Stats

Question 1

An investigator wants to test the hypothesis that the average number of aggressive acts that children exhibit in an unfamiliar situation is related to gender and sociability (“sociable” or “shy”). He obtains a sample of 30 boys and 30 girls who have been rated as either sociable or shy and then has observers count the number of aggressive acts each child exhibits in an unfamiliar situation during a 30-minute play period. The best statistical test to analyze the data the investigator collects in this study is which of the following?

Select one:

a.
Two-way ANOVA

b.
T-test for independent samples

c.
One-way ANOVA

d.
Chi-square test

Answer 1

The research study involves two independent variables (sociability and gender) and a single dependent variable that is measured on a ratio scale (number of aggressive acts). The appropriate statistical test is the two-way analysis of variance.

The correct answer is: Two-way ANOVA

Question 2

An organizational psychologist is hired by a company to help identify job applicants who should be considered for managerial level positions. In this situation, the psychologist wants to develop a selection test battery that will provide the following information: “Which group (manager or non-manager) does a job applicant most closely resemble?” Which of the following methods for combining selection test scores will be most useful for answering this question?

Select one:

a.
Multiple regression

b.
Factor analysis

c.
Canonical correlation

d.
Discriminant function analysis

Answer 2

There are several methods for combining predictor scores to estimate performance on a criterion. When the criterion is group membership (i.e., when the criterion is measured on a nominal scale), discriminant function analysis is an appropriate method.

The correct answer is: Discriminant function analysis

Question 3

A researcher uses a factorial ANOVA to statistically analyze the effects of four types of training strategies and three levels of self-efficacy on a measure of job performance. The results indicate that there are significant main effects of each independent variable and a significant interaction. The researcher will conclude that:
Select one:

a.
The most effective type of training depends on level of self-efficacy

b.
Training is effective regardless of level of self-efficacy

c.
Each type of training is equally effective for each level of self-efficacy

d.
Overall, training is effective only for people with a certain level of self-efficacy

Answer 3

Because the interaction is significant, this means that the effects of the types of training may differ for different levels of self-efficacy – e.g., training method #1 might be most effective for people with low self-efficacy, while training method #2 might be most effective for people with high self-efficacy.

The correct answer is: The most effective type of training depends on level of self-efficacy

Question 4

External validity is likely to be a problem when:
Select one:

a.
The results of a research study indicate that a test’s validity coefficient differs for members of different groups

b.
An investigator uses a nonparametric statistical test to analyze the data she collected in a research study

c.
The research design used by an investigator involves sequentially administering the different levels of the IV to the same group of participants

d.
The research study conducted by an investigator does not include a no-treatment control (comparison) group

Answer 4

External validity refers to the generalizability of research results to different participants, settings, and conditions. This external validity of the research study described in this answer is threatened by multiple treatment interference because it involves exposing all participants different levels of the IV. Consequently, it will not be possible to generalize the results to situations in which individuals receive only one level of the IV.

The correct answer is: The research design used by an investigator involves sequentially administering the different levels of the IV to the same group of participants

Question 5

For her math class assignment, a high school student will compare the average number of hours that students in her school spend playing computer games each day to the national average. To analyze the data she collects, the student will use which of the following statistical tests?
Select one:

a.
Independent samples t-test

b.
Single-sample chi-square test

c.
Multiple-sample chi-square test

d.
Single-sample t-test

Answer 5

The t-test is used to compare two means, and when one of the means is a sample mean and the other is a known population mean, the appropriate t-test is the single-sample t-test.

The correct answer is: Single-sample t-test

Question 6

In a positively skewed distribution, from smallest to largest in magnitude, the measures of central tendency are:
Select one:

a.
Mode, mean, median

b.
Mean, median, mode

c.
Mode, median, mean

d.
Mean, mode, median

Answer 6

Remembering that the “tail tells the tale” and that the median is always the middle score would have helped you identify the correct answer to this question: In a positively skewed distribution, the mode has the smallest value, the median has the middle value, and the mean (which is affected most by the extreme scores in the positive tail) has the largest value.

