 # Power Analysis

How much data is enough to use for statistical consulting? What should be the sample size? These questions generally arise from statistical consulting clients. The answer to all this is, that it depends on multiple factors including the purpose of your study, population size, the risk of selecting a “bad” sample, and the allowable sampling error. It is not always feasible to perform the statistical experiment multiple times. Hence to best estimate the sample size or to validate the sample, if it is sufficient, we require to conduct a power analysis for your study.

Power analysis helps you estimate how much sample size is necessary to capture the effect of the study at the desired significance level. It also determines the probability of detecting an effect under sample size constraints, so that we can decide upon if we want to alter or abandon the experiment. If the sample size increases, the power of your test also increases. A larger sample means that you have collected more information, hence it is easier to correctly reject the null hypothesis.

There are two kinds of power analysis, a priori, and post hoc. Priori power analysis is the type that is required for dissertation research and defence. It offers you a clear picture of the target number of participants before you begin recruitment and data collection. We at SPSS tutor, use structural equation modelling to conduct power analyses on more complex psychometric studies.

## While doing power analysis keep in mind three major considerations :-

1. The first method is to do a random sampling which is known as sampling design. The size of the sample should be appropriate for the statistical analysis. As discussed earlier, a good size sample, approximately n=150+, is usually needed for multiple regression and analysis of covariance.
2. The sample size formulas provide the number of responses that need to be obtained. The sample size also depends on the number of statistical tests that you intend to conduct.
3. The size of the sample should be appropriate for the statistical analysis. As discussed earlier, a good size sample, approximately n=150+, is usually needed for multiple regression and analysis of covariance

## We can say there, are these four quantities that have an intimate relationship

:
1. sample size
2. effect size
3. significance level = P(Type I error) = probability of finding an effect that is not there
4. power = 1 - P(Type II error) = probability of finding an effect that is there

The fourth one can be determined while values for the 3 variables are given.

Kick-start your project now for power analysis with the SPSS tutor and we can provide you with this within a minimum period of 1-2 days.