R Code for Descriptive Statistics and Reliability Analysis

Univariate Descriptives

Univariate analysis looks at one variable at a time to understand its distribution. Depending on the measurement level, you will look for different statistics:

• For Nominal variables: Use frequencies and percentages.
• For Continuous/Ordinal variables: Use the mean, median, standard deviation, and range.

In R, you can use dplyr::mutate to change variable types (e.g., converting a numeric variable to a factor) and dplyr::select to isolate specific variables for inspection. A powerful way to get a quick overview is the summarytools::dfSummary function, which creates a comprehensive summary table including missing values and distributions.

Bivariate Descriptives

Bivariate analysis examines the relationship between two variables. A common method for categorical data is the cross-tabulation table, which shows the frequency of observations for every combination of two variables (e.g., how many women with a university education were in a specific experimental condition).

Reliability Analysis and Scale Construction

If you have multiple items (like a series of questions) that are intended to measure a single construct—such as "internalization of the beauty ideal"—you must perform a reliability analysis. This assesses the internal consistency of the items.

The Four-Step Process

To move from individual items to a single reliable scale, follow these steps:

1. Check Correlations: Use sjPlot::tab_corr to see if your items correlate with one another. If you see negative correlations, some items might be "reverse-coded".
2. Recoding and Standardisation:
   • Recoding: If an item is phrased in the opposite direction of others, you must recode it so all items point in the same direction. For a 7-point scale, the formula is: $New\ score = (Max + 1) - Old\ score$ $New\ score = 8 - Old\ score$
   • Standardisation: If items use different scales (e.g., one is 1–7 and another is 1–10), convert them to z-scores so they have a mean of 0 and a standard deviation of 1.
3. Perform Reliability Analysis: Use psych::alpha to calculate Cronbach’s alpha ($\alpha$).

   Exam Tip: A Cronbach’s alpha ($\alpha$) value of 0.70 or higher is generally considered an acceptable rule of thumb for reliability.

4. Scale Construction: Once reliability is confirmed, create the scale by calculating the mean of the items.

Summary Check: When reporting a scale, always specify if it was constructed using the mean of the original items or the standardized (z-score) items, as this changes the resulting mean and standard deviation.

Interpreting Correlations

Finally, once your scales are constructed, you can examine correlations between them. When interpreting the correlation coefficient ($r$), keep Cohen's guidelines in mind:

• $|r| = .10$: Weak
• $|r| = .30$: Moderate
• $|r| = .50$: Strong

A positive correlation means both variables increase together, while a negative correlation means as one increases, the other decreases. Always check the p-value to ensure the relationship is statistically significant.