Power Analysis: A Basic Introduction (2021)

Ajay Ohri

In this article, you will understand Statistical power is the power of the hypothetical test to test whether the effect has a true effect for a data time set, Power analysis is used for estimating the minimum sample size required for an experiment for an expected significance level size effect and statistical power, How to calculate and analyze plot power test in python for an effective experimental design. 

The statistical power is analyzing the results of the experiment and the measure of its effect whether it is true or false. The power of statistical test results is the confidence one has in the results concluded. A tool for measuring the sample size and the effect it has. The statistical analysis is interpreted in the Greek letter alpha and shows some relevance to the results obtained.

Overview of the article:

  1. Statistical hypothetical testing 
  2. What is Statistical power?
  3. Power Analysis

1. Statistical hypothetical testing 

A presumption of the outcome is called the null hypothesis.

The null hypothesis for Pearson’s correlation test does not indicate any difference between the two variables. The student’s hypothesis test indicating the null hypothesis determines there is no difference between the means of the populations. 

P-value where it is probable to obtain equal or extreme that deviates from that observed in the data.


Significance level ( alpha): A margin that specifies a statistically significant finding while interpreting p-value.

P-value is the probability or the assumed value, whereas the actual value may be different, then the test could be wrong, with this p-value there is a possibility that there could be an error. If the p-value seems to be less than the significant level, the null hypothesis seems to be rejected and if P-value seems to be more than the significant level it is accepted. The p-value indicates statistically significant levels. 

  • There are two types of errors
  • Type I Error: The p-value is optimistically low and the null hypothesis is rejected with no significant effect.
  • Type II Error: Null hypothesis is not rejected when there is a significant effect ( false negative) when the p-value is pessimistically high.
  • With the above interpretations, the significance level is null hypothesis rejection if it were true, then the possibility of type 1 error would be false positive.

2. What is Statistical power analysis?

Statistical power the hypothetical test power is that the test aptly rejects the null hypothesis.

The statistical analysis can show an error when the null hypothesis is rejected in two instances showing false positive or negative. 

2.Pr( True Positive)=1-Pr ( False negative).

In other words, statistical power signifies more power for accepting an alternative hypothesis, if the alternative hypothesis is true.

For interpreting statistical power, the experimental setups exist for high statistical power

  • Low statistical power: Higher risks of making Type II errors eg: false negative.
  • High statistical power: The smaller chance of making Type II errors

Too low statistical power in an experimental result can be concluded invalid about the meaning of the result. Hence, a minimum range of statistical power must be devised.

The experimental design with a statistical power of 80% is considered good e.g. 0.80. This refers that there is a 20% chance of encountering a Type II area. This differs for a 5% likelihood of encountering Type I error for the significant level of a standard value.

3. Power Analysis

Statistical power a puzzle with 4 related areas: These are;

  • Effect Size: The magnitude of a quantified result present in the population. Effect size is calculated using a specified statistical measure such as Pearson’s correlation coefficient for relating the variable or cohen’s d for the difference between groups. 
  • Sample Size: The estimate of observations in the sample 
  • Significance: The significance level that is used in the statistical test 
  • Statistical power: The chance of accepting the alternative hypothesis is true.

These variables are related, example a large sample size makes an effect easier to identify and the statistical power analysis can be raised in a test with improvement in the significance level. The sample size, the effect it has on the sample size, and the correlations of the data are a part of statistical analysis. These four parameters are evaluated and are important for detecting an effect of the amplified significance level. The statistical power lies in evaluating a significant sample size for effect with significantly expected and accepted result. 

A power analysis is estimating or evaluating one of these 4 parameters with the values provided for the other three parameters. This is a powerful tool for designing and analyzing the experiments that can be interpreted using a statistical hypothesis test.


The statistical hypothesis test is performed for evaluating the p values whether they are false positive and negative with a significant impact on the design and analysis of the experiment. 

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