Statistical Power

Quantitative Results

One can interpret or conjecture about data statistically, with the help of statistical inference. Thus, statistical inference is to infer about something statistically. Statistical inference basically involves Estimation and Testing of Hypothesis.

Since our discussion involves Statistical Power, we shall discuss Testing of Hypothesis.Hypothesis Testing consists of null and alternative hypothesis, typically denoted as H0 & H1 respectively. Null hypothesis is a statement in which no difference or effect is expected. Thus, if H0 is rejected, then one can say that there is no significant difference in the tested data. H1 is the complement of H0, i.e.; if H1 is accepted, then one can say that there is some significant difference in the tested data.

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The acceptance or rejection of the null and alternative hypothesis results in errors. There are basically two types of errors: Type I and Type II. Type I error is the event of rejecting a null hypothesis when a null hypothesis is true. The probability of a type I error is called the significance level. Type II error is when a researcher fails to reject a null hypothesis when a null hypothesis is false. In practical study, Type II is a more serious error than Type I, especially in Pharmaceutical research (involving drugs).

Due to the Type II error, Statistical Power has been created. Statistical Power is the probability (1-β) of rejecting null hypothesis when it is false, and this null hypothesis should be rejected in order to avoid Type II error. Therefore, one needs to keep the Statistical Power correspondingly high, as the higher our Statistical Power, the fewer Type II errors we can expect.

The analysis on Statistical Power, i.e. Power Analysis, can be done either upon the prior-collected-data or the post-collected-data.

Statistical Power usually depends upon:

  • -The desired power level
  • -The desired level of significance in the test
  • -The strength of association or the effect size in the population
  • -The sensitivity of the data
  • · –The size of the sample

In Statistical Power, the power level specifies the level or the chance of not making a Type II error. Usually, the researcher takes the power level as 0.80. In other words, the researcher has an 80% chance of not making a Type II error.

In Statistical Power, the level of significance is the minimum possible chance that a sample is likely to get associated with the population. Suppose the level of significance is 5%.  This means that the sample drawn from the population should have at least 5% of the characteristics of the population from where it has been drawn.

In Statistical Power, the effect size or the strength of association is basically the strength of the relation between the two variables. Thus, the greater the effect size, the greater its Statistical Power. Thus, there are more chances that the test is valid. Therefore, a greater effect size emphasizes a greater Statistical Power.

In Statistical Power, the sensitivity is referred to the number of true positives out of the total of true positives and false negatives. In layman’s language, sensitivity recognizes the truly correct data. This means that a high sensitivity will yield good data and therefore a high Statistical Power, which means data having less number of Type II errors. Therefore, the sensitivity of data is a very important factor for Statistical Power.

In Statistical Power, the determination of the sample size of the prior data is a very crucial factor. It is a sample size which keeps the value of Statistical Power high. This means that the larger our sample size, the greater the Statistical Power.