Sample size calculations.pdf

Sample size Calculation Dr. Notaila Fayed T.A of Public health and Epidemiology Why Sample Size calculation?  Factors determining the sample size: 1. Significance level /p-value ( α level). 2. Power (1 - β level). 3. Desired effect (Difference) or ( Desired Precision). 4. Variability (Varian...

Sample size Calculation Dr. Notaila Fayed T.A of Public health and Epidemiology Why Sample Size calculation?  Factors determining the sample size: 1. Significance level /p-value ( α level). 2. Power (1 - β level). 3. Desired effect (Difference) or ( Desired Precision). 4. Variability (Variance). 5. Study Hypothesis (Alternative Hypothesis). 6. Available Resources (A trade-off). Significance level ( α level): ▪ p-value at which we will consider the result as statistically significant or not (conventionally it is 5%). ▪p-value: The probability that the observed effect or phenomena is due to chance. ▪ The more stringent significance level (e.g.1%) the larger required sample size.  Type 1 error ( α- error): : ▪ The probability of finding a difference with our sample compared to population, and there really isn’t one. ▪ Probability of rejecting a true null hypothesis ▪ Known as the α (or cto be more confident, it be.001. ▪ Usually set at 5% (or 0.05) Power (1 - β level): ▪ The capacity of the study to detect differences or relationships that actually exist in the population. ▪ The likelihood of finding a statistically significant effect of a given magnitude if one truly exists?. ▪ It is the probability of finding an effect when an effect actually exists. ▪ The greater the power, the larger required sample size.  Type 2 error (β- error): : ▪ The power is related to the β (or “type 2 error”) error which is the risk of accepting null hypothesis while it is false i.e. The probability of not finding a difference that actually exists. ▪ So, power= 1- β, where β not more than 20% so power is more than 80% is acceptable. ▪ So, there is an inverse relation between sample size and β error.  Effect size or desired Precision: ▪ Magnitude of difference to be detected. ▪ Effect: is the presence of a phenomenon, relationship or difference you looking for (primary outcome) ▪ It is the generic term to describe the magnitude of the relationship between an independent variable and a dependent variable. ▪ The smaller effect/confidence interval (i.e, high precision), the larger sample size will be required.  Effect size or desired Precision: ▪ Example: ▪ In Surveys/ Single group research >> Width of Confidence interval(margin of error/Precision) ▪ In Comparative Studies >> Difference(in means or proportions)  Variability in the population: ▪ It is measured by “Variance”. ▪ Its measurement depends on type of outcome measure: -Continuous: standard deviation square (S2) -Dichotomous: p(1-p) ▪ The Larger variability, the larger sample size will be needed  Alternative Study Hypothesis: ▪ One-tailed is easier to identify/prove >> small required sample size. ▪ Two-tailed is more general and difficult to identify >>> larger sample size will be needed. Sample Size  Tools for calculating sample size: ▪ 1.Use of formulae (for each study design). ▪ 2.Nomograms. ▪ 3.Ready made tables. ▪ 4.Computer software. Tools for calculating sample size: Tools for calculating sample size: Tools for calculating sample size: Tools for calculating sample size: