A study has a placebo given to one group, GROUP P, and a medication given to another group, GROUP M. This medication could be given to prevent colon cancer, anemia, or any other ailment that may cause death.

A follow up in 5 years is performed. 99% of GROUP M have survived. 98% of GROUP P have survived.

  • When does survival rates between groups become significant?
  • Any other information regarding how framing statistics alter the perceived significance also appreciated? In psychology, framing as a loss or a gain changes one perception.

What you are basically asking for is a called a "power analysis" in statistics.

If all you have are proportion data (i.e., 99% vs 98% surviving), then for a two-sided test of the null hypothesis that Group M and Group P have the same survival rate, with an alpha of 0.05, and expected probabilities as you've stated them, you would need at least 2254 subjects per group to have an 80% probability of correctly rejecting the null hypothesis ("80% power," calculated using the package 'pwr' for R).

If you have additional information, like the date of death, you could instead do a survival analysis and possibly have a bit more power.

I suspect framing the number or ratio of deaths rather than the percentages of survival will be perceived as more convincing, but it does not matter for statistical significance in the slightest.

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