Statistical Power – A Complete Guide
Published by at September 20th, 2021 , Revised On August 3, 2023
Definition
In research, a researcher sometimes might or might not find something ‘statistically significant‘ in the data that has been collected. The likelihood of something statistically significant being found in data is called statistical power. It is, of course, a statistical measure. Statistical power is only accounted for when it is known that a certain effect exists in the research population.
In other words, statistical power is a decision by a researcher/statistician that results of a study/experiment can be explained by factors other than chance alone. The statistical power of a study is also referred to as its sensitivity in some cases.
Explaining Statistical Power
Statistical power is denoted as 1 – β.
What this means is that if the power is high, the probability of claiming that there is no effect when there is one becomes low. In other words, when the power is high, that implies the researcher has claimed there is no statistical significance in the data, even though there is. Contrary to this, when the power is low, that means the researcher has successfully detected the statistical significance that exists in the data.
Importance of Statistical Power
Firstly, high statistical power helps researchers go back to the sample, re-evaluate, re-analyze, and so on. Second, statistical power analysis may be used to put an estimate on the minimum sample size required for an experiment, research, etc.
Standard Statistical Power
Researchers generally claim statistical power ought to be equal to or greater than. 8. in other words, one should have an 80% (or greater) chance of detecting a statistically significant effect in a sample when there is one.
This means the degree of confidence a researcher has about the result not occurring by chance alone. A confidence level commonly present in some statistical tests is 95%, which results in a p-value of 5%.
Factors Influencing Statistical Power
Four main factors might influence statistical power. They are:
- Sample size – has a direct relationship with statistical power; the bigger the sample size, the higher the power and vice versa (given other parameters are kept constant).
- Data collection method – certain data collection methods, such as stratified sampling, cause low error variance and, consequently, increase power. To increase the power even further, a different design can be adopted. Bear in mind, though, that statistical power calculation, as well as its analysis, depends on the kind of experimental design used.
- The difference between group means – has a direct relationship with power; the high the difference, the lower and power and vice versa.
- Variability among subjects – has an inverse relationship with power; the larger the variance, the smaller the power.
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How to Increase Statistical Power
To increase statistical power in a research/experiment, 5 different factors can be altered, and they are:
- Increasing alpha α: Setting it to the standard value used in most researches, which is .05. However, it should not be increased so much so that a true null hypothesis, is rejected. That would be a type I error.
- Selecting a larger value for differences: This increases power because it is easier to identify larger differences in population means.
- Decreasing random error: There are two ways to decrease random error. Firstly, a researcher can simply try to not make it in the first place. Or, if it has been made, explain it through a control variable so it becomes explained variation. Variation accounted for, that is.
- Secondly, a researcher can use some kind of repeated measuring design. Since there are multiple measurements on a subject, variance in error can be separated from variance in subjects.
- Increase sample size: This is a very practical and commonly-used method to increase statistical power. It provides further information about the sample population. And that, in turn, increases the power.
- Using a directional/one-tailed hypothesis: This kind of hypothesis has more power to help pinpoint the statistical significance. At the same time, though, a directional hypothesis can also decrease power in some cases.
Statistical Power and P-value
With regards to whether they are the same or not, significance (p-value) is the probability that one rejects a null but true hypothesis. And power is the probability of rejecting a null and false hypothesis. Furthermore, power and p-values both measure the same thing: the probability of rejecting a null hypothesis.
Whether that hypothesis is false or true is what differentiates the two (among other factors). In the same context, just as an 80% chance or greater is considered a ‘good’ statistical power, a p-value of 5% or lower is considered statistically significant.
What ‘Isn’t’ Statistically Significant
If there is such a thing as statistical power and it corresponds to statistical significance, is there such a thing as statistically NOT significant? As it turns out, yes, there is. It is used for results where differences as large as that is, equal to (or larger than), the observed difference is expected to occur by chance more than 1 out of 20 times. In other words, the p-value is > 0.05 for the data to be statistically not significant.
Calculating Statistical Power
Calculating statistical power is a complex method and is usually done using computers and other online calculators. The kind of method or tool to use is determined by the type of tests, sample, data collection method and so on.
PowerAndSampleSize provides at least 19 interactive calculators for statistical power calculations. There are also other online platforms offering tools to calculate statistical power. For instance, on StatPages, numerous types of tools are offered to determine power, depending on sample size, type of test, and many other factors.
Almost every researcher and/or statistician can make use of these online tools to calculate statistical power by inputting different parameters into the calculators. The entire process is called power analysis. And even for power analysis, different software is used, the most common ones being SAS and PASS.
Furthermore, calculating sample size with statistical power analysis is also a part of this process.
While reading through statistical power, mention of ‘underpowered statistics’ might be present. The term is mainly used for samples in research. An ‘underpowered’ study is one that lacks a significantly large sample size. Or rather, it is not large enough to gauge answers to the research question(s) at hand. Contrarily, an ‘overpowered’ research study is one with a very large sample size. Size is so large that more resources might be needed to work with it.
In simple terms, a low statistical power implies there is a significant chance of committing Type II error, that is, a false negative hypothesis is accepted. On the other hand, a high statistical power implies a small chance of committing Type II error.
The four elements of statistical power are the same as the four ‘factors’ influencing statistical power. And they are sample size, the method used to collect data, the difference between group means, and variability among subjects. The first three have a direct relationship with statistical power; one increases and so does the other. The last factor, variability among subjects, has an inverse relationship with statistical power.
