Chapter 9, 10, 11 Homework

The degrees of freedom for a two-way chi-square statistic are:

(r-1)(c-1)

Choose the weakest correlation:

-.28 -.76 +.66 Correct: +.12

Choose the strongest correlation:

-.28 Correct: -.76 +.66 +.12

If r = .84, the coefficient of determination is equal to:

.29 .50 Correct: .71 .84

If r = .37, the coefficient of determination is equal to:

.92 Correct: .14 .63 .86

The coefficient of determination is:

1-r^2 r^2 SStotal-SSerror/SStotal Correct both: b and c

If a = 8 and b = 3, what would be the predicted outcome (y) for a person with X = 6?

19 Correct: 26 30 51

If a = 3 and b = 5, a person scoring X = 8 would be predicted to have a Y score of:

23 29 34 Correct: 43

The correlation between two variables that are TOTALLY unrelated would be:

A. 1 B. -1 C. .5 D. 0 D

The degrees of freedom for a chi-square test applied to a cross-tabulation with 4 rows and 3 columns is equal to:

A. 2 B. 6 C. 4 D. 7 B.

Which of the following is not a requirement for using the chi-square statistic?

A. A comparison of only one group is necessary B. At least nominal level data C. Random sampling should be employed D. Independent samples A.

If fear of crime initially decreases with age, but then after age 40 reverses itself, this correlation would be an example of:

A. A positive relationship B. A negative relationship C. A curvilinear relationship D. Cannot tell from the above information. C.

The __________ is a very useful statistic for finding spurious relationships.

A. Pearson's square B. Pearson's r C. partial correlation correction D. partial correlation coefficient D

A researcher takes a sample and wants to compare the results to the population from which it was drawn. The independent variable consists of three categories and the dependent variable is measured at the ordinal level. What test would the researcher use to see if results are significant?

A. The Mann-Whitney U test B. An ANOVA test C. The median test D. The Kruskal-Wallis test D.

Which of the following is FALSE of nonparametric tests?

A. They require a normal distribution. B. They can use nominal level data. C. They are less powerful than parametric tests. D. All of the above are false. A.

In statistics, r is called:

A. Yate's correction B. Regression coefficient C. Pearson's correlation coefficient D. t value C

Parametric tests require:

A. a normal distribution. B. equal sample sizes. C. more than two samples. D. none of the above A.

A researcher takes a sample and wants to compare the results to the population from which it was drawn. The independent variable is "gender" and the dependent variable is a yes/no response to whether they favor the abortion. What test would the researcher use to see if results are significant?

A. a parametric test B. a median test C. a t test D. a chi-square test D.

Nonparametric tests are useful when:

A. all of the above. B. the researcher cannot assume normality. C. there is a small number of cases. D. data are not measured at the interval level. A.

As the observed frequencies get closer to the expected frequencies, the value of the chi-square statistic:

A. becomes larger. B. becomes smaller. C. does not change. D. not enough information provided B.

An important first step in assessing the relationship of two interval level variables is to:

A. calculate a correlation coefficient. B. look at a scatter plot. C. do a test of significance. D. calculate the variance of the independent variable. B

Which of the following is NOT a requirement of the median test?

A. comparing two or more medians B. ordinal data C. random sampling D. nominal data D.

A positive correlation between variables X and Y implies:

A. high scores on X are associated with high scores on Y. B. high scores on X are associated with low scores on Y. C. low scores on X are associated with low scores on Y. D. the variables X and Y are not strongly related. A.

A negative correlation between variables X and Y implies:

A. high scores on X are associated with high scores on Y. B. high scores on X are associated with low scores on Y. C. low scores on X are associated with low scores on Y. D. the variables X and Y are not strongly related. B

A strong correlation between variables X and Y implies:

A. high scores on X are associated with high scores on Y. B. low scores on X are associated with low scores on Y. C. X is a good predictor of Y. D. X is not good predictor of Y. C

Nonparametric tests REQUIRE:

A. none of the above are required. B. nominal level measurement. C. equal sample sizes. D. more than two samples. A.

The set of frequencies obtained in an actual frequency distribution are the:

A. observed frequencies. B. expected frequencies. C. marginal frequencies. D. A and C A.

The frequencies proposed under the terms of the null hypothesis are the:

A. observed frequencies. B. expected frequencies. C. marginal frequencies. D. A and C B.

If the variable Crime increases as the variable Police Presence decreases, the correlation is said to be:

A. positive. B. negative. C. strong. D. curvilinear B

The correlation coefficient:

A. presents the strength of the relationship. B. presents the direction of the relationship. C. varies from -1.0 to +1.0. D. all of the above D

If a chi-square expected frequency is less than 10, one should:

A. reject the null hypothesis. B. use Yates' correction. C. accept the null hypothesis. D. square all values. B.

A strong curvilinear relationship between two variables might yield a Pearson's r that is:

A. strong and positive. B. strong and negative. C. weak or close to 0. D. large in expected frequency. C

A chi-square test of significance is essentially concerned with:

A. the distinction between expected and observed frequencies. B. only observed frequencies. C. the distinction between two interval level variables. D. the distinction between one ordinal and one interval level variable. A.