The correct answer is: Mode, median, mean

Question 7

Sampling error is due to:
Select one:

a.
Random factors that produce a nonrepresentative sample

b.
The unreliability of the test

c.
The invalidity of the test

d.
Non-random factors that produce a nonrepresentative sample

Answer 7

As the result of random (chance) factors, the sample may not “mirror” the population in important characteristics. This is referred to as sampling error.

The correct answer is: Random factors that produce a nonrepresentative sample

Question 8

The Central Limit Theorem predicts that a sampling distribution of the mean will increasingly approach a normal shape:
Select one:

a.
Only when the population distribution does not deviate from the normal

b.
Only when the sample distributions do not deviate significantly from the normal

c.
Regardless of the shape of the population distribution as the number of samples increases

d.
Regardless of the shape of the population distribution as the sample size increases

Answer 8

This is the correct description of the prediction of the Central Limit Theorem. Note that it is the size of the sample that is the critical factor. (The Central Limit Theorem always assumes an infinite number of samples.)

The correct answer is: Regardless of the shape of the population distribution as the sample size increases

Question 9

The probability of making a Type I error is increased by:
Select one:

a.
Conducting a two-tailed (rather than a one-tailed) test

b.
Changing the level of significance from .01 to .05

c.
Changing beta from .01 to .05

d.
Conducting a single multivariate test rather than several univariate tests

Answer 9

The probability of making a Type I error is directly affected by the level of significance (alpha). The larger the level of significance, the greater the likelihood of a Type I error.

The correct answer is: Changing the level of significance from .01 to .05

Question 10

To calculate the F-ratio for a one-way ANOVA:
Select one:

a.
MSB is multiplied by MSW

b.
MSB is divided by MSW

c.
MSW is subtracted from MSB

d.
MSW is divided by MSB

Answer 10

The F-ratio is calculated by dividing a measure of treatment plus error by a measure of error only in order to obtain an estimate of treatment effects. MSB (mean square between) is a measure of treatment plus error, while MSW (mean square within) is a measure of error only, and the F-ratio is calculated by dividing MSB by MSW.

The correct answer is: MSB is divided by MSW

Question 11

To increase power, you would:
Select one:

a.
Reduce sample size

b.
Reduce alpha

c.
Increase sample size

d.
Increase beta

Answer 11

Increasing sample size makes it easier to statistically detect the effects of the independent variable; i.e., it increases power. Other ways to increase power include increasing the magnitude of alpha, using a reliable dependent variable measure, and using a parametric statistical test.

The correct answer is: Increase sample size

Question 12

When using an ABAB design, you are:
Select one:

a.
Administering one treatment to two different behaviors

b.
Administering one treatment to two different groups

c.
Administering one treatment at two different times

d.
Administering two different treatments at two different times

Answer 12

The ABAB design has two no treatment (A) phases and two treatment (B) phases. The same treatment is administered during the B phases.

The correct answer is: Administering one treatment at two different times

Question 13

Which of the following correlation coefficients is useful for determining the degree of association between two nominal variables?
Select one:

a.
Pearson

b.
Biserial

c.
Contingency

d.
Spearman

Answer 13

The contingency coefficient is used to determine the correlation between two nominal (categorical) variables – for example, between a parent’s parenting style (authoritative, authoritarian, permissive, or rejecting/neglecting) and his/her educational achievement (high school graduate, undergraduate degree, master’s degree, doctoral degree).

The correct answer is: Contingency

Question 14

Which of the following provides a measure of shared variability and is calculated by squaring the correlation coefficient?
Select one:

a.
Kappa statistic

b.
Coefficient of concordance

c.
Eta

d.
Coefficient of determination

Answer 14

The coefficient of determination is calculated by squaring the correlation coefficient (r) and provides a measure of shared variability, or the amount of variability in one variable that is explained by variability in another variable.

