and negative difference scores are summed separately
When computing the Wilcoxon T what numbers are summed?
Compare actual probabilities that could have been developed by chance
When conducting a chi-square test it is appropriate to
from smallest to largest for the combined groups
When converting a list of original scores into ranks, list all observations
Refers to the extent to how closely the observed frequencies fit the expected frequencies
When referring to the chi-square test, GOODNESS-OF-FIT
chi-square tables
When sample sizes are not extremely small, critical values for the H test can be obtained from the
The chi square table
When testing a Kruskal-Wallis H for statistical significance, the result is referred to:
the normal curve table
When testing a rank sum for statistical significance, the critical value can be obtained from:
= H/C
When there is a large number of tied scores which of the following is appropriate for computing?
The population distributions are identical in all other respects except for central tendency
When using the MANN WHITNEY U test to test for the difference between means an important assumption is that
The test focuses on differences in central tendency
With the Wilcoxon T test one must assume that the two treatment populations have identical shapes or are both symmetric when
the number of subjects or matched pairs with nonzero difference scores
With the Wilcoxon T test sample size is defined as
In a 2x2 chi-square analysis
Yates's correction for continuity should be used
6
A chi-square test for independence has df = 2. What is the total number of categories (cells in the matrix) that were used to classify individuals in the sample?
the population distribution departs substantially from normality and the sample size is less than 20
A nonparametric test should be used especially when:
Meat-eaters prefer Coke, whereas vegetarians prefer Pepsi.
A researcher suspects that vegetarians prefer Pepsi and meat-eaters prefer Coke. The researcher obtains a sample of 80 people, and the results are: 30 vegetarians prefer Pepsi, 10 vegetarians prefer Coke; 5 meat-eaters prefer Pepsi, and 35 meat-eaters prefer Coke. If chi square is statistically significant using the .05 criterion, what should the researcher decide?
There is not sufficient reason to believe that gender and political preference are related in this county
A researcher wishes to test the hypothesis that, in a particular county, gender and political preference (Democrat versus Republican) happen to be related. The researcher obtains a sample of 80 voters registered in this county, and the results are: 17 men are Republicans, 23 men are Democrats, 22 women are Republicans, and 18 women are Democrats. Given that the critical value of chi square needed to reject the null hypothesis is 3.84, what should the researcher decide?
gender and political preference are related in this county
A researcher wishes to test the hypothesis that, in a particular county, gender and political preference (Democrat versus Republican) happen to be related. The researcher obtains a sample of 80 voters registered in this county, and the results are: 26 men are Republicans, 14 men are Democrats, 15 women are Republicans, and 25 women are Democrats. Given that the critical value of chi square needed to reject the null hypothesis is 3.84, what should the researcher decide?
9/50 + 9/50
A soda manufacturer wishes to test the hypothesis that more people like his brand than Brand X. The manufacturer obtains a sample of 100 people and finds that 53 people prefer his brand and 47 prefer Brand X. In this study, chi square is equal to:
21 and 21
A statistics class has 42 students. The instructor wishes to test the hypothesis that the number of students who like the course is equal to the number of students who dislike the course. If using the chi square test, what are the appropriate expected frequencies?
28 and 14
A statistics class has 42 students. The instructor wishes to test the hypothesis that two-thirds of the students like the course. If using chi square, which of the following would be appropriate expected frequencies?
34 students like the course and 8 students dislike it
A statistics class has 42 students. Which of the following is in the form of frequency data?
the null hypothesis is rejected if the observed U is less than or equal to the critical U
An unusual feature of hypothesis tests involving U is that
there is no relationship between the political preferences of fathers and sons
Each person in a sample of 180 male college students is cross-classified in terms of his own political preference (Democrat, Republican, Other) and that of his father (Democrat, Republican, Other). The null hypothesis would state that
The observed distribution of frequencies does not equal the expected distribution of frequencies for each category
For non-directional chi-square tests the alternative hypothesis is
The observed distribution of frequencies equals the expected distribution of frequencies for each category
For non-directional chi-square tests the null hypothesis is
true
For the MANN-WHITNEY U test, when n is greater than 20, U is converted to a z score
20, z, normal
For the MANN-WHITNEY U test, when n is greater than _____, U is converted to _____ and the _____ distribution is used.