Expected frequencies represent:

A. the frequencies one would expect if the null hypothesis were true. B. the frequencies one would expect if the null hypothesis was not true. C. the frequencies one would expect if the sample were normally distributed. D. none of the above A.

The median test determines:

A. the likelihood that the median will be the most frequent score. B. the likelihood the mean and the median and the mode will all have the same value. C. the likelihood that the samples were drawn from populations with equal medians. D. none of the above C.

A chi-square test should be used with caution when:

A. the population is not assumed to be normally distributed. B. the total sample size exceeds 100. C. there is an expected frequency > 5. D. there is an expected frequency < 5. D.

If a correlation between variables A and B is found to be equal to -1.16:

A. the relationship is negative. B. the relationship is significant. C. there has been a miscalculation. D. none of the above C

If a Pearson's r of +95 is calculated for A and B is calculated to be +.95, we can confidently report that:

A. variable B is definitely caused by variable A. B. variable B is probably caused by variable A. C. variable A is caused by variable B. D. none of the above D.

Small expected frequencies cause the value of the chi-square statistic to:

A.become much larger. B. become much smaller. C. not change. D. not enough information provided A.

The direction of a correlation is indicated by:

Correct: its sign (+ or - ). its numerical value. both A and B none of the above

If the variable Self-Control increases as the variable Education increases, the correlation is said to be:

Correct: positive. negative. strong. curvilinear

The coefficient of determination explains:

Correct: the proportion of variance in Y that is determined or explained by X. the proportion of variance in Y that is NOT determined or explained by X. the proportion of variance in Y that is attributed to error. the proportion of variance in X that is attributed to error.

The formula for Chi-Square x^2 is

E(fo-fe)^2/fe

A chi-square tests depends the interval level of measurement.

False

A correlation coefficient is considered a measure of variation.

False

Correlation coefficients do NOT indicate the strength of a relationship.

False

In a chi-square test of significance, the dependent variable is measured at the interval level.

False

Pearson's correlation coefficient assesses the strength and direction of curvilinear relationships.

False

Regression equations can only have one independent variable.

False

The degrees of freedom for a chi-square test depend on the sample size.

False

r^2 is the coefficient of nondetermination.

False

Which of the following is NOT a requirement for regression analysis?

Interval data Straight line relationship Random sampling Correct: All of the above ARE requirements

The increase or decrease in Y expected with each unit change in X is known as:

The Y-intercept, a The error term, e Correct: The regression coefficient or slope, b Proportionate reduction in error, PRE

A chi-square test is a nonparametric test of significance.

True

A correlation coefficient of -.60 is a stronger correlation than a correlation coefficient of +.55

True

A weak correlation coefficient could result from a curvilinear relationship.

True

X is generally considered to be the independent variable in a regression analysis.

True

Which of the following is not a component of the regression equation?

Y-intercept slope error Correct: standard deviation

1-r^2 is known as the:

coefficient of determination. Correct: coefficient of nondetermination. code of decimals. complement of r.

The variable being predicted in a regression analysis is called the:

independent variable. Correct: dependent variable. regression variable. contingency variable.

Regression analysis creates a mathematical function which predicts the value of the __________ on the basis of the __________.

independent variable; dependent variable Correct: dependent variable; independent variable correlation; variance variance; correlation

The strength of the correlation is indicated by:

its sign (+ or - ). Correct: its numerical value. both A and B none of the above

In a one-way chi-square, the appropriate number of degrees of freedom is:

k-1

Correlation can vary with respect to:

moment. direction. strength. Correct: B and C

The square of Pearson's r (r^2) is known as the:

percentage reduction in variance (PRV). proportionate reduction in error (PRE). the coefficient of determination. Correct: both b and c

If the variable Crime Attractiveness increases as the variable Age remains constant, the correlation is said to be:

positive. negative. strong. Correct: zero.

In a regression equation, a refers to:

the amount of change in Y for each unit change in X. the amount of change in X for each unit change in Y. the X-intercept (point where the regression line crosses the X-axis when Y = 0). Correct: the Y-intercept (point where the regression line crosses the Y-axis when X = 0).

The difference between the observed points and the regression line points is equal to:

the correlation. the slope. Correct: the error term. the Y-intercept.

In regression analysis:

the independent variable must be categorical in nature. the variables being investigated must not be correlated. the independent variable is indisputably influenced by the dependent variable. Correct: one variable is believed to be influenced by the other.

The coefficient of non-determination explains:

the proportion of variance in Y that is determined or explained by X. Correct: the proportion of variance in Y that is NOT determined or explained by X. the proportion of variance in Y that is attributed to error. the proportion of variance in X that is attributed to error.

When the points in a scatter plot cluster closely around the regression line, the correlation can be said to be:

weak. Correct: strong. neutral. negative.

The mathematical equation for a regression line is typically written:

y= a +bX + e