The correct answer is: Coefficient of determination

Question 15

To determine the degree of association between pregnancy status (pregnant or not) and the number of items selected on a stress event checklist, you would use which of the following?
Select one:

A.
Pearson r

B.
Spearman rho

C.
Biserial

D.
Point biserial

Answer 15

The correct answer is D.

In this situation, you are correlating a variable representing a true dichotomy (pregnant versus not pregnant) with a variable representing a ratio (continuous) scale of measurement (number of stress events). The point biserial correlation coefficient is appropriate when one variable is a true dichotomy and the other is continuous.

Answer A: The Pearson r is appropriate when both variables are measured on a continuous scale.

Answer B: Spearman rho is appropriate when both variables are expressed in terms of ranks. In this question, neither variable is measured using a rank order.

Answer C: The biserial correlation coefficient is used when one variable is an artificial dichotomy (a continuous variable that has been artificially or arbitrarily dichotomized) and the other variable is continuous.

Question 16

To use scores obtained on the eight subscales of the Parental Activities Scale to predict scores on the five subscales of the Child Adjustment Profile, you would use:
Select one:

A.
multiple regression.

B.
canonical correlation.

C.
multiple discriminant analysis.

D.
cluster analysis

Answer 16

The correct answer is B.

In this situation, multiple X scores will be used to predict multiple Y scores. Canonical correlation is an extension of multiple regression and is appropriate when there is more than one Y variable.

Answer A: You would choose multiple regression when using scores on two or more X variables to predict a single Y score.

Answer C: You would use multiple discriminant analysis when the Y variable is nominal and two or more X variables will be used to place the examinee into a category on Y.

Answer D: You would use cluster analysis to identify or confirm homogeneous subgroups.

Question 17

Multiple regression analysis has several advantages over the analysis of variance including all of the following except_____.
Select one:

A.
it eliminates the need for a two-stage analysis involving a global significance test that is followed, when appropriate, by “fine grain” significance tests

B.
it is not limited to categorical (or categorized continuous) variables

C.
it enables the researcher to determine if entering additional independent variables affects the dependent variable beyond the effects found for previously entered variables

D.
it allows the researcher to estimate the effects of the independent variables on the dependent variable with the effects of measurement error removed

Answer 17

The correct answer is D.

This is the only response that does not describe an advantage of either multiple regression or the ANOVA, which makes it the correct response. At least one reason for R. A. Fisher’s development of the ANOVA was to have a mathematically simpler alternative to multiple regression for analyzing the effects of qualitative variables. However, with the availability of computers, the need for the ANOVA has been questioned.

Answer A: This is an advantage of multiple regression. All of the information is provided with a single analysis as opposed to the two-step process required when using the ANOVA.

Answer B: This is also an advantage of multiple regression. It can be used for independent variables measured on any scale of measurement and doesn’t require that continuous variables be categorized (which has the effect of reducing the usefulness of the data).

Answer C: The “stepwise” method of multiple regression does have this advantage.

Question 18

In a _____ distribution of scores, the mean is less than the median and the median is less than the mode.
Select one:

A.
leptokurtic

B.
platykurtic

C.
negatively skewed

D.
positively skewed

Answer 18

The correct answer is C.

In a skewed distribution, the distribution is asymmetrical and the mean, median and mode have different values due to the presence of a few outliers in the positive or negative end of the distribution. In a negatively skewed distribution, the mean is affected most by the few outliers in the negative (low) end of the distribution and has the lowest value.

Answer A: The term leptokurtic is used to describe a distribution of scores that is more “peaked” than the normal distribution.

Answer B: The term platykurtic is used to describe a distribution of scores that is flatter than the normal distribution.

Answer D: In a positively skewed distribution, the mean is larger than the median which is larger than the mode.

Question 19

A researcher would use the Solomon four-group design to:
Select one:

A.
reduce practice effects.

B.
eliminate demand characteristics.

C.
evaluate the effects of pretesting.

D.
determine if there are any selection biases.

Answer 19

The correct answer is C.

