Deck 14: Strategies When Population Distributions Are Not Normal: Data Transformations and Rank-Order Tests

Question 1

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 members of the sample considered without the outlier would not lead to a significant result.
D)improve the reliability of the statistical procedure.

Answer 1

lead to a significant result when the other members of the sample considered without the outlier would not lead to a significant result.

Question 2

In a square-root transformation,

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

Answer 2

moderate numbers become only slightly lower,but high numbers become much lower.

Question 3

Which of the following represents the correct scores if 4,25,25,and 100 are 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

Answer 3

1,2.5,2.5,4

Question 4

Which of the following represents the correct scores if 1,4,25,and 81 are transformed using a square-root transformation?

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

Question 5

Assumptions for statistical procedures are about

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

Question 6

Which of the following represents the correct scores if 4,25,25,and 100 are transformed using a square-root transformation?

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 7

A common transformation procedure when scores are positively skewed is the

A)square-root transformation.
B)squared transformation.
C)exponential transformation.
D)sign-reversal transformation.

Question 8

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)robust to violations of assumptions.

Question 9

One indication that a population is not normally distributed is when

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)a ceiling or floor effect is present in a large sample.

Question 10

Data transformations are legitimate

A)because no information is lost or distorted.
B)when performed post hoc.
C)because the order of scores is not altered.
D)when they favor a researcher's hypothesis.

Question 11

Which transformation has the strongest influence on a positively skewed distribution?

A)square-root
B)log
C)inverse
D)reflection

Question 12

Which of the following represents 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 13

Prior to using a procedure that is "distribution-free," the sample scores would probably be transformed using the

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

Question 14

When the assumption of a normal curve is seriously violated,the ordinary t test

A)resembles an analysis of variance.
B)is conducted using √t instead of t.
C)gives an incorrect result.
D)is robust.

Question 15

When a distribution is negatively skewed,which of the following transformations should be performed first?

A)square-root
B)log
C)inverse
D)reflection

Question 16

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

A)duplicate scores which will make the sample more normal.
B)sample only members of the population who will make the sample normal.
C)transform the sample scores.
D)delete the scores that make the distribution nonnormal if the results are not significant.

Question 17

A sample drawn from a normally distributed population

A)might have more members than the population.
B)is sometimes approximately normally distributed.
C)is always approximately normally distributed.
D)is never approximately normally distributed.

Question 18

Having discovered an extreme score in a sample of scores,the first thing to do is to

A)discard the score.
B)make sure the score was not recorded in error.
C)perform a log transformation.
D)perform an inverse transformation.

Question 19

A distribution of rank-ordered scores will always be

A)a normal curve.
B)bimodal.
C)rectangular.
D)skewed.

Question 20

The first step in considering a data transformation is to

A)examine the transformed sample distribution.
B)apply the most appropriate transformation.
C)examine the sample data to determine the shape of the distribution.
D)conduct Cochran's Test for Nonnormality.

Question 21

The rank-order test that would be used in the same kind of research situation as a t test for independent means is

A)the Wilcoxon signed-rank test.
B)the Wilcoxon rank-sum test.
C)the Kruskal-Wallis H test.
D)Spearman's rho.

Question 22

Which of the following is a disadvantage that is applicable to rank-order tests but not data transformations?

A)They may distort the scores in ways that make the scores lose their original meaning.
B)They do not always make the data normal in all groups.
C)They cannot always be used.
D)They must be analyzed using less familiar nonparametric tests.

Question 23

Bootstrap tests are an example of a(n)

A)computer-intensive method.
B)post-hoc test.
C)unequal distribution comparison.
D)marginal test.

Question 24

The mean and variance of rank-ordered scores depends on

A)the number of groups.
B)the most frequent score.
C)the number of scores that are ranked.
D)the mean and variance of the untransformed scores.

Question 25

If a Results section includes a sentence stating that "comparisons…were made using the Wilcoxon rank-sum test," the type of test used was

A)a rank-order test.
B)analysis of variance.
C)a computer-intensive test.
D)a t test for independent means.

Question 26

The correct null hypothesis for a rank-order test comparing two groups is that

A)the moderate ranks are evenly distributed.
B)the highest ranks are evenly distributed.
C)the populations have equal means.
D)the medians of the two populations are equal.

Question 27

In research articles,data transformations are usually mentioned in the

A)discussion section.
B)reference list.
C)participants section.
D)results section.

