This is the formula for
[ Select ]
Pearson’s r correlation
z-test for an individual score
between-subjects t-test
pooled variance
.

Question

This is the formula for 
[ Select ]
Pearson’s r correlation
z-test for an individual score
between-subjects t-test
pooled variance
 .

BlackTom AI · Accepted Answer

The question provides a displayed formula and asks you to identify what this formula is the formula for.
First, consider the structure of the numerator: ∑(X − X̄)(Y − Ȳ). This is the sum of the products of deviations of X and Y from their respective means, which is a hallmark of the covariance-like term used in correlation calculations.
Next, examine the denominator: it has √[∑(X − X̄)² ∑(Y − Ȳ)²]. This represents the product of the standard deviations (or standard errors) of the X and Y variables, i.e., the normalization factor that scales the covariance into a correlation coefficient bounded between −1 and 1.
Putting these pieces together, the formula computes a standardized measure of the linear association between two variables, which is exactly what Pearson’s r represents.
Now consider the other options briefly to see why they do not match this expression:
- z-test for an individual score: This involves a z-score calculation typically using a single observation, its deviation from a mean, and a standard deviation; the expression shown here uses sums over pairs of deviations from means for two variables, not a single standardized score.
- between-subjects t-test: This test uses a t-statistic comparing means across groups and involves group means and pooled variances, not the covariance-like numerator over the product of standard deviations as in the shown formula.
- pooled variance: This refers to an estimate used in certain t-tests and ANOVA contexts; it is a single pooled estimate of variance, not the two-variable normalization shown here.
In summary, the formula depicted is the Pearson’s r correlation coefficient, which quantifies the strength and direction of a linear relationship between two variables by normalizing the covariance with the product of their standard deviations.

11398 SEM-2 2025 BRUCE ON-CAMPUS AND SEM-2 2025 BRUCE REALTIME Final Exam (Remotely Proctored)

This is the formula for [ Select ] Pearson’s r correlation z-test for an individual score between-subjects t-test pooled variance .

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