The Solomon four-group design combines the pre-test/posttest control group design with the post test only control group design. The purpose of Solomon four-group design is to evaluate the effects of pretesting on a study’s internal and external validity.

Answer A: Techniques like using alternate forms can help reduce practice effects.

Answer B: Researchers use techniques like deception to help reduce demand characteristics.

Answer D: To help control for selection bias, researchers use random selection from subgroups of the population to assist with ensuring they are representative of the larger population.

Question 20

You would use a factorial ANOVA to statistically analyze data when_____.
Select one:

A.
the study includes two or more dependent variables

B.
there are more than two levels of a single independent variable

C.
the study includes two or more independent variables

D.
the effects of a confounding variable must be statistically removed

Answer 20

The correct answer is C.

You would use a factorial ANOVA to analyze data when a factorial design is used and the dependent variable is measured on an interval or ratio scale. A research design is considered “factorial” when it includes two or more independent variables, and you use a factorial ANOVA to analyze the main effects of each independent variable as well as their interaction(s).

Answer A: A MANOVA (multivariate analysis of variance) would be the appropriate test when the study includes two or more dependent variables.

Answer B: A one-way ANOVA would be the appropriate test when there are more than two levels of a single independent variable.

Answer D: An ANCOVA (analysis of covariance) would be used when the effects of a confounding variable must be statistically removed.

Question 21

Adding a constant to every score in a distribution of scores will_____.
Select one:

A.
increase the distribution’s mean

B.
increase the distribution’s standard deviation

C.
increase the distribution’s mean and standard deviation

D.
not increase the distribution’s mean or standard deviation

Answer 21

The correct answer is A.

Adding a constant only affects the mean and other measures of central tendency. It does not affect the variability (spread) of scores in the distribution. As noted in the Statistics and Research Design chapter of the written study materials, adding or subtracting a constant to each score changes the mean and multiplying or dividing by a constant changes both the mean and the standard deviation.

Answer B: Adding a constant will not affect the variability (spread) of scores in the distribution. It only affects the mean and other measures of central tendency.

Answer C: Adding a constant would only affect the mean and other measures of central tendency, but would not have an affect on the standard deviation or variability of scores in the distribution.

Answer D: Adding a constant would affect the mean and other measures of central tendency, but it would not affect the variability (spread) of scores in the distribution or standard deviation.

Question 22

In a normal distribution of test scores, approximately ____% of scores are more than two standard deviations above the mean.
Select one:

A.
2.5

B.
5

C.
7.5

D.
10

Answer 22

The correct answer is A.

In a normal distribution, approximately 95% of scores fall between scores that are -2 and +2 standard deviations from the mean. This means that about 2.5% of scores are less than the score that is 2 standard deviations below the mean and about 2.5% are more than the score that is 2 standard deviations above the mean.

Answer B: For this question, you must identify the % of scores that fall more than two standard deviations above the mean. Knowing that roughly 95% of scores fall between scores that are -2 and +2 standard deviations from the mean, leaves you with 5% of scores that fall above and below the mean. About 2.5% of scores are less than the score that is 2 standard deviations below the mean and about 2.5% are more than the score that is 2 standard deviations above the mean.

Answer C: About 95% of scores fall between scores that are -2 and +2 standard deviations from the mean. This means that about 2.5% of scores are less than the score that is 2 standard deviations below the mean and about 2.5% are more than the score that is 2 standard deviations above the mean.

Answer D: About 95% of scores fall between scores that are -2 and +2 standard deviations from the mean. This means that about 2.5% of scores are less than the score that is 2 standard deviations below the mean and about 2.5% are more than the score that is 2 standard deviations above the mean.

Question 23

A researcher would choose an ANCOVA to _____.
Select one:

A.
statistically remove error variance that is attributable to a known extraneous variable

B.
determine if the effects of an extraneous variable moderate the relationship between the IV and DV

C.
simultaneously assess more than one hypothesis about the IV’s effects on the DV

D.
test the effects of an IV on more than one DV without increasing the experiment-wise error rate

Answer 23

The correct answer is A.

