SAMPLE SIZE DETERMINATION AND POWER CALCULATION – A COMPARISON BETWEEN SAS AND R PROGRAMMING

Choosing the proper sample size for an investigation is one of the crucial jobs required of a statistician. Regardless of whether the statistician is deciding the number of patients to select in a clinical trial, electors to finish a political survey, or mice to remember for a lab experiment, the same information elements of power, significance criteria, and effect size can be utilized too effectively. An expansion in the number of considered patients may straightforwardly expand the sensitivity of an experiment. This aids through an abatement in standard error and, subsequently, expands our capacity to recognize genuine treatment contrast. Without a minimum required sample size, the experiment with a helpless possibility of recognizing genuine treatment contrasts may be a waste of time and cash. Enrolling an excessive number of subjects can make possibly unnecessary exposure inferior treatments. Sample size determinations can be finished by hand or through one of the numerous accessible software packages, for example, SAS and R. This blog is about the comparison between SAS and R Programming. 

STATISTICAL POWER

Power is a powerful and regularly utilized strategy for statistical power analysis and sample size determination. Statistical power is defined as the probability of not rejecting the null hypothesis when it is false that is, the probability of a correct rejection. Mathematically, it can be represented as Pr(𝑟𝑒𝑗𝑒𝑐𝑡𝐻0 |𝐻1 𝑖𝑠𝑡𝑟𝑢𝑒) or as 1 – β, where β is equal to the probability of Type II error. Because power is a probability, it can take on values between 0 and 1. In spite of the fact that this may incredibly vary based on the study design and field of study, customary edges for statistical power are typically around 0.8 to 0.9 (80% to 90%).

Statistical power and sample size are inextricably linked, with a positive correlation between power and sample size. An assortment of factors influences the power of a test including the sample size, the effect size, and the intrinsic changeability in the data, a higher prerequisite of statistical power will yield a higher required sample size. Of these factors, you have the most power over the sample size. Statistical power can be utilized to figure the minimum sample size needed to recognize a determining effect size. 

TYPE I AND TYPE II ERROR

When we deal with making inferences based on the results from the sample, we cannot do so with 100% confidence. Acceptance or rejection of the null hypothesis can be stated only with a certain amount of error or with a certain amount of confidence (100% error). The error can be of two types, termed as Type-I and Type-II.

• Type I Error: Rejection of null hypothesis when the null hypothesis is actually true (i.e., false-positive) or finding an effect when actually there is no effect. This is represented by α and can be written mathematically as Pr(𝑟𝑒𝑗𝑒𝑐𝑡𝐻0 |𝐻0 𝑖𝑠 𝑡𝑟𝑢𝑒).
• Type II Error: Acceptance of null hypothesis when the alternative hypothesis is true (i.e., false negative) or not finding an effect when actually there is an effect. This is represented by β and can be written mathematically as Pr(𝑎𝑐𝑐𝑒𝑝𝑡𝐻0 |𝐻1 𝑖𝑠 𝑡𝑟𝑢𝑒).

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