# Sample size and power in relationship

### Power Analysis, Statistical Significance, & Effect Size | Meera

One can select a power and determine an appropriate sample size beforehand or do power analysis afterwards. However, power analysis is beyond the scope. Power will depend on sample size as well as on the difference to be The first picture is for sample size n = 25; the second picture is for. A “power analysis” is often used to determine sample size. Control of Type II errors is more difficult as it depends on the relationship among several variables, .

Established statistical procedures help ensure appropriate sample sizes so that we reject the null hypothesis not only because of statistical significance, but also because of practical importance. These procedures must consider the size of the type I and type II errors as well as the population variance and the size of the effect.

The probability of committing a type I error is the same as our level of significance, commonly, 0. Ideally both types of error are minimized. Alpha is generally established before-hand: The larger alpha values result in a smaller probability of committing a type II error which thus increases the power. Power is the area under the distribution of sampling means centered on which is beyond the critical value for the distribution of sampling means centered on The basic factors which affect power are the directional nature of the alternative hypothesis number of tails ; the level of significance alpha ; n sample size ; and the effect size ES.

We will consider each in turn. Suppose we change the example above from a one-tailed to a two-tailed test. There are now two regions to consider, one above 1. If the power is less than 0. What is statistical significance? Testing for statistical significance helps you learn how likely it is that these changes occurred randomly and do not represent differences due to the program.

To learn whether the difference is statistically significant, you will have to compare the probability number you get from your test the p-value to the critical probability value you determined ahead of time the alpha level. If the p-value is less than the alpha value, you can conclude that the difference you observed is statistically significant.

P-values range from 0 to 1. The lower the p-value, the more likely it is that a difference occurred as a result of your program. Alpha is often set at. The alpha level is also known as the Type I error rate.

What alpha value should I use to calculate power? An alpha level of less than. The following resources provide more information on statistical significance: Creative Research Systems, Beginner This page provides an introduction to what statistical significance means in easy-to-understand language, including descriptions and examples of p-values and alpha values, and several common errors in statistical significance testing. Part 2 provides a more advanced discussion of the meaning of statistical significance numbers.

## Sample size estimation and power analysis for clinical research studies

Beginner This page introduces statistical significance and explains the difference between one-tailed and two-tailed significance tests. The site also describes the procedure used to test for significance including the p value What is effect size? When a difference is statistically significant, it does not necessarily mean that it is big, important, or helpful in decision-making.

It simply means you can be confident that there is a difference. The mean score on the pretest was 83 out of while the mean score on the posttest was Although you find that the difference in scores is statistically significant because of a large sample sizethe difference is very slight, suggesting that the program did not lead to a meaningful increase in student knowledge.

### Sample size estimation and power analysis for clinical research studies

To know if an observed difference is not only statistically significant but also important or meaningful, you will need to calculate its effect size. Rather than reporting the difference in terms of, for example, the number of points earned on a test or the number of pounds of recycling collected, effect size is standardized. In other words, all effect sizes are calculated on a common scale -- which allows you to compare the effectiveness of different programs on the same outcome.

How do I calculate effect size? There are different ways to calculate effect size depending on the evaluation design you use.