Question 1

Generally, when more variables are added to a prediction equation

Accepted Answer

Adding more variables to a prediction equation generally leads to more variance in the criterion variable being accounted for, as additional predictors may capture unique sources of variance in the outcome measure that were not captured by the initial set of predictors. However, this may also depend on the quality and relevance of the additional predictors being added.

Question 2

A Pearson r correlation is best used for data that is expressed as

Accepted Answer

A Pearson r correlation is used for continuous data, which is represented by numerical values on a continuous scale, such as height or weight. It is not appropriate for ordinal data, which can only be ranked in order, such as survey responses on a Likert scale. Therefore, the best choice is D, only continuous.

Question 3

Low reliability of variables

Accepted Answer

When variables have low reliability, it means that they are not consistently measuring what they are intended to measure, which affects the accuracy and consistency of the data. As a result, it decreases the chances of finding significant relationships between variables, as the data obtained may not accurately reflect the underlying constructs being studied.

Question 4

In a single prediction question (Y=a + bX), X represents a(n)

Accepted Answer

In the equation Y=a + bX, X represents an individual's score on the predictor variable, which is used to predict the criterion score (Y). Therefore, the best choice is C. Option A is incorrect as Y is the predicted criterion score. Option B is incorrect as X represents one individual's score, not a distribution of scores in the sample. Option D is incorrect as the constant (a) is calculated from the scores but not represented by X.

Question 5

Joe uses age, family size, and income to predict scores on a survey of happiness. The results were statistically significant with a coefficient of determination of 64%. He collects a new sample and examines the regression equation. In Joe's second sample, the common variance will likely __________ due to __________.

Accepted Answer

The correct answer is C because the common variance, which is represented by the coefficient of determination, is likely to decrease due to shrinkage in the second sample. Shrinkage occurs when the regression equation is tested on a new sample with a different distribution than the original sample, which leads to a decrease in the coefficient of determination. This means that the prediction accuracy of Joe's regression equation will likely be lower in the second sample, as the relationship between the predictor variables and happiness may not be as strong or significant in the new population.

Question 6

George suspects that there is a curvilinear relationship in his data set. Which of the following correlation coefficient should George calculate?

Accepted Answer

Eta correlation is specifically designed to measure the strength and direction of curvilinear relationships between variables, making it the appropriate choice for George's situation.

Question 7

Gretchen wanted to see whether, given a sample of teachers' that graduated from colleges and Universities, GPA in college was related to starting salary as a teacher. Which correlation coefficient should Gretchen calculate?

Accepted Answer

Pearson r is the appropriate correlation coefficient to use when examining the relationship between two continuous variables, such as college GPA and starting salary. Eta, Kendall's tau, and Spearman rho are better suited for non-parametric data or when there are ordinal variables involved.

Question 8

Which of the following measures is used when the criterion variable in a prediction study is categorical?

Accepted Answer

Discriminate function analysis is specifically designed for prediction studies where the criterion variable is categorical, such as differentiating between groups or predicting group membership. Multiple regression, path analysis, and canonical correlation are more appropriate when the criterion variable is continuous.

Question 9

Joni teaches a preschool class. She has eight students and ranks them based upon math and reading ability. She would like to see if there is a relationship between how well her students are ranked in math and in reading. Which of the following correlations should she use?

Accepted Answer

Kendall's tau is a nonparametric correlation that can be used to measure the relationship between two ranked variables. In this case, Joni has ranked her students based on their math and reading ability, making Kendall's tau a suitable choice for analyzing the relationship between the two variables. Kendall's tau is also robust to the presence of ties in the data, which may occur when two or more students have the same math or reading ability ranking.

Question 10

The common variance shared by the predictor and criterion variables is referred to as the

Accepted Answer

The coefficient of determination, also known as R-squared, measures the proportion of variance in the criterion variable that can be explained by the predictor variable(s). Therefore, it represents the common variance shared by the predictor and criterion variables. The standard error of regression and standard error of determination both refer to the degree of variability in the residuals, or the difference between predicted and actual values, and are not directly related to the common variance shared by the predictor and criterion variables. The coefficient of regression is not a commonly used term in regression analysis.

