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Quantitative Research Methods and Experimental Design
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Quantitative Research Methods and Experimental Design
Chapters 5-7 Flashcards
Study
1
Question
How does a theoretical construct differ from an operational definition in quantitative research?
Answer
A construct is an unobservable phenomenon of interest (such as self-esteem or depression). An operational definition is a guiding description providing a concrete framework to measure that construct.
2
Question
What primary feature distinguishes a ratio scale of measurement from an interval scale?
Answer
A ratio scale includes a true absolute zero indicating the complete absence of the measured phenomenon. Interval scales have equal units between points but lack a true zero point.
3
Question
Why do quantitative counseling researchers frequently utilize quasi-interval scales for survey instruments?
Answer
Subjective differences between response options on ordinal scales (such as Likert items) are treated as definitive and equidistant. This allows scores to undergo mathematical operations and continuous data analysis.
4
Question
What five forms of validity evidence are recognized by testing standards for evaluating measurement instruments?
Answer
Validity evidence includes test content, response processes, internal structure, relationships to other variables, and consequences of testing. (Mnemonic handle: CRISP — Content, Response, Internal, Similar variables, Practical consequences).
5
Question
What numerical cutoffs define adequate, good, and very good score reliability estimates?
Answer
A coefficient of .70 indicates adequate consistency, .80 indicates good consistency, and .90 or higher indicates very good consistency of scores.
6
Question
Why is reliability correctly described as a property of scores rather than a property of the scale itself?
Answer
Reliability varies across specific samples and demographic groups completing the instrument. Therefore, reliability estimates must be calculated and reported for each distinct study sample.
7
Question
How does standard deviation relate mathematically and conceptually to statistical variance?
Answer
Variance is the squared value of the standard deviation. Standard deviation expresses the average amount of error or dispersion from the mean in original score units.
8
Question
Under the empirical 68-95-99 rule, what percentage of scores falls between -1 and +1 standard deviation of a normal distribution?
Answer
Approximately 68% of all scores fall within 1 standard deviation of the mean. 95% fall within 2 standard deviations, and 99% fall within 3 standard deviations.
9
Question
What formula calculates a standard z-score from an individual raw score, sample mean, and standard deviation?
Answer
The formula is \(z = \frac{X - \bar{X}}{\sigma}\), where \(X\) is the raw score, \(\bar{X}\) is the group mean, and \(\sigma\) is the standard deviation.
10
Question
How do T-scores standardize raw performance relative to standard z-scores?
Answer
T-scores have a fixed mean of 50 and a standard deviation of 10. A z-score of 0 corresponds to a T-score of 50, while a z-score of +1.0 corresponds to a T-score of 60.
11
Question
What standard interpretation guidelines apply to Pearson correlation coefficient values between .40 and .60?
Answer
A correlation coefficient between +/- .40 and .60 indicates a moderate relationship. Values between .20 and .40 are low, and values between .60 and .80 are substantial.
12
Question
How do Type I and Type II errors differ regarding the status of the null hypothesis?
Answer
A Type I error occurs when a researcher incorrectly rejects a true null hypothesis (finding a false positive). A Type II error occurs when a researcher fails to reject a false null hypothesis (missing a real effect).
13
Question
What defines a Type III error in quantitative hypothesis testing?
Answer
A Type III error occurs when a researcher correctly rejects the null hypothesis but provides the right statistical answer to the wrong research question by overreaching interpretations.
14
Question
Which three primary factors determine whether an observed empirical finding achieves statistical significance?
Answer
Statistical significance is determined by the actual magnitude of the result, the amount of error in the measurement, and the sample size utilized.
15
Question
Why does inflating sample size increase the likelihood of detecting statistical significance in hypothesis testing?
Answer
Increasing sample size decreases the standard error in the denominator of the test statistic. This artificially inflates the resulting test value even when the underlying association is negligible.
16
Question
How does practical significance fundamentally differ from statistical significance in empirical evaluation?
Answer
Statistical significance tests the probability that a result occurred outside of chance. Practical significance evaluates the real-world magnitude and meaningfulness of the effect via effect size measures.
17
Question
What specific benchmark values define small, medium, and large effect sizes for Cohen's d?
