Question

A correlational design investigates relationships between or among variables in a single population. What is the inferential statistical test most commonly used with this design?

Answer 1

The inferential statistical test most commonly used with correlational designs is the Pearson correlation coefficient.

Step-by-step explanation:

In correlational research, the Pearson correlation coefficient (r) is the go-to inferential statistical test for examining the strength and direction of the linear relationship between two continuous variables within a single population.

The Pearson correlation coefficient quantifies the degree of association between variables, ranging from -1 to 1, where -1 indicates a perfect negative correlation, 1 indicates a perfect positive correlation, and 0 indicates no correlation. The formula for calculating the Pearson correlation coefficient (r) is as follows:

`\[ r = (n(\Sigma xy) - (\Sigma x)(\Sigma y))/(√([n(\Sigma x^2) - (\Sigma x)^2][n(\Sigma y^2) - (\Sigma y)^2])) \]`

Here, n represents the number of observations, x and y are the two variables being correlated,
`\( \Sigma \)` denotes the sum, and xy , x² , and y² represent the product of x and y , the square of x , and the square of y , respectively.

The resulting correlation coefficient can be interpreted to understand the strength and direction of the relationship. A positive r indicates a positive correlation, a negative r indicates a negative correlation, and the magnitude of r reflects the strength of the association.

Researchers use hypothesis testing to determine whether the observed correlation is statistically significant or likely due to random chance, helping to make meaningful inferences about the relationship in the broader population. The Pearson correlation coefficient is widely used due to its simplicity, ease of interpretation, and applicability to a wide range of research questions in various disciplines.