Determining the optimal sample size for criterion validity depends on several factors, including the variability in the population, the strength of the relationship between the two measures, and the desired level of precision in the estimate.

A common approach to estimate the sample size for criterion validity is to use the correlation coefficient between the two measures. For a medium-sized correlation coefficient of 0.3, a sample size of 100 would provide reasonable power to detect a significant relationship. However, if the correlation coefficient is expected to be smaller, a larger sample size may be needed to detect a significant relationship.

Another approach to estimating the sample size is to use power analysis. Power analysis takes into account factors such as the alpha level, effect size, and sample size to determine the probability of detecting a significant relationship. An effect size of 0.3 is generally considered a moderate effect size for correlation coefficients, and a power of 0.8 is typically desired. Using these parameters, a sample size of 87 would be needed to detect a medium-sized correlation coefficient with 80% power and a significance level of 0.05.

In summary, a sample size of at least 87 participants would be needed to detect a medium-sized correlation coefficient between a 36-item PA scale and a pedometer with 80% power and a significance level of 0.05. However, the optimal sample size may vary depending on the specific context and research question.

Determining the optimal sample size for criterion validity depends on several factors, including the magnitude of the correlation expected between the two measures, the desired level of statistical power, and the level of significance used in the analysis. Generally, a larger sample size would increase the statistical power of the analysis, which would allow for detecting smaller correlations with greater confidence.

As a general rule of thumb, some researchers recommend a minimum sample size of 50 to 100 participants to establish criterion validity. However, the optimal sample size can vary depending on the specific research question and the characteristics of the population being studied.

To determine the optimal sample size for your study, it is recommended to conduct a power analysis using software such as G*Power. This will help you to determine the minimum sample size needed to achieve the desired level of statistical power based on the expected correlation between the YPAS and Omron HJ0325 pedometer measures.

Determining the optimal sample size for criterion validity depends on several factors, including the expected effect size, desired level of statistical power, and the acceptable level of type I error rate (alpha).

In general, a larger sample size increases the statistical power of the analysis and reduces the likelihood of type I error. However, the optimal sample size may vary depending on the specific research question and context.

As a general guideline, a sample size of at least 100 participants is typically recommended for criterion validity studies. However, larger sample sizes may be necessary to detect smaller effect sizes or to increase the precision of the estimates.

It's also important to consider the reliability of the measures being compared, as this can impact the validity of the results. In addition, the sample should be representative of the population of interest, and participants should be recruited using appropriate sampling methods to reduce bias.

Overall, while there is no one-size-fits-all answer to what the optimal sample size should be, it's important to carefully consider the factors mentioned above and consult with a statistician or research expert to determine an appropriate sample size for your study.