Question 28

The rank-order test that would be used in the same kind of research situation as a t test for dependent means is

A)the Wilcoxon signed-rank test.
B)the Wilcoxon rank-sum test.
C)the Kruskal-Wallis H test.
D)Spearman's rho.

Question 29

Which procedure can be performed without the aid of computers?

A)approximate randomization test
B)Mann-Whitney U test
C)bootstrap test
D)randomization test

Question 30

In most research situations,randomization tests are conducted by

A)looking on special tables for the probability of a difference score.
B)summing all the possible difference scores.
C)computers.
D)distributing difference scores across ranks.

Question 31

The rank-order test that would be used in the same kind of research situation as the correlation coefficient is

A)the Wilcoxon signed-rank test.
B)the Wilcoxon rank-sum test.
C)the Kruskal-Wallis H test.
D)Spearman's rho.

Question 32

For the scores 0.8,1.1,1.7,1.7,2.3,and 2.6,the shape of the distribution is __________.

A)approximately normal
B)positively skewed
C)negatively skewed
D)rectangular

Question 33

Which of the following is part of the randomization test procedure?

A)ordering the difference scores from lowest to highest
B)rank-ordering the scores within each group
C)looking up the cutoff score or critical value in a standard table
D)applying a square-root transformation

Question 34

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

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

Question 35

The rank-order test that would be used in the same kind of research situation as an analysis of variance is

A)the Wilcoxon signed-rank test.
B)the Wilcoxon rank-sum test.
C)the Kruskal-Wallis H test.
D)Spearman's rho.

Question 36

A disadvantage of both data transformations and rank-ordered tests is that they

A)are not as familiar as computer-intensive methods.
B)can distort the meaning of the scores.
C)cannot be used for complex situations.
D)may not normalize the distribution of scores.

Question 37

The relative advantages of data transformations versus rank-order tests in terms of power

A)have not been well established.
B)were well established in the 1980s.
C)were well established in the 1920s.
D)are irrelevant.

Question 38

Some statisticians have shown that instead of using the special procedures involved in rank-order tests,approximately the same results can be obtained by transforming the scores into ranks and then

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

Question 39

Which of the following is a nonparametric test?

A)analysis of variance
B)t test for dependent means
C)Spearman's rho
D)t test for independent means

Question 40

For the scores 12,13,14,15,16,and 17,the shape of the distribution is __________.

A)approximately normal
B)positively skewed
C)negatively skewed
D)rectangular

Question 41

The null hypothesis in a rank-order test for two groups is that the two populations have the same __________.

Question 42

If a research article included a statement that "level of intensity was compared to reaction time using a Wilcoxon rank-sum test," the statistical test was a(n)__________ test.

Question 43

A square-root transformation might be used to make a distribution of scores that is __________ more normal.

Question 44

Procedures that allow one to analyze scores from nonnormal samples using the standard parametric procedures such as t tests and analyses of variance are __________.

Question 45

The purpose of a data transformation is to __________.

Question 46

A researcher wants to compare attitudes towards fraternities at two different colleges using a t test for independent means.The scores for five randomly selected students at College A were 1,9,16,25,and 49.The scores for five randomly selected students at College B were 9,25,36,49,and 81.
After applying a square-root transformation,the attitude scores for College A are __________.

Question 47

In a rank-order procedure,scores of 7,8,15,and 15 would be converted to __________.(Give a list of numbers.)

Question 48

A nonparametric version of the t test for independent means is the __________ test.

Question 49

In a rank-order procedure,scores of 6,10,17,and 25 would be converted to __________.(Give a list of numbers.)

Question 50

An extreme score that is at the far end of a sample distribution is called a(n)__________.

Question 51

One type of computer-intensive method is a(n)__________.

Question 52

If examining the scores in a sample suggests that the population distribution appears to be nonnormal,one solution is to apply a(n)__________,and then,having met the normal-curve assumption,carry out an ordinary parametric test.

Question 53

The general name for a test that can be performed on scores from a population with a distribution of any shape is __________.

Question 54

The advantages of the familiar,precise parametric techniques over nonparametric methods can be obtained by __________.

Question 55

A researcher wants to compare attitudes towards fraternities at two different colleges using a t test for independent means.The scores for five randomly selected students at College A were 1,9,16,25,and 49.The scores for five randomly selected students at College B were 9,25,36,49,and 81.
After applying a square-root transformation,the attitude scores for College B are __________.

Question 56

If a ceiling or floor effect is present,the distribution of the scores will probably be __________.

