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Correlational Research and Regression Analysis
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Correlational Research and Regression Analysis
Chapter 6 Flashcards
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1
Question
What is the primary purpose of conducting correlational research?
Answer
Correlational research examines the statistical relationship between or among a set of variables without manipulating them. It provides foundational predictive and theoretical models for counseling research.
2
Question
How do independent and dependent variables differ from predictor and criterion variables?
Answer
Independent and dependent variables apply to experimental designs where an intervention is manipulated. Predictor and criterion variables apply to correlational designs where pre-existing phenomena predict an outcome without manipulation.
3
Question
What defines a criterion variable in correlational research?
Answer
A criterion variable represents the outcome or phenomenon of interest being predicted. It serves the role analogous to a dependent variable in experimental designs.
4
Question
What defines a predictor variable in correlational research?
Answer
A predictor variable is an observed measure that relates to or forecasts the criterion variable. It takes the place of an independent variable without being experimentally manipulated.
5
Question
Why is the assumption of linearity important in correlational research?
Answer
Most standard correlation analyses assume a direct straight-line relationship between predictor and criterion variables. If the true relationship is curvilinear, linear correlation models will underestimate or misrepresent the true association.
6
Question
How can a relationship between coping skills and behavioral problems manifest as curvilinear?
Answer
Behavioral problems decrease as coping skills initially increase, but only up to a threshold. Under extreme stress, high coping demands may eventually coincide with an uptick in behavioral problems.
7
Question
What distinguishes a univariate correlational design from a multivariate design?
Answer
A univariate design contains only a single criterion variable, regardless of predictor count. A multivariate design includes two or more criterion variables alongside two or more predictors.
8
Question
What does Pearson's product-moment correlation coefficient evaluate?
Answer
Pearson's \(r\) measures the strength and direction of a linear relationship between two continuous variables. It provides an exploratory descriptive index ranging from \(-1.0\) to \(+1.0\).
9
Question
What does a \(p\)-value indicate when reporting a correlation coefficient?
Answer
The \(p\)-value indicates whether the observed correlation is statistically significant. It reflects the probability of observing the result if the true population correlation were zero.
10
Question
How do regression procedures differ in purpose from Pearson's \(r\)?
Answer
Pearson's \(r\) is an exploratory statistic that describes an association between two variables. Regression establishes a mathematical prediction model to forecast criterion values from predictor scores.
11
Question
Why can regression procedures establish prediction models but not causal explanations?
Answer
Regression models calculate mathematical associations rather than controlling extraneous variables through experimental manipulation. Predictive utility demonstrates practical and theoretical relatedness without demonstrating causality.
12
Question
In the simple regression formula \(\hat{Y} = a + bX\), what does each symbol represent?
Answer
\(\hat{Y}\) is the predicted criterion score, \(a\) is the constant intercept where \(X = 0\), \(b\) is the slope beta weight, and \(X\) is the predictor score.
13
Question
What does the slope \(b\) represent in a simple regression equation?
Answer
The slope \(b\) represents the expected rate of change in \(\hat{Y}\) for every one-unit increase in \(X\). In simple regression with standardized variables, it corresponds directly to Pearson's \(r\).
14
Question
If a regression equation is \(\hat{Y} = 4.25 + 0.73X\), what is the predicted score when \(X = 25\)?
Answer
Substituting \(25\) yields \(\hat{Y} = 4.25 + 0.73(25) = 4.25 + 18.25 = 22.50\). This indicates a higher predicted outcome score corresponding to an elevated predictor score.
15
Question
What statistical test is used to evaluate the overall significance of a regression model?
Answer
The \(F\) test is used to determine whether the relationship between the predictor set and the criterion variable is statistically significant.
16
Question
What does the coefficient of determination \(R^2\) quantify in regression analyses?
Answer
\(R^2\) quantifies the proportion of total variance in the criterion variable explained by the predictor model. It serves as an index of practical significance and effect size.
17
Question
What are Cohen's benchmark values for interpreting \(R^2\) effect sizes in regression?
Answer
Cohen classifies \(R^2 = .02\) as a small effect, \(R^2 = .13\) as a medium effect, and \(R^2 = .26\) as a large effect.
18
Question
What conceptual point is illustrated when an \(R^2\) of \(.26\) is classified as a large effect?
Answer
Even a large effect leaves \(74\%\) of the criterion variance unexplained by the model. Researchers must recognize that substantial unexplained variance remains even in strong counseling models.
19
Question
Why is multiple regression classified as a univariate statistical procedure?
Answer
Multiple regression employs two or more predictor variables but only one criterion variable. A design is univariate whenever there is a single outcome being predicted.
20
Question
Why might some beta weights in a multiple regression equation carry negative signs?
Answer
Negative beta weights indicate an inverse relationship between that specific predictor and the criterion variable. As scores on that predictor increase, the predicted criterion score decreases.
21
Question
What is multicollinearity and why does it pose a problem in multiple regression?
Answer
Multicollinearity occurs when two or more predictor variables correlate very highly, such as \(r \ge .80\). It confounds the regression model by underestimating the unique contribution of individual predictors.
22
Question
How can researchers resolve multicollinearity when two predictors measure redundant constructs?
Answer
Researchers can combine the redundant scales into a single composite predictor variable. Alternatively, they can remove one of the overlapping measures from the regression equation.
23
Question
What two distinct levels of reporting are required in multiple regression research?
Answer
First, researchers evaluate the overall model using the \(F\) test and \(R^2\). Second, if the model is significant, they evaluate each individual predictor's statistical significance and unique effect size.
24
Question
Why does a statistically significant overall regression model not guarantee that all predictors are useful?
Answer
The overall model \(F\) test reflects aggregate explained variance. A single strong predictor can drive model significance while other included predictors contribute negligible unique variance.
25
Question
What is the difference between structure coefficients and squared semipartial correlation coefficients \((sr^2)\)?
Answer
Structure coefficients represent the correlation between a predictor and what is predicted. Squared semipartial correlations \((sr^2)\) account for model error and measure only the unique variance a predictor adds.
26
Question
In a variance Venn diagram with criterion \(Y\) and predictors \(X_1\) and \(X_2\), what do the separate segments represent?
Answer
Segments overlapping \(Y\) uniquely represent unique variance contributions (\(sr^2\)). The central intersection of all three circles represents shared variance among both predictors and the criterion.
27
Question
What types of analyses are classified as multivariate correlational designs?
Answer
Multivariate correlational analyses include canonical correlation, path analysis, and structural equation modeling. These procedures simultaneously evaluate complex relationships among multiple predictors and multiple criteria.
28
Question
What is the function of a moderator variable in regression analysis?
Answer
A moderator variable alters the strength or direction of the relationship between a predictor and a criterion. Moderation represents an interaction effect where the predictor-outcome link depends on moderator levels.
29
Question
What is the function of a mediator variable in a path model?
Answer
A mediator variable explains the underlying mechanism through which a predictor influences a criterion. Controlling for the mediator weakens or eliminates the direct relationship between the predictor and criterion.
30
Question
In mediation analysis, what is the difference between direct path \(c\) and mediated path \(c'\)?
Answer
Path \(c\) represents the total direct effect of the predictor on the criterion without the mediator. Path \(c'\) represents the remaining direct effect after controlling for the mediating variable.