Arrange the steps for manually computing Pearson's r in the correct order.

When manually computing Pearson’s $r$, what is indicated when an individual has a positive cross-product of $z$-scores (such as $+1.88$)?

A researcher is manually computing Pearson’s $r$ for a study on stress (Variable $X$: Mean = $10$, $SD$ = $2$) and sleep quality (Variable $Y$: Mean = $50$, $SD$ = $5$). Match each participant's set of raw scores to the specific $z$-score cross-product they contribute to the final calculation.

In the manual calculation of Pearson's $r$, a participant with $z$-scores of $-2.0$ on both variables provides a larger positive contribution to the final correlation coefficient than a participant with $z$-scores of $+1.0$ on both variables.

Suppose you are designing a dataset for a research methods lab to demonstrate a Pearson's $r$ of exactly $+0.25$ with a sample size of $N = 4$ participants. You have already determined the cross-products of the $z$-scores for the first three participants to be $+0.60$, $-0.10$, and $+0.90$. To achieve your intended outcome, what specific value must you 'assign' as the cross-product for the fourth participant?

When manually computing Pearson's $r$, the cross-products are calculated by multiplying the raw scores of the two variables together for each individual.

A researcher manually computing Pearson's $r$ stops after summing the cross-products of the $z$ scores for a sample. To critique this approach, one would argue that the researcher has not yet accounted for sample size and must still calculate the _____ of the cross-products to reach a standardized evaluation of the relationship.

A researcher studying daily exercise minutes (Variable $X$: $M = 30$, $SD = 10$) and mood ratings (Variable $Y$: $M = 70$, $SD = 15$) is manually computing Pearson's $r$. Match each participant's z-score description to the correct cross-product value.

When manually computing Pearson's $r$, the reason raw scores must be converted to $z$ scores before cross-products are computed is that variables measured on different _____ would otherwise produce cross-products that reflect measurement artifacts rather than genuine co-variation.

A research methods student is peer-reviewing a classmate's manual computation of Pearson's $r$. Arrange the following evaluation steps in the most logical sequence to systematically verify and judge the result before accepting it.

Explain the step-by-step process of manually computing Pearson's $r$ from the raw scores of two quantitative variables, including how individual score transformations lead to the final correlation coefficient.

Describe what the positive cross-product ($1.88$) indicates about the first participant's scores relative to the group means, and explain what the final mean of the cross-products ($+0.53$) reveals about the overall relationship between sleep hours and alertness.

Given a participant with a score of $4$ on variable $X$ (mean = $4.00$, standard deviation = $1.90$) and a score of $30$ on variable $Y$ (mean = $40.00$, standard deviation = $11.78$), calculate their individual $z$ scores and compute their resulting cross-product.