Researchers use the ANCOVA to statistically remove the effects of an extraneous variable (i.e., error variance) so it is easier to detect the effects of the IV on the DV.

Answer B: This doesn’t describe the specific benefit of using an ANCOVA to remove the effects of an extraneous variable.

Answer C: This isn’t why an ANCOVA is used. Researchers use ANCOVAs to statistically remove the effects of an extraneous variable to make it easier to detect the effects of the IV on the DV.

Answer D: This describes the MANOVA (multivariate analysis of variance).

Question 24

A multiple regression equation yields a predicted criterion score for an examinee based on the examinee’s scores on the predictors included in a test battery. When computing a multiple regression equation, each test is weighted_____.
Select one:

A.
in direct proportion to its correlation with the criterion and in inverse proportion to its correlation with the other predictors in the test battery

B.
in inverse proportion to its correlation with the criterion and in direct proportion to its correlation with the other predictors in the test battery

C.
in direct proportion to its correlation with the criterion and with the other predictors in the test battery

D.
in inverse proportion to its correlation with the criterion and with the other predictors in the test battery

Answer 24

The correct answer is A.

When choosing tests for a test battery used to predict status on a criterion, each test should correlate highly with the criterion but not with the other tests in the battery in order to provide the most useful (nonredundant) information. By computing the multiple regression equation so that each test is weighted in direct proportion to its correlation with the criterion and in inverse proportion to its correlation with other tests, the test with the highest criterion-related validity and the least amount of overlap (correlation) with the other tests will be given the largest weight, while the test with the lowest criterion-related validity and the most overlap with the other tests will be given the smallest weight.

Answer B: This is the opposite of what you would do to predict a criterion score. When choosing tests for a test battery used to predict status on a criterion, each test should correlate highly with the criterion but not with the other tests in the battery in order to provide the most useful (nonredundant) information.

Answer C: You would not want other predictors in the test battery to be directly proportionate. When choosing tests for a test battery used to predict status on a criterion, each test should correlate highly with the criterion but not with the other tests in the battery in order to provide the most useful (nonredundant) information.

Answer D: If each test is weighted in inverse proportion to its correlation with the criterion and the other predictors in the test battery, then each test with the least amount of overlap would have the largest weight and would not provide useful information about the predicted criterion score. When choosing tests for a test battery used to predict status on a criterion, each test should correlate highly with the criterion but not with the other tests in the battery in order to provide the most useful (nonredundant) information.

Question 25

Which of the following would be most useful for combining the results of several research studies that each evaluated the effectiveness of the same treatment for a particular disorder?
Select one:

A.
P-value

B.
Kappa coefficient

C.
Coefficient alpha

D.
Effect size

Answer 25

The correct answer is D.

This describes a meta-analysis and an effect size is the index you would calculate when conducting a meta-analysis. It converts data from different studies (which may have different sample sizes, different outcome measures, etc.) to a common metric so you can combine and compare the results of the studies.

Answer A: Although the p-value indicates the level of significance (probability that the null hypothesis is false), it is not as useful as an effect size for combining the results of different studies.

Answer B: The kappa coefficient is used to evaluate inter-rater reliability.

Answer C: Coefficient alpha is used to assess internal consistency reliability.

Question 26

When conducting a one-way ANOVA to compare the effects of four different diets on weight loss, an F-ratio of _____ suggests that there may be a significant difference between the types of diets?
Select one:

A.
15.5

B.
0.9

C.
0

D.
-1.5

Answer 26

The correct answer is A.

The F-ratio is calculated by dividing the mean square between by the mean square within. Mean square between is a measure of treatment effects plus error, while mean square within is a measure of error only. A treatment effect is suggested when the numerator of the F ratio (mean square between) is larger than the denominator (mean square within) resulting in an F value greater than +1.0.

Answers B, C, and D: When conducting a one-way ANOVA to compare the effects of four different diets on weight loss, an F-ratio of 15.5 suggests that there may be a significant difference between the types of diets.