Question 57

The mean and variance of a rank-ordered distribution depend on __________.

Question 58

If a sample's scores are skewed to the right,the transformation that can be used to make the distribution of scores closer to a normal curve is a(n)__________ transformation.

Question 59

A researcher wants to compare attitudes towards fraternities at two different colleges using a t test for independent means.The scores for five randomly selected students at College A were 1,9,16,25,and 49.The scores for five randomly selected students at College B were 9,25,36,49,and 81.
For College A's transformed scores,the mean is __________,and the standard deviation is __________.

Question 60

A nonparametric version of the t test for dependent means is the __________ test.

Question 61

A researcher wants to compare attitudes towards fraternities at two different colleges using a t test for independent means.The scores for five randomly selected students at College A were 1,9,16,25,and 49.The scores for five randomly selected students at College B were 9,25,36,49,and 81.
The pooled estimate of the population variance (S²_pooled)is __________.

Question 62

Describe the distributions of the following scores:
a.0.5,0.9,1.1,34,38,43
b.3,35,115,119,123,124,131,136,140

Question 63

A consultant to a large real estate sales company decided to see if sales agents who attended a seminar on the value of having an internal locus of control had different sales rates than those who attended an ordinary sales seminar.Ten agents were randomly selected and randomly assigned to a group.After the seminar,members of the experimental (internal locus)group ranked 7,5.5,4,10,and 2 in sales; members of the control (ordinary sales)group ranked 3,9,1,8,and 5.5 in sales.
a.Using a standard t test for independent means on the ranks and the .05 significance level,did type of seminar make a difference in sales rates in the company?
b.Explain your analysis to a person who is familiar with the t test for independent means,but not with rank-order procedures or the issues associated with them.

Question 64

A developmental psychologist comparing infants of three different temperaments on their ability to recognize faces found that the scores for the infants with Temperament I were 577,131,and 629; the scores for the infants with Temperament II were 508,483,and 220; and the scores for the infants with Temperament III were 1907,1104,and 1569.
a.Conduct a standard one-way analysis of variance,but with ranks instead of recognition scores.Using the .05 level,do these results suggest that among infants in general,these kinds of temperaments make a difference in ability to recognize faces?
b.Explain and justify your analysis to a person who is familiar with the one-way analysis of variance,but not with rank-order procedures or the issues associated with them.

Question 65

Describe the distributions of the following scores:
a.-998,-971,-968,-5,-3,-3
b.-7,-3,-1,0,1,2,3,8

Question 66

A researcher wants to compare attitudes towards fraternities at two different colleges using a t test for independent means.The scores for five randomly selected students at College A were 1,9,16,25,and 49.The scores for five randomly selected students at College B were 9,25,36,49,and 81.
The standard deviation of the comparison distribution (S_difference)is __________.

Question 67

A sports psychologist was interested in whether imagery would change the performance of five bowlers.Performance was assessed when bowling in a normal manner and when bowling with imagery instructions (i.e.,concentrate on pleasant settings for 10 seconds before each turn); order of conditions was randomized.The scores were as follows: a.Conduct a t test for dependent means with the original difference scores using the .01 level.
b.Apply a square root transformation to the difference scores,and then conduct another t test with these transformed scores.
c.Explain the reasons for using the transformation and the implications of the difference in results of these two methods.Write your explanation for a person who is familiar with the t test for dependent means,but not with data transformations.

Question 68

A researcher wants to compare attitudes towards fraternities at two different colleges using a t test for independent means.The scores for five randomly selected students at College A were 1,9,16,25,and 49.The scores for five randomly selected students at College B were 9,25,36,49,and 81.
For College B's transformed scores,the mean is __________,and the standard deviation is __________.

Question 69

A researcher wants to compare attitudes towards fraternities at two different colleges using a t test for independent means.The scores for five randomly selected students at College A were 1,9,16,25,and 49.The scores for five randomly selected students at College B were 9,25,36,49,and 81.
Given that the critical value (.05 level,two-tailed)is __________,the researcher's decision should be __________.

Question 70

A researcher wants to compare attitudes towards fraternities at two different colleges using a t test for independent means.The scores for five randomly selected students at College A were 1,9,16,25,and 49.The scores for five randomly selected students at College B were 9,25,36,49,and 81.
The t score calculated for the t test for independent means is __________.

Question 71

Describe the distributions of the following scores:
a.101,120,131,143,146,2902
b.-109,-0.9,-0.1,-0.1,0,0.3,0.4