Unless your goal is strictly that of replicating a study to see whether an ES as big (or bigger) than that observed in a prior study would be obtained (which, in the last 20 years, has become a point of interest for those concerned with replicability of study findings), the way to consider ES as part of a priori sample size planning is:
Decide on what the smallest effect of interest (e.g., non-ignorable and of practical import, in your judgment) would be such that, if it existed in the population, you'd like your study to have a good probability of detecting it. This becomes your target ES...and this may be wildly different from what was reported in an existing study result.
So, the fact that the published study failed to report SD(s) isn't the point, as you can elect to use a standardized difference metric, or a variance accounted for metric. The point is to have a meaningful target ES.
Yes, you can calculate the required sample size for a new study if you know the effect size from a previous study, along with other information such as desired power and significance level. The sample size calculation is based on statistical principles and aims to ensure that the study has a high probability of detecting an effect of a certain size if it exists.
The formula to calculate the required sample size typically involves the following factors:
Effect Size (ES): This is the difference between the groups being studied (e.g., treatment group vs. control group) and is usually expressed as a standardized measure like Cohen's d for continuous outcomes or odds ratio for binary outcomes. If you have the effect size from a previous study, you can use that value.
Desired Power (1 - β): Power is the probability of correctly detecting a true effect if it exists. Commonly chosen values for power are 0.80 or 0.90, indicating an 80% or 90% chance of detecting an effect if it's there.
Significance Level (α): This is the threshold for determining statistical significance. Commonly used values are 0.05 or 0.01.
Type of Hypothesis Test: Depending on the research question and the type of data (continuous, categorical, etc.), you'll choose an appropriate test (t-test, chi-square test, etc.).
Hello Rizqy Ahp, I have Armitage and Berry; Statistcal Methods in Medical Research book. Sample size is page 200-205 about. My book is falling apart though, the binding has perished and all the pages are falling out. Is it at your library?