How is the statistical application of Pearson r used for hypothesis testing.

Through application of the Spearman Correlation what type of data is the Pearson formula used for.

The Pearson r tests for a linear relationship between two variables in the population of interest. Spearman correlation is a nonparametric counterpart of the parametric Pearson r.

The statistical application of Pearson r, also known as Pearson correlation coefficient, is commonly used for hypothesis testing to examine the strength and direction of the linear relationship between two continuous variables. Here's how it is used:

1. Establish hypothesis: First, researchers define a null hypothesis (H0) and an alternative hypothesis (Ha) regarding the relationship between the two variables. The null hypothesis suggests that there is no significant correlation, while the alternative hypothesis proposes that there is a significant correlation.

2. Collect data: Data is collected for both variables of interest. These variables must be measured on a continuous scale.

3. Calculate Pearson correlation coefficient: The formula for Pearson r is used to compute the correlation coefficient, which quantifies the strength and direction of the linear relationship between the variables. The range of the correlation coefficient is between -1 (perfect negative correlation) and +1 (perfect positive correlation), with 0 indicating no correlation.

4. Conduct hypothesis test: Next, a statistical test is performed using the calculated Pearson correlation coefficient. The most common test is the t-test or z-test, depending on the sample size. The test evaluates whether the observed correlation coefficient is significantly different from zero.

5. Interpret the results: If the p-value associated with the test is below a pre-determined significance level (such as 0.05), the null hypothesis is rejected, indicating that there is evidence of a significant correlation between the variables. If the p-value is greater than the significance level, the null hypothesis cannot be rejected, suggesting that there is insufficient evidence to support a significant correlation.

Regarding the Spearman correlation, it is a nonparametric measure of correlation that does not assume a linear relationship between variables. However, the Spearman correlation can be used to analyze both continuous and ordinal data. On the other hand, the Pearson correlation formula is specifically designed for analyzing continuous data, where the variables are measured on a continuous scale.