Statistics Module 6: Chapter 11-12

Advanced topic: What is the formula for the proportionate reduction in error? a) (SSError - SSTotal) / SSError b) (SSError + SSTotal) / SSError c) (SSTotal - SSError) / SSTotal d) SSTotal / (SSError + SSTotal)

(SSTotal - SSError) / SSTotal

Why are errors squared in a regression? a) to give more weight to smaller errors b) because summing positive and negative errors will cancel them out c) multiplying positive and negative errors will always result in negative numbers d) errors are not actually squared in a regression

Because summing positive and negative errors will cancel them out

When the relationship between two variables is shown by listing the variables on both the top and left side, the table is called a a) correlation matrix b) scatter diagram c) binomial effect size display d) C table

Correlation matrix

Error in regression is figured by a) Y - X b) Y - Ŷ c) Y - b d Y - a

Y - Ŷ

The item below is based on the following scenario. An educational psychologist wants to predict how well students will do on a particular multiple-choice test based on a measure of their ability to follow instructions. Their actual scores are 3, 7, and 11, and their respective predicted scores are 5, 7, and 9. Advanced topic: What is SSError? a) (3-7)2 + (7-7)2 + (11-7)2 b) (5-7)2 + (7-7)2 + (9-7)2 c) (3-5)2 + (7-7)2 + (11-9)2 d) (5-9)2 + (7-9)2 + (9-9)2

(3-5)2 + (7-7)2 + (11-9)2

The item below is based on the following scenario. An educational psychologist wants to predict how well students will do on a particular multiple-choice test based on a measure of their ability to follow instructions. Their actual scores are 3, 7, and 11, and their respective predicted scores are 5, 7, and 9. Advanced topic: What is SSTotal? a) (3-7)2 + (7-7)2 + (11-7)2 b) (5-7)2 + (7-7)2 + (9-7)2 c) (3-5)2 + (7-7)2 + (11-9)2 d) (5-9)2 + (7-9)2 + (9-9)2

(3-7)2 + (7-7)2 + (11-7)2

The item below is based on the following scenario. An educational psychologist wants to predict how well students will do on a particular multiple-choice test based on a measure of their ability to follow instructions. Their actual scores are 3, 7, and 11, and their respective predicted scores are 5, 7, and 9. Advanced topic: What is the proportionate reduction in error? a) (32 - 8) / 32 = 0.75 b) (8 - 32) / 8 = -3 c) 32 / (8 + 32) = 0.80 d) (8 + 32) / 8 = 5

(32 - 8) / 32 = 0.75

When conducting a t test for the correlation coefficient in a study with 16 individuals, the degrees of freedom will be a) 14 b) 15 c) 30 d) 31

14

When drawing a regression line for a linear prediction rule, the minimum number of predicted points on a graph that must be located is a) 1 b) 2 c) 1 if it is a positively sloped line; 2 if it is a negatively sloped line d) 2 if it is a positively sloped line; 1 if it is a negatively sloped line

2

If a person's score on a questionnaire has been found to predict observed social skills, and the linear prediction rule uses a regression constant of 16 and a regression coefficient of 3, the predicted level of social skills for a person with a score of 10 on the questionnaire is a) 10 b) 46 c) 160 d) 190

46

If a child psychologist reports that age in months predicts appetite level for a group of infants using a linear prediction rule in which a = 1 and b = 2, the appetite level for a four-month-old infant is a) 4 b) 8 c) 9 d) 12

9

When making predictions using a linear prediction rule, the baseline number that is added to each prediction is a) a b) b c) X d) Ŷ

A

A study indicates that in general the more fruit students eat before a test, the better they do on the test. However, beyond a certain point, the more fruit students eat, the worse they do on the test. Thus, the relation between amount of fruit eaten and test performance is an example of a) a positive linear correlation b) a curvilinear correlation c) a negative linear correlation d) no correlation

A curvilinear correlation

What is the direction of causality when two variables, A and B, have a strong linear correlation? a) A causes B b) B causes A c) some third variable is causing both A and B d) All of the above are possible

All of the above are possible

The average of the cross-products of Z scores is a better indicator of the relationship between two variables than the sum of the cross-products of Z scores because the average a) appropriately measures the strength of the relationship whereas the sum does not b) appropriately measures the direction of the relationship whereas the sum does not c) is converted to a standard scale from -10 to +10 whereas the sum is not d) is formed using a combination of the two variables' measurement scales whereas the sum is not

