The relationship between sample size and the number of scale items is influenced by several factors, including the type of statistical analysis, the complexity of the scale, and the research objectives. Here are the key aspects of this relationship:

1. General Guidelines for Determining Sample Size

• Exploratory Factor Analysis (EFA): A common rule of thumb is to have 5 to 10 respondents per item. For example, if a scale has 20 items, a sample size between 100 and 200 is recommended.
• Confirmatory Factor Analysis (CFA): Typically requires a larger sample size than EFA, often 200 to 300 participants as a minimum.
• Structural Equation Modeling (SEM): Requires an even larger sample size, typically at least 5 to 10 times the number of observed variables.

2. Impact of the Number of Scale Items on Sample Size

• A larger number of scale items often requires a larger sample size to ensure stable factor structures and reliable parameter estimates.
• Shorter scales may allow for smaller sample sizes, but reliability and validity must be assessed carefully.

3. Variable-to-Sample Ratio

• A common guideline is a 5:1 to 10:1 ratio of participants to items.
• For example, a 30-item scale would ideally require 150 to 300 participants.

4. Statistical Considerations

• Power Analysis: Conducting a power analysis can help determine the optimal sample size based on effect sizes and significance levels.
• Monte Carlo Simulations or bootstrapping methods can be used to estimate the required sample size for complex models.

5. Exceptions and Context-Specific Considerations

• If the scale items are highly correlated or redundant, a smaller sample may suffice.
• If the scale is measuring a multidimensional construct, a larger sample is needed to capture the complexity.