Answer
For Cohen's d, an effect size of .20 is small, .50 is medium, and .80 is large. These values express group mean differences in standard deviation units.
18
Question
What benchmark conventions are used to interpret small, medium, and large values for eta-squared (\(\eta^2\)) and omega-squared (\(\omega^2\))?
Answer
For both \(\eta^2\) and \(\omega^2\), an effect size of .01 is considered small, .06 is medium, and .14 is large.
19
Question
How is the Percent Improvement (PI) metric calculated for evaluating client clinical outcomes?
Answer
The formula is \[100 \times \frac{\text{Pretreatment Scores} - \text{Posttreatment Scores}}{\text{Pretreatment Scores}}\] It evaluates individual or group symptom reduction over an intervention.
20
Question
What Percent Improvement (PI) threshold indicates clinically significant change in counseling outcome research?
Answer
A PI of 50% or higher indicates clinical significance. A PI between 25% and 49% indicates improvement without clinical significance, and below 25% indicates no improvement.
21
Question
How do criterion variables and predictor variables differ in correlational research designs?
Answer
Criterion variables take the place of dependent variables and represent what is being predicted. Predictor variables take the place of independent variables and represent phenomena used to predict the criterion. Memory Hook: Think of 'Predictor' as the Propeller pushing forward, and 'Criterion' as the Catch or destination where it lands.
22
Question
What happens when researchers assume linearity for a relationship that is actually curvilinear?
Answer
Assuming linearity obscures the true relationship and underestimates its strength because standard linear correlation tools only evaluate straight-line trends. For example, coping skills may reduce behavioral problems only up to an optimal threshold before increasing stress creates an upward curve.
23
Question
What do each of the components represent in the simple regression equation \(\hat{Y} = a + bX\)?
Answer
\(\hat{Y}\) is the predicted criterion value, \(a\) is the constant or intercept when \(X = 0\), and \(b\) is the beta weight or slope representing the amount of change in \(\hat{Y}\) per unit increase in \(X\).
24
Question
What are Cohen's benchmark values for interpreting \(R^2\) effect sizes in multiple regression?
Answer
A small effect is \(R^2 = .02\) (2% variance explained), a medium effect is \(R^2 = .13\) (13% variance explained), and a large effect is \(R^2 = .26\) (26% variance explained). Memory Hook: Remember '2 - 13 - 26', where each step roughly doubles.
25
Question
Why does multicollinearity create problems in multiple regression models?
Answer
Multicollinearity occurs when two or more predictor variables are highly correlated (such as \(r \ge .80\)). This confounds their relationship with the criterion variable and causes the unique contribution of one or more predictors to be severely underestimated.
26
Question
How does unique variance differ from shared variance when evaluating multiple predictor variables?
Answer
Unique variance, represented by squared semipartial correlation coefficients (\(sr^2\)), is the proportion of variance in the criterion explained exclusively by one predictor. Shared variance represents overlapping variance explained by two or more predictors simultaneously.
27
Question
How does a moderator variable differ conceptually from a mediator variable?
Answer
A moderator influences the strength or direction of the relationship between a predictor and criterion (an interaction effect). A mediator explains the underlying mechanism or process through which the predictor influences the criterion (a pathway or indirect effect). Contrast Hook: A Moderator Modulates the volume, while a Mediator Middlemans the message.
28
Question
What test and effect size metric are used when evaluating the relationship between two categorical variables?
Answer
A chi-square test for association is used to evaluate statistical significance, and the phi coefficient (\(\varphi\)) is used to measure practical significance and effect size. Effect benchmarks are \(.10\) (low), \(.30\) (moderate), and \(.50\) (large).
29
Question
When is logistic regression preferred over simple or multiple linear regression?
Answer
Logistic regression is used when the criterion (dependent) variable is dichotomous or categorical rather than continuous. It uses a chi-square model test and expresses effect sizes through an odds ratio.
30
Question
Why is strong theoretical grounding essential when conducting correlational research?
Answer
Correlation does not establish causation, and without theory, researchers risk identifying spurious correlations—variables that correlate strongly by random coincidence without any meaningful real-world connection.