Appropriately measures the strength of the relationship whereas the sum does not

The average of the cross-products of Z scores is a better indicator of the relationship between two variables than the sum of the cross-products of Z scores because the average a) appropriately measures the strength of the relationship whereas the sum does not b) appropriately measures the direction of the relationship whereas the sum does not. c) is converted to a standard scale from -10 to +10 whereas the sum is not d) is formed using a combination of the two variables' measurement scales whereas the sum is not

Appropriately measures the strength of the relationship whereas the sum does not

A reduction in a correlation due to the unreliability of a measure is a) attenuation b) a restriction in range c) negative coorelation d) binomial effect

Attenuation

When figuring a correlation coefficient, an outlier a) usually has only a small effect on the computed correlation b) can have a strong effect on the computed correlation c) generally increases the statistical power of a study d) can be balanced by the effects of attenuation

Can have a strong effect on the computed correlation

The proportionate reduction in error is preferred over the correlation coefficient for a) determining the direction of casuality b) eliminating any third variables that may have been affecting the results c) reducing any errors that may have occured d) comparing correlations with each other

Comparing correlations with each other

If a counseling psychologist wants to predict college grades from high school grades, college grades are the a) predictor variable b) criterion variable c) independent variable d) causal variable

Criterion variable

The last step when figuring the correlation coefficient is to a) multiply the sum of the cross-products of Z scores by the sample size b) divide the sum of the cross-products of Z scores by the sample size c) add the sample size to the sum of the cross-products of Z scores d) subtract the sample size from the sum of the cross-products of Z scores

Divide the sum of the cross-products of Z scores by the sample size

The sum of squared errors is the sum of a) each score on the criterion variable minus the predicted score, squared b) each squared score on the criterion variable minus each squared predicted score c) each score on the predictor variable minus the predicted score, squared d) each squared score on the predictor variable minus each squared predicted score

Each score on the criterion variable minus the predicted score, squared

On a scatter diagram, the vertical distance between the dot for the actual score and the regression line represents the a) slope b) regression constant c) squared error d) error

Error

Which assumption is applicable to regression but not to correlation? a) linear relationship between the variables b) independence of people (or cases) c) error scores are normally distributed d) each variable is equally distributed at each point of the other variable

Error scores are normally distributed

One way to handle a situation in which high scores go with high scores and low scores with low scores but the pattern of scores is not linear is to a) convert all scores toZ scores before figuring the correlation coefficient b) add a random variable to the presumed predictor variable c) figure the Wilcoxon R d) figure Spearman's rho

Figure Spearman's rho

Which of the following calculations is necessary for figuring the correlation coefficient? a) finding the grand mean b) finding the cross-products of each person's X and Y raw scores c) finding the means of X and Y d) finding the difference between each person's X and Y raw scores

Finding the means of X and Y

In a linear prediction rule using a standardized regression coefficient, a) the regression constant is always equal to 1 b) for each increase of one standard deviation in the predictor variable, the predicted standard deviation of the criterion variable increases by the standardized regression coefficient c) the predicted value for the criterion variable is a t score d) for each increase of one standard deviation in the predicted variable, the predicted standard deviation of the predictor variable increases by the standardized regression coefficient

For each increase of one standard deviation in the predictor variable, the predicted standard deviation of the criterion variable increases by the standardized regression coefficient

The person given credit for inventing correlation is a) Ronald Fisher b) Francis Galton c) William Gossett d) Ralph Rosnow

Francis Galton

When figuring a correlation coefficient, scores are first converted to Z scores because a) the standard deviation is the same for every variable b) scores can never be more than 2 standard deviations from the mean c) all scores are on a consistent 0 to 1 scale d) high scores are positive numbers, and low scores are negative numbers

High scores are positive numbers, and low scores are negative numbers

A regression coefficient indicates a) whether the correlation is significant or not b) how many units of change in the predicted value of the criterion variable for each unit of change in the predictor variable c) the accuracy of predictions based on the reduction in squared error as a proportion of the total squared error d) the fixed amount that should be added when making a prediction for any particular person

How many units of change in the predicted value of the criterion variable for each unit of change in the predictor variable

Under what conditions can the possibility that Y causes X be ruled out when two variables, X and Y, are strongly correlated? a) if the correlation is positive b) if the correlation is negative c) if X occurs before Y d) if Y occurs before X

If X occurs before Y

Under what conditions can an experimenter be confident that X is the cause of Y if two variables, X and Y, are strongly correlated? a) if people are randomly assigned to levels of X in a true experiment b) if people are randomly assigned to levels of Y in a true experiment c) if X is measured before Y d) if Y is measured before X

