You can use the Krejcie and Morgan formula to determine the sample size based on the size of the population/universe

Article Determining Sample Size for Research Activities

In fact, there is a table that has been generated using this formula- https://www.semanticscholar.org/paper/Determining-Sample-Size-for-Research-Activities-Krejcie-Morgan/de62bfbd044784fe0e60e8a11c1de959b6a7f4bd/figure/0

Based on variables, as a rule of thumb, researchers generally collect 10 responses per variable.

Hi

Thank you for your reply!

Are there any articles which insist 10 responses per variable?

Thanks!

Two simpler methods reported in two articles: MA Hertzog,Res. In Nursing and Health,31: 180, Consideration in Determining Sample size for pilot studies.and RV Krejcie and DW Morgan, Educational and Psychological Measurement, 1970,30: 607,Determining sample size for Research Activities.

Yuto Yasuda https://www.sciencedirect.com/science/article/abs/pii/S0895435615000888

Study suggesting 10 responses per variable.

General approach to estimating the sample size for your sequential mediation model:

1. **Determine the desired statistical power**: Statistical power refers to the probability of correctly detecting an effect if it truly exists. Commonly used levels of statistical power are 0.80 or 0.90, implying an 80% or 90% chance of detecting a significant effect if it is present.

2. **Specify the desired level of significance**: The level of significance (typically denoted by α) is the threshold below which a p-value is considered statistically significant. The most common level is α = 0.05, implying a 5% chance of making a Type I error (false positive).

3. **Estimate effect sizes**: Since you mentioned that there is no previous research showing the correlations between the variables, it can be challenging to estimate effect sizes. However, you can make educated guesses or assumptions based on similar studies or related research.

4. **Select an appropriate statistical method**: Sequential mediation models can be analyzed using techniques such as structural equation modeling (SEM) or bootstrapping. The choice of method may influence the sample size calculation, so it's important to determine the specific analysis approach.

5. **Use sample size estimation software**: There are various software packages and online calculators available that can assist in sample size estimation for mediation models. These tools often require inputs such as effect sizes, desired power, significance level, and the specific analysis method.

Hope it helps:credit AI