Pearson's r: Real-World Examples in Psychological Research

📚 Quick Study Guide

• 🔢 Pearson's r measures the strength and direction of a linear relationship between two continuous variables.
• 📈 Values range from -1 to +1, where:
  • -1 indicates a perfect negative correlation.
  • 0 indicates no correlation.
  • +1 indicates a perfect positive correlation.
• 🧪 It is used to assess relationships, not causation.
• 📝 Formula: $r = \frac{\sum_{i=1}^{n}(x_i - \bar{x})(y_i - \bar{y})}{\sqrt{\sum_{i=1}^{n}(x_i - \bar{x})^2} \sqrt{\sum_{i=1}^{n}(y_i - \bar{y})^2}}$
• 💡 Interpretation depends on the context of the research.

🧠 Practice Quiz

1. Which of the following real-world scenarios can be best analyzed using Pearson's r in psychological research?
   1. Measuring the difference in anxiety levels between two treatment groups.
   2. Assessing the relationship between hours of sleep and test performance.
   3. Categorizing participants into different personality types.
   4. Comparing the effectiveness of different therapy techniques.
2. In a study examining the relationship between self-esteem and social anxiety, a Pearson's r value of -0.75 was found. What does this indicate?
   1. High self-esteem causes high social anxiety.
   2. There is a strong positive relationship between self-esteem and social anxiety.
   3. There is a strong negative relationship between self-esteem and social anxiety.
   4. There is no relationship between self-esteem and social anxiety.
3. A researcher wants to investigate the correlation between the number of hours spent studying and exam scores. Which statistical test is most appropriate?
   1. T-test
   2. ANOVA
   3. Pearson's r
   4. Chi-square test
4. In a study, the Pearson's r value between exercise frequency and happiness levels is found to be 0. What does this suggest?
   1. Exercise causes happiness.
   2. Higher exercise frequency leads to lower happiness levels.
   3. There is no linear relationship between exercise frequency and happiness levels.
   4. Higher exercise frequency leads to higher happiness levels.
5. Which of the following values of Pearson's r indicates the strongest correlation?
   1. 0.10
   2. -0.60
   3. 0.45
   4. -0.90
6. A study finds a Pearson's r of 1.2 between two variables. What is the most appropriate conclusion?
   1. There is a perfect positive correlation.
   2. There is a very strong positive correlation.
   3. The calculation is incorrect, as Pearson's r cannot exceed 1.
   4. There is a perfect negative correlation.
7. What is a limitation of using Pearson's r in psychological research?
   1. It can only be used with categorical data.
   2. It cannot detect non-linear relationships.
   3. It requires a large sample size.
   4. It can only be used with experimental data.