Give a plausible example of a three-variable research problem in which partial correlation would be a useful analysis. Define 1, 2, and . Make sure that you indicate which of your three variables is the “controlled for” variable ( 2). What results might you expect to obtain for this partial correlation, and how would you interpret your results (e.g., spurious correlation, mediation, moderation, and so on)? 600 words
A plausible example of a three-variable research problem in which partial correlation analysis would be a useful tool is the study of the relationship between social media usage, self-esteem, and academic performance among college students. In this hypothetical study, the three variables of interest are social media usage (Variable 1), self-esteem (Variable 2), and academic performance (Variable 3).
In this research problem, partial correlation analysis would be used to examine the relationship between social media usage and academic performance, while controlling for the influence of self-esteem. The main objective is to determine whether the relationship between social media usage and academic performance remains significant after accounting for the potential confounding effect of self-esteem.
To conduct this analysis, we need to obtain data on social media usage, self-esteem, and academic performance for a sample of college students. Social media usage can be measured by the average daily time spent on social media platforms, self-esteem can be assessed using a validated scale, and academic performance can be measured by students’ grade point averages (GPA).
Once the data is collected, we can calculate the partial correlation between social media usage and academic performance, controlling for self-esteem. The partial correlation coefficient (r) ranges from -1 to 1 and indicates the strength and direction of the relationship between the two variables of interest, while holding the third variable constant.
In this example, social media usage (Variable 1) is the predictor variable, academic performance (Variable 3) is the outcome variable, and self-esteem (Variable 2) is the controlled for or confounding variable. By controlling for self-esteem, we aim to determine whether there is a direct association between social media usage and academic performance, independent of self-esteem.
The results of this partial correlation analysis might yield several possible outcomes and interpretations.
First, if the partial correlation between social media usage and academic performance remains significant and strong (e.g., r = 0.50, p < 0.05) after controlling for self-esteem, this would suggest that social media usage has a direct impact on academic performance, beyond the influence of self-esteem. In this case, the relationship between social media usage and academic performance is not spurious but rather a genuine direct association, indicating that higher levels of social media usage are associated with lower academic performance, even after accounting for self-esteem. On the other hand, if the partial correlation becomes non-significant or weak (e.g., r = 0.10, p > 0.05) after controlling for self-esteem, this would imply that the relationship between social media usage and academic performance is fully mediated by self-esteem. In other words, self-esteem plays a crucial role in explaining the association between social media usage and academic performance, rendering the direct association insignificant. This would suggest that social media usage indirectly affects academic performance through its influence on self-esteem.
Furthermore, if the partial correlation changes substantially in magnitude and significance (e.g., r = 0.30, p > 0.05) after controlling for self-esteem, it may indicate that self-esteem moderates the association between social media usage and academic performance. This would imply that the relationship between social media usage and academic performance differs depending on the level of self-esteem. For example, social media usage may have a negative impact on academic performance only for individuals with low self-esteem, while it may not have a significant effect for those with high self-esteem.
In summary, partial correlation analysis can be a useful tool in studying three-variable research problems, such as examining the relationship between social media usage, self-esteem, and academic performance. By controlling for the influence of self-esteem, we can gain insights into the direct, mediated, or moderated associations between these variables. The interpretation of the results will depend on the magnitude, significance, and theoretical implications of the partial correlation coefficient obtained.