T
For the Wilcoxon T test the one uses the sampling distribution of _____ for testing the null hypothesis
appropriate, assuming that the population distributions have roughly similar variabilities and shapes
Given an exclusive concern about a population difference in a particular direction, a directional U test is
the results are not likely to be useful for practical purposes
If a statistically significant value of chi square is converted to a phi coefficient of .08, this indicates that:
small enough to qualify as a common outcome
If the null hypothesis is true, discrepancies between observed and expected frequencies will tend to be
100
If the null hypothesis specifies that men and women are equally likely to attend graduate school, then among a random sample of 200 graduate students, the expected frequency of women equals
the results, if significant, are likely to be useful for practical purposes
If the phi coefficient associated with a 2 x 2 chi-square analysis is .57, this indicates that:
is generally a bad idea because ranks convey less information may produce a better measure of correlation if one variable is highly skewed ***both of the above***
If we have continuous scores on two variables, converting the scores to ranks and computing the Spearman rank-order correlation coefficient:
4/20 + 4/10 = 0.60
In a particular county, two-thirds of the registered voters are Republican and the rest are Democrats. For a sample of 30 voters, 22 plan to vote for the Republican candidate for county leader, and 8 plan to vote for the Democrat. To test whether it looks like the electorate is planning to vote along party lines, chi square is equal to:
15
In a two-way chi-square test involving ninety-six participants classified into six religious categories and four political preferences, how many degrees of freedom will be associated with the critical chi-square value?
Can be based on prior information developed by the researcher Can be based on hypothetical distributions Can be based on what would be expected if chance assigned subjects to categories ***All of the above***
In conducting a chi-square test the EXPECTED FREQUENCY
1/3
In the one-day chi-square test, the null hypothesis makes a statement about two or more population proportions. If the null hypothesis specifies that voters are equally likely to prefer three political candidates for govenor, each hypothesized population proportion will equal
two-way chi-square test with 4 degrees of freedom
In the previous question, the situation can be described as the
the lack of relationship between qualitative variables
In the two-way case for chi square, the null hypothesis makes a statement about
distribution-free
Insofar as the U, T, and H tests can be conducted in the absence of assumptions about the population distributions, these tests can be referred to as
3.33
Refer to the two-variable chi-square study shown below. The entries in the table represent observed frequencies. Men Women Prefer Coke 8 2 Prefer Pepsi 4 6 The chi-square statistic for this example is equal to:
1
Refer to the two-variable chi-square study shown below. The entries in the table represent observed frequencies. Men Women Prefer Coke 8 2 Prefer Pepsi 4 6 To find the critical chi square value for this example, the chi square table should be entered with how many degrees of freedom?
4
Refer to the two-variable chi-square study shown below. The entries in the table represent observed frequencies. Men Women Prefer Coke 8 2 Prefer Pepsi 4 6 What is the expected frequency in the Women-Prefer Pepsi cell?
75
THE FOLLOWING QUESTION REFERS TO THE TABLE BELOW SHOWING THE OBSERVED FREQUENCIES WITH WHICH SAMPLES OF MALE AND FEMALE COLLEGE STUDENTS DESCRIBE THEIR POLITICAL PREFERENCE AS EITHER LIBERAL OR CONSERVATIVE. CONSERVATIVE LIBERAL TOTAL MALES 30 70 100 FEMALES 20 80 100 TOTAL 50 150 200 The expected frequency of liberals among males equals
150
THE FOLLOWING QUESTION REFERS TO THE TABLE BELOW SHOWING THE OBSERVED FREQUENCIES WITH WHICH SAMPLES OF MALE AND FEMALE COLLEGE STUDENTS DESCRIBE THEIR POLITICAL PREFERENCE AS EITHER LIBERAL OR CONSERVATIVE. CONSERVATIVE LIBERAL TOTAL MALES 30 70 100 FEMALES 20 80 100 TOTAL 50 150 200 The total number of liberals equals
Positively skewed
The X^2 distribution is
?; ? > ? or ? > ?
