Detailed Notes on Correlation Analysis and Reporting

Mental Health and Anxiety Correlation
  • Mental Health Rating Scale: Rated from 1 to 10, where 1 is horrible and 10 is the best.
  • The correlation between mental health and anxiety levels indicates that:
    • A negative correlation exists: As mental health improves (rating increases), anxiety days per week decrease.
    • Correlation Coefficient (r): A range between -0.5 and -1 indicates a strong negative correlation.
Understanding Correlation
  • The correlation coefficient tells us the direction and strength of the relationship:
    • Perfect Correlation: r = -1 (indicative of a perfect inverse relationship).
    • Strong Correlation: r values closer to -1 or 1 (e.g., -0.58 is considered a strong negative correlation).
R-Squared Value
  • R-squared Value (r^2): Indicates the percentage of variance explained by the correlation:
    • Calculate by squaring the correlation coefficient.
    • E.g., If r = -0.58, then r-squared = $(-0.58)^2 = 0.3364$ (approximately 33.64% variance).
Reporting Results in APA Style
  • Essential elements to report for correlation results:
    • The correlation coefficient (r).
    • Statistical significance (p value).
    • Sample size (N).
    • Example: "There was a strong association observed between participants’ mental health and anxiety (r(17) = -0.58, p < 0.01)."
Non-Significant Findings
  • If a correlation is not statistically significant:
    • Example: Mental Health and Exercise Study showed an r-value of 0.14 (not significant, p > 0.05).
    • It's crucial to note the sample size, which often affects significance outcomes.
    • Non-significant findings should still report the correlation coefficient and p value:
    • Example: "Moreover, there was no relationship between mental health and exercise habits (r(17) = 0.14, p > 0.05)."
Descriptive Statistics
  • Descriptive statistics (mean and standard deviation) of relevant variables should be reported:
    • Example for Exercise: Average hours worked out = 2.74 hours; standard deviation = 2.47 hours.
Conducting Analysis with Standard Tools
  • Use statistical software/calculators for:
    • Performing Pearson's correlation.
    • Summarizing descriptive statistics.
    • Employing chi-square tests for categorical data, particularly useful for yes/no questions.
Writing Results Section
  1. State Hypothesis: Clearly articulate the hypothesis being tested (e.g., the relation between mental health and exercise).
  2. Descriptive Statistics: Provide a summary table of means and standard deviations.
  3. Inferential Statistics: Present results from Pearson's correlation or other tests with appropriate context and interpretation:
    • Example: "A Pearson's correlation was used to analyze the relationship between mental health and anxiety."
  4. Statistical Interpretation:
    • Clarify implications of significant or non-significant results in layman's terms for broader audience understanding.