If people are randomly assigned to levels of X in a true experiment

Which of the following is true about hypothesis testing for a linear prediction rule? a) If the correlation coefficient is significant, the regression coefficient will be significant b) If the correlation coefficient is significant, the standardized regression coefficient will be significant, but the unstandardized (ordinary) regression coefficient will not c) The t test for the correlation coefficient tests the significance of the regression constant d) The t test for the correlation coefficient tests the significance of both the regression constant and the regression coefficient

If the correlation coefficient is significant, the regression coefficient will be significant

The term for the subjective overestimation of the strength of the relationship between two variables is a) illusory correlation b) negative correlation c) positive correlation d) inflated correlation

Illusory correlation

A score that has an extreme value in relation to other scores in a distribution is a(n) a) outlier b) deviation c) outlaw d) miscalculation

Outlier

The difference between a positive correlation and a negative correlation is that a) in a negative correlation, high scores go with high scores and low with low; in a positive correlation, high scores go with low scores and low with high. b) in a negative correlation, high scores go with low scores and low with high; in a positive correlation, high scores go with high scores and low with low. c) negative correlations are curvilinear; positive correlations are straight lines. d) negative correlations represent a weak relationship; positive correlations represent a strong relationship.

In a negative correlation, high scores go with low scores and low with high; in a positive correlation, high scores go with high scores and low with low.

If a counseling psychologist wants to predict college grades from high school grades, college grades are the a) is robust to moderate violations of its assumptions b) is robust to even extreme violations of its assumptions c) is slightly less robust than other t tests to violations of its assumptions d) is much less robust than other t tests to violations of its assumptions

Is robust to moderate violations of its assumptions

The multiple correlation coefficient of a criterion variable with two predictor variables a) is usually smaller than the sum of the correlation coefficients of the criterion variable with each predictor variable. b) is usually larger than the sum of the correlation coefficients of the criterion variable with each predictor variable c) is exactly the same as the sum of the correlation coefficients of the criterion variable with each predictor variable d) can be larger, smaller, or the same as the sum of the correlation coefficients of the criterion variable with each predictor variable

Is usually smaller than the sum of the correlation coefficients of the criterion variable with each predictor variable.

When testing the significance of the correlation coefficient, the null hypothesis is usually that in the population, the true correlation a) is less than 1 b) is zero c) is greater than the actual correlation d) is less than the actual correlation

Is zero

Low reliability of the variables reduces the correlation coefficient because a) the Z scores are less likely to follow a normal curve b) the cross-products of the Z scores are less likely to follow a normal curve c) it adds random noise to the computations d) it reduces random influences that would otherwise add to the overall variance

It adds random noise to the computations

Making a scatter diagram before figuring the correlation coefficient is a good idea because a) there is no point in figuring the correlation if a clear line is formed on the graph. b) there are different procedures depending on whether there appears to be a positive or a negative correlation c) it allows estimation of the degree and direction of correlation to provide a check on eventual figuring d) a correlation coefficient should be figured only if a clear curvilinear correlation is seen.

It allows estimation of the degree and direction of correlation to provide a check on eventual figuring

Which limitation is applicable to both correlation and regression? a) The degree of predictability will be underestimated if the underlying relationship is linear b) Nothing can be inferred about the direction of causality c) Restrictions in range and unreliable measures are uncommon d) The relative importance of different predictor variables cannot be assessed

Nothing can be inferred about the direction of causality.

The result of multiplying two Z scores is always a) Positive if the individual has a high raw score on one variable, a low raw score on the other variable, and the Z for the high raw score is larger than the Z for the low raw score b) Positive if the individual has low raw scores on both variables c) Negative if the individual has high raw scores on both variables d) Zero

Positive if the individual has low raw scores on both variables

Spearman's rho handles curvilinearity in the relation between two variables by first converting all scores to a) ranks b) deviation scores c) Z scores d) logs of the original scores

Ranks

A person's predicted score on the criterion variable is found by multiplying the person's score on the predictor variable by a particular number called a a) coefficient of redundancy b) regression constant c) proportionate reduction in error d) regression coefficient

Regression coefficient

If every increase of one point on a test-anxiety scale is associated with a decrease of 2 points on predicted performance on a test, 2 represents the slope, which is also the a) regression coefficient b) regression constant c) proportionate reduction in error d) standardized regression coefficient

Regression coefficient

The situation in which you figure a correlation but only a limited range of the possible values on one of the variables is included in the group studied is called a) restriction in range b) attenuation c) proportionate reduction in error d) unreliable measurement

