# How to calculate power loss

## Abstract

### Why

Calculating the sample size is essential to reduce the cost of a study and to prove the hypothesis effectively.

### How

Referring to pilot studies and previous research studies, we can choose a proper hypothesis and simplify the studies by using a website or Microsoft Excel sheet that contains formulas for calculating sample size in the beginning stage of the study.

### More

There are numerous formulas for calculating the sample size for complicated statistics and studies, but most studies can use basic calculating methods for sample size calculation.

**Keywords:** Sample size

In recent years, as the institutional review board has become mandatory, estimation of the sample size has attracted people's attention. Still, many clinicians need to learn why the sample size needs to be calculated and how to calculate it.

It is thought by some researchers that if they conduct a sample size calculation, they need to investigate a high number of samples whereas they only have limited time and money. Some of them even treat it as a kind of rite of passage. Also, they think it is too hard to calculate because they need to use complicated formulas.

Rather, sample size calculation is an indispensable process for obtaining optimal results. Indeed, researchers should know how to calculate sample size because they have limited time and money. Simply, to save time and money, researchers should calculate the sample size.

As researchers usually want to prove that the experimental group is superior to the control group, this article will focus on the superiority trial and we will discuss the non-inferiority trials next time.

## WHY

Many researchers want to show that the two groups are truly distinct, but they will fail to find significant differences if the sample size is not big enough. Also, they can waste time and money by continuing an investigation past the time it needs to be continued because they do not know when the testing has been completed since they haven't calculated the sample size before the investigation begins. If the sample size is already large enough to prove that the experimental group is superior, maintaining treatment for the control group could be an ethical problem because the treatment they are receiving is obviously inferior. Thus, it is clear that calculation of sample size is essential ethically and also effectively to get the greatest satisfaction at

the lowest cost.

## WHEN

Calculation of the sample size is carried out during the planning stage. Thus, calculating the sample size is usually conducted in prospective random control studies. Retrospective studies use statistical power rather than the calculation of sample sizes and we call these 'post hoc power analyses'. We are going to learn about the need and the worth of these 'post hoc power analyses' later.

Also, because researchers expect to uncover findings by referring to previous research studies or pilot studies, the calculation of sample size is done after references are investigated, and before the full-scale research begins.

## HOW

The method is pretty simple. First, there is the primary outcome, according to whether the primary outcome is binary variable like pass/fail or a continuous variable like weight/height/score, the methods will be explained one by one in the next section.

### When the Primary Outcome Is a Binary Variable

Let's make an assumption that the success rate of the control group and the experimental group is 70% and 85% respectively, as calculated by previous research or pilot study. Visit http://www.sealedenvelope.com/power/binary-superiority/ and click 'calculate' after putting in the success rate which is mentioned above.

As the results show, the sample size required per group is 118 and the total sample size required is 236 ( Fig. 1 ). The statistical significance level, alpha, is typically 5% (0.05) and adequate power for a trial is widely accepted as 0.8 (80%). The higher the power (power = 1 - beta) for a trial, the larger the sample size that is required. The right part in Fig. 1. 'You could say

', shows an example of a sentence that can be used in the paper. The meaning of alpha and beta is very important, but it will be left out because it has already been explained precisely in many statistical references.

An example of sample size calculation for a binary outcome superiority trial. Adaped from http://www.sealedenvelope.com/power/binary-superiority/ with permission from Sealed Envelope.

Compared with several other websites, the results of 'www.sealedenvelope.com ' are different a little. These differences are thought to be due to the roundings.

### When the Primary Outcome Is a Continuous Variable

If the means and standard deviation of the experimental and control group are 76, 83 and 10 respectively, 66 samples (33 samples per each group) are calculated ( Fig. 5 ).

Source: www.ncbi.nlm.nih.govCategory: Forex

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