Question 11

A Phi coefficient is used for

Accepted Answer

A Phi coefficient is used for true dichotomous level data which is a type of data where the variable can only take two possible values/categories. Examples of true dichotomous level data are gender (male/female), pass/fail, yes/no etc.

Question 12

Data collection for types of correlation studies is generally

Accepted Answer

Data collection for types of correlation studies is generally shorter than most types of quantitative research because they typically involve the gathering of numerical data through surveys or existing datasets, rather than extensive fieldwork or experimental design.

Question 13

The criterion variable in a prediction study is the name for the

Accepted Answer

The criterion variable is the variable that is being predicted in a prediction study. It is the outcome variable of interest, and the variable that researchers are trying to estimate or forecast. The other options listed (A, C, and D) are not correct because they do not accurately describe the criterion variable.

Question 14

In a single prediction question (Y=a + bX), Y represents a(n)

Accepted Answer

In the regression equation Y=a+bX, Y represents the predicted criterion score, which is the dependent variable that is being predicted by the independent variable X with the help of the regression coefficients (a and b). Therefore, option A is the correct choice. Option B is incorrect because Y is not a distribution of scores, but a single predicted score. Option C is incorrect because Y is not an individual's score, but a predicted score based on a given value of X. Option D is incorrect because the constant is represented by the intercept (a) in the regression equation, while Y represents the predicted criterion score.

Question 15

When using correlational analysis with multiple predictors and multiple criterion variables, the appropriate procedure is

Accepted Answer

Canonical correlation is the appropriate statistical procedure when dealing with multiple predictors and multiple criterion variables, as it assesses the relationships between two sets of variables.

Question 16

Cheryl used age, education, and income to predict scores on a life satisfaction survey. Her regression equation accounted for 58% of the variance in life satisfaction. She collects a new sample and applies her equation. This process is referred to as

Accepted Answer

The process described is known as cross-validation, which involves testing the accuracy of a model on a new sample to assess its reliability and effectiveness in predicting outcomes. This helps to avoid overfitting and ensures that the model has generalizability.

Question 17

Jack administered an achievement test with an internal consistency reliability of .65. Jack should interpret this result as

Accepted Answer

Internal consistency reliability coefficients range between 0 and 1. A reliability coefficient of 0.65 suggests low internal consistency, and indicates that the items on the test may not be measuring the same construct consistently. Generally, a reliability coefficient of at least 0.70 is considered acceptable for research purposes.

Question 18

Shrinkage refers to

Accepted Answer

Shrinkage refers to the phenomenon where the coefficients of a predictive model are "shrunk" towards a central value, usually zero. This is done in order to avoid overfitting of the model to the training data, which can lead to reduced accuracy when the model is applied to new data. Therefore, option A is the correct choice.

Question 19

A correlation between reading and math achievement scores on a national standardized test for first graders indicates a correlation of r = .90. How much variance do these scores share?

Accepted Answer

The correlation coefficient (r) measures the strength and direction of the relationship between two variables. The coefficient of determination (r^2) indicates the proportion of variance shared by the two variables. To calculate r^2, we square the correlation coefficient: r^2 = 0.9^2 = 0.81, or 81%. Therefore, choice C is correct as the two variables share 81% variance.

Question 20

Regarding sampling, one strategy to facilitate obtaining accurate results when there will be subgroup correlations is to select a

Accepted Answer

A stratified sample is a sampling technique that divides the population into subgroups or strata and then selects a random sample from each stratum. This ensures that each subgroup is represented in the sample, which enables accurate subgroup correlations to be determined. Choosing a random sample or a purposive sample would not necessarily ensure accurate subgroup correlations, and a cluster sample may not be the most effective technique if there are distinct and important subgroups within the population.

Quiz 8: Correlational Research