Restriction in range

Advanced topic: What is the difference between the SSError and SSTotal? a) SSError is an individual score; SSTotal takes into account the error of an entire study. b) SSError uses the prediction rule; SSTotal predicts from the mean c) SSError predicts from the mean; SSTotal uses the prediction rule d) SSError takes into account the variance of both populations; SSTotal takes into account only the variance in the predictor variable

SSError uses the prediction rule; SSTotal predicts from the mean

Advanced topic: The sum of the squared errors when predicting from the mean is called a) SSError b) proportionate reduction in error c) SSTotal d) proportion of variance accounted for

SSTotal

A graph that shows the pattern of the relation of two variables is a a) histogram b) scatter diagram c) frequency polygon d) box plot

Scatter diagram

The items below are based on the following scenarios. Which graph depicts no correlation? a) Scenario A b) Scenario B c) Scenario C d) Scenario D

Scenario C

The items below are based on the following scenarios Which graph depicts a negative correlation? a) Scenario A b) Scenario B c) Scenario C d) Scenario D

Scenario D

A regression line a) is drawn on a graph in which scores for the predicted variable are on the horizontal axis b) is rarely a straight line c) can be shown on a bar graph d) shows the relation between values of the predictor and criterion variables

Shows the relation between values of the predictor and criterion variables

A scatter diagram a) is a bar graph that shows the frequencies of the different values in a distribution b) is a line graph that looks like a mountain-peak skyline and shows the frequencies of the different values in a distribution c) shows the relation of two variables as dots in a two-dimensional graph d) is also called a random distribution frequency plot

Shows the relation of two variables as dots in a two-dimensional graph

The best linear prediction rule is the one that has the least a) error when predicting from the mean b) squared error when predicting from the mean c) error when predicting using that rule d) squared error when predicting using that rule

Squared error when predicting using that rule

To compare correlations with each other, the proportionate reduction in error can be figured by a) multiplying each correlation coefficient by 10 b) calculating the square root of each correlation coefficient c) squaring each correlation coefficient d) multiplying each correlation coefficient by 2.

Squaring each correlation coefficient

Advanced topic: If the correlation coefficient for a study is known, figuring the proportionate reduction in error requires a) dividing the correlation coefficient by 2 b) taking the square root of the correlation coefficient c) squaring the correlation coefficient d) multiplying the correlation coefficient by 2

Squaring the correlation coefficient

If a psychologist interested in the relation between number of years working for a particular company and loneliness at work surveyed 40 workers at this company and figured a correlation between these two variables of -.90, the correlation is considered a a) weak positive linear correlation b) weak negative linear correlation c) strong positive linear correlation d) strong negative linear correlation

Strong negative linear correlation

The regression constant is also referred to as a) error b) a slope c) the X intercept d) the Y intercept

The Y intercept

When correlations are reported in a research article, which of the following information is least likely to be provided? a) the value of r b) the significance level c) the Z scores d) a correlation matrix

The Z scores

When multiple regression statistics are reported in a psychology research article, a) the correlation coefficients for the predictor variables usually appear in the text b) the unstandardized regression coefficients for the predictor variables usually appear in the text c) the standardized regression coefficients for the predictor variables usually appear in the text d) the coefficients for the predictor variables (be it b, β, or both) usually appear in a table

The coefficients for the predictor variables (be it b, β, or both) usually appear in a table

The standardized regression coefficient in a bivariate linear prediction rule equals a) the intercept of the regression line using raw scores b) the slope of the regression line using raw scores c) the correlation coefficient d) the correlation coefficient squared

The correlation coefficient

When making a scatter diagram, a) the values on the vertical axis go from highest at the bottom to lowest at the top. b) the overall shape should be roughly square c) two dots are used to mark each score d) outlying values are excluded to maintain the proper shape

The overall shape should be roughly square

The regression coefficient in the best linear prediction rule is a) the product of the sum of the deviation scores on the predictor variable, multiplied by the sum of the deviation scores on the criterion variable, divided by the predictor variable's sum of squared deviations from the mean. b) the sum of the products of the deviation scores, divided by the predictor variable's sum of squared deviations from the mean c) the product of the sum of the deviation scores on the predictor variable, multiplied by the sum of the deviation scores on the criterion variable, divided by the criterion variable's sum of squared deviations from the mean d) the sum of the product of the deviation scores, divided by the criterion variable's sum of squared deviations from the mean

The sum of the products of the deviation scores, divided by the predictor variable's sum of squared deviations from the mean