The _____ hypothesis being tested in the MANN-WHITNEY U test for a directional hypothesis is _____
5;10
The assumptions of the chi-square test are violated when the expected frequencies for each category are less than _____ when df greater_than_or_equal_to.png 2 and less than _____ when df = 1.
the shape or proportions for a population distribution
The chi-square test for goodness of fit evaluates ______.
categories
The chi-square test is designed for use when observations are classified according to
Goodness-of-fit
The extent to which observed frequencies in a chi-square test match the expected frequencies is called
both should receive a rank of 3.5
The following scores were measured on an interval scale. If the scores are converted to an ordinal scale (ranks), what values should be assigned to the two individuals who started with scores of X = 5? Scores: 2, 3, 5, 5, 7, 10, 18
value of chi square
The larger the discrepancies between observed and expected frequencies, the larger the
equals or exceeds the critical chi square
The null hypothesis should be rejected if the observed chi square
The distribution of scores in the populations underlying each group are identical
The null hypothesis tested in KWANOVA is that
formula for chi square
The one-way and two-way chi-square tests are indistinguishable in terms of the
? (E-O) equals 0
The reason the E - O is squared is because
When n is less than 9; n is between 9 and 21; and n is 21 or greater
There are different tables for the critical values of the MANN-WHITNEY U test for which of the following samples?
When both variables consist of exactly two categories
Under what conditions can the phi-coefficient be used to measure effect size for a chi-square test for independence?
10
Using a sample of 120 creative artists, you wish to test the null hypothesis that creative artists are equally likely to have been born under any of the twelve astrological signs. Assuming that the twelve astrological signs each contain an equal number of calendar days, the expected frequency for each category equals
assigned the mean of the ranks that would have been used had the scores been slightly different
When converting original scores to ranks, if three original scores have identical values, they should be
The smaller of or is used
When evaluating the significance of the MANN-WHITNEY U test,
The scores are independently sampled The scores are randomly sampled The scores in the population are continuously distributed The populations have similar shapes or are both symmetric ***All of the above***
Which of the following are legitimate assumptions of KWANOVA?
None of the expected frequencies should be less than 2 A participant must fall in only one category No response should be related to or dependent on any other response ***all of the above***
Which of the following assumptions must be satisfied in order for chi square to give accurate results?
None of the expected frequencies should be less than 2 none of the above No response should be related to or dependent on any other response A participant must fall in only one category ***All of the above***
Which of the following assumptions must be satisfied in order for chi square to give accurate results?
Cramérs phi
Which of the following can be used with frequency tables that are larger than 2 x 2?
GPA
Which of the following does not represent a discrete category?
The observations are measured on a continuous measurement scale
Which of the following is not an assumption of the chi-square test?
A statistically significant chi-square statistic obtained from a two-variable analysis
Which of the following should be converted to either a phi coefficient or Cramérs phi?
As the number of categories increases the critical value of X^2 increases
Which of the following statements is true for X^2?
the test focuses on differences in central tendency
With the Wilcoxon T test one must assume that the two treatment populations have identical shapes or are both symmetric when
less than
With the Wilcoxon T the null hypothesis is rejected when the obtained value is _____ the critical value
Less than
With the Wilcoxon T the null hypothesis is rejected when the obtained value is _____ the critical value.
UA + UB = (nA)(nB)
You can check your calculations for the Mann-Whitney U by using the relationship ____.
an excessively large sample size
You should question the practical importance of a statistically significant chi-square test that is based on
