Models

Hypothesis

Null hypothesis: there is no correlation between patients’ initial treatment ages and the percent improvement in SE (%).

Alternative hypothesis: there is a correlation between patients’ initial treatment ages and the percent improvement in SE (%).

Correlation Model

Pearson

When considering the relationship between the two factors, Pearson’s correlation coefficient and Spearman’s ranking order correlation coefficient are the most common tools. Pearson’s test is best used when there are no outliers in the data (Kent State University, 2021), whereas Spearman’s test is most accurately used when the data has significant outliers. Since there are no outliers in this set of data, Pearson’s test is chosen.

If the coefficient > 0, then there is a positive correlation. Which is, by increasing one value, the other value also increases. If the coefficient < 0, then there is a negative correlation, meaning by increasing one value, the additional value decreases.

Here, the r-value is 0.4902269, which is greater than 0. Since this value is between 0 and 0.5, it is considered a weak positive correlation.

Although it is suggested that there is a weak positive correlation between two variables, we still need to examine its statistical significance, that is, whether the relationship with this sample exists in the population (University of Connecticut, 2009). A significance level (α) is chosen to be 0.05, meaning there is at least 95% chance that the relationship in this sample also exists in the population (University of Connecticut, 2009). Since the p-value 0.003249 is smaller than 0.05, the relationship is statistically significant. Therefore, the alternative hypothesis is accepted.