An assumption for a significance test of the correlation coefficient is that in the populations, a) the variance of each variable is the same b) the variance of the deviation scores for each variable is the same c) the variance of each variable is the same at each point of the other variable d) the variance of the squared deviations of each variable is the same at each point of the distribution of the squared deviations of the other variable

The variance of each variable is the same at each point of the other variable

Considering the number of possible linear prediction rules for predicting Y from X, for any particular set of scores, a) all rules are equally valid, and it does not matter which one is used b) there is one best rule for positive predictions and one best rule for negative predictions. c) there is one best rule for predicting low scores and one best rule for predicting high scores d) there is only one best rule

There is only one best rule

How does Ralph Rosnow and Robert Rosenthal's position on the interpretation of correlations differ from traditional views? a) They argue that even low correlations can have important implications b) They argue that low correlations (below .10) should be treated as if they are zero in virtually all cases c) They argue that correlational research designs can provide evidence of causality in most cases d) They argue that even with an experimental design, it is not possible to determine causality from a correlation

They argue that even low correlations can have important implications

Advanced topic: What does it mean when SSTotal minus SSError equals zero? a) this is the best case - it means there is zero error b) this is the worst case - it means the prediction model has reduced zero error c) the proportionate reduction in error is 50% d) the underlying correlation is negative

This is the worst case - it means the prediction model has reduced zero error

If the correlation between two personality traits is .07, the correlation is considered a a) weak positive linear correlation b) weak negative linear correlation c) strong positive linear correlation d) strong negative linear correlation

Weak positive linear correlation

In psychology research articles, a) linear prediction rules are usually presented for bivariate but not multiple regression. b) when results for bivariate prediction are reported, it is most likely to be with regression lines. c) if multiple regression results are reported, the bivariate correlations will usually not be reported. d) if a standardized regression coefficient (β) is reported, the bivariate correlation (r) will almost always be reported as well.

When results for bivariate prediction are reported, it is most likely to be with regression lines.

When is it inappropriate to conduct a t test for the correlation coefficient? a) when the correlation is negative b) when the correlation is positive c) when the relationship is linear d) when the relationship is nonlinear

When the relationship is nonlinear

When is the correlation coefficient zero? a) never b) when there is no linear correlation c) when there is a perfect linear correlation d) when there is a perfect negative linear correlation

When there is no linear correlation

The term in a linear prediction rule that represents the intercept of a regression line is a) a b) b c) X d) Ŷ

a

When a person's score on one variable is used to make predictions about a person's score on another variable, the procedure is called a) a correlation b) hypothesis testing c) bivariate prediction d) multicollinearity

bivariate prediction

When figuring a correlation coefficient, the absolute value of the summed cross-products a) gets larger when the scores of more people are included in the analysis b) gets smaller as the variance of the scores for each variable increases c) gets larger as the measurement scale for each variable becomes more restricted d) is negative when the scores of large numbers of people are included in the analysis.

gets larger when the scores of more people are included in the analysis

Illusory correlations are cause by a) any mistake that occurs during the figuring of the correlation coefficient b) comparing correlations without converting them to proportionate reductions in error c) incorrect theories based on prejudices d) the combined effects of restriction in range and curvilinearity

incorrect theories based on prejudices

The statistical procedure used to make predictions about people's poetic ability based on their scores on a general writing ability test and their scores on a creativity test is a) ridge regression b) multiple regression c) bivariate regression d) proportion of variance accounted for

multiple regression

In the equation Ŷ = a + (b)(X), b is the symbol for the a) correlation coefficient b) regression coefficient c) proportionate reduction in error d) regression constand

regression coefficient

The regression constant in the best linear prediction rule is a) the mean of the criterion variable minus the result of multiplying the regression coefficient by the mean of the predictor variable b) the mean of the criterion variable plus the result of multiplying the regression coefficient by the mean of the predictor variable c) the mean of the criterion variable minus the result of dividing the regression coefficient by the mean of the predictor variable d) the mean of the criterion variable plus the result of dividing the regression coefficient by the mean of the predictor variable

the mean of the criterion variable minus the result of multiplying the regression coefficient by the mean of the predictor variable

The multiple regression formula with two predictor variables is a) Ŷ = a + (b1/X1) + (b2/X2). b) Ŷ = a1 + a2 + (b1/X1) + (b2/X2). c) Ŷ = a + (b1)(X1) + (b2)(X2). d) Ŷ = a1 + a2 + (b1)(X1) + (b2)(X2).

Ŷ = a + (b1)(X1) + (b2)(X2).

In a bivariate linear prediction, the null hypothesis is that a) β = 0 b) β = 1 c) β ≠ 0 d) β ≠ 1

β = 0