Introduction to Correlational Analysis and Non-Parametric Testing in JASP

Setting Up Correlational Analysis in JASP

• Variable Measurement: The variables identified for analysis are the scores of respondents for "neurocognitive" (later referred to as "neuroticism") and "conscientiousness."

• Analysis Navigation Path:

  • Select the Analysis menu.

  • Navigate to Descriptives.

  • Click on Descriptive Statistics.

  • Move the target variables into the Variable box.

  • Select transposed descriptive table.

  • Uncheck the option for assumption data to focus on the raw descriptive outputs.

Assessing Normality of Data

• Sample Size Considerations: The criteria for normality testing depend on the number of respondents.

  • If the sample size is more than $50$.

  • If the sample size is more than $300$.

• Visual Normality (Q-Q Plot):

  • For sample sizes greater than $300$, use the Q-Q plot as the primary basis for checking normality.

  • Normally Distributed Data: In a Q-Q plot, the data points should align closely with the diagonal line.

• Statistical Normality (Shapiro-Wilk/"Week"):

  • If there are less than $50$ respondents, statistical tests are more critical.

  • Go to Regression, then Correlation, and click assumption checks.

  • Select pairwise normality check and look for the week (likely Shapiro-Wilk) and the associated p-value.

  • Interpretation of p-values:

    • If the p-value is greater than or equal to $0.05$, the data is considered normally distributed (e.g., a p-value of $0.13$ indicates normality).

    • If the p-value is less than $0.05$, the data is not normal.

• Skewness Thresholds:

  • Check the dependent abdominal response (skewness).

  • If the value is less than $3.29$, the data is normally distributed.

  • If the value is greater than $3.29$, the data is not normally distributed.

Checking Linearity and Homoscedasticity

• Scatter Plot Customization: Click on customizable plots and select scatter plot to visualize relationship dynamics.

• Linearity:

  • Identify the direction of the data.

  • Linear: Data follows a straight-line direction.

  • Curvilinear: Data follows a curved pattern.

  • In the provided case, the relationship is identified as linear.

• Homoscedasticity:

  • Check for a pattern in the scatter plot.

  • Homoscedastic data should not show a specific pattern (like a fan-out).

  • If a fan-out pattern exists, it may indicate heteroscedasticity.

Outlier Detection and Non-Parametric Alternatives

• Boxplot Analysis: To identify significant outliers, click on the boxplot within the descriptives section.

• Identifying Outliers: If dots appear outside the whiskers of the boxplot, these represent significant outlier data.

• Effect on Statistical Choice:

  • If assumptions (normality, no outliers, linearity) are met, Pearson's r is appropriate.

  • If assumptions are violated, non-parametric alternatives must be used.

• Non-Parametric Options:

  • Spearman's rho.

  • Kendall's tau-b (specifically Robust Kendall's tau-b in this study).

Conducting Kendall's Tau-b Correlation

• Analysis Setup:

  • Select Kendall's tau-b in the correlation coefficient options.

  • Check display pairwise.

  • Check flag significant correlations to identify results with an asterisk.

• Determining Significance:

  • The p-value indicates if there is a statistically significant relationship.

  • In the provided example, the p-value is less than $0.001$.

  • Three asterisks (***) on the correlation coefficient indicate significance at the $0.001$ alpha level ($\alpha = 0.001$).

• Additional Metrics:

  • Confidence Interval: Should be reported for parametric tests (Pearson's r) but was noted for general identified reporting.

  • Effect Size: The level of magnitude of the relationship.

Interpretation of Results for Neuroticism and Conscientiousness

• Correlation Coefficient Value: The Kendall's tau-b value is $-0.25$.

• Nature of Relationship:

  • Negative Relationship: Indicated by the negative sign, meaning as one variable increases, the other decreases (and vice versa).

  • Inverse Relationship: Neuroticism and conscientiousness are inversely associated.

  • Strength: The relationship is described as weak.

• Significance: Because the p-value is < 0.001, the variables are significantly correlated or associated.

Effect Size and G*Power Analysis

• Cohen's Convention: According to Cohen's conventions for correlation coefficients:

  • A value of $0.25$ indicates a small effect size.

• G*Power Procedure:

  • To calculate the required sample size for a given effect, use the G*Power software.

  • Select Exact test family.

  • Select Correlation: Bivariate normal model.

  • Input Parameters:

    • Tail(s): As per the research hypothesis.

    • Effect size: Use the absolute value of the coefficient, which is $0.25$.

    • Alpha (\alpha): Set at $0.05$.

    • Power (1 - \beta): The minimum accepted power is $80\%$ (represented as $0.80$).

  • Calculated Sample Size: For a statistically significant result with these parameters, the minimum required sample size is $123$ respondents.