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# Statistical Significance

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Last Update: November 23, 2023.

## Introduction

In research, statistical significance measures the probability of the null hypothesis being true compared to the acceptable level of uncertainty regarding the true answer. We can better understand statistical significance if we break apart a study design.[1][2][3][4][5][6][7]

When creating a study, the researcher has to start with a hypothesis; that is, they must have some idea of what they think the outcome may be. For example, a study is researching a new medication to lower blood pressure. The researcher hypothesizes that the new medication lowers systolic blood pressure by at least 10 mm Hg compared to not taking the new medication. The hypothesis can be stated: "Taking the new medication will lower systolic blood pressure by at least 10 mm Hg compared to not taking the medication." In science, researchers can never prove any statement as there are infinite alternatives as to why the outcome may have occurred. They can only try to disprove a specific hypothesis. The researcher must then formulate a question they can disprove while concluding that the new medication lowers systolic blood pressure. The hypothesis to be disproven is the null hypothesis and typically the inverse statement of the hypothesis. Thus, the null hypothesis for our researcher would be, "Taking the new medication will not lower systolic blood pressure by at least 10 mm Hg compared to not taking the new medication." The researcher now has the null hypothesis for the research and must specify the significance level or level of acceptable uncertainty.

Even when disproving a hypothesis, the researcher can not be 100% certain of the outcome. The researcher must then settle for some level of confidence, or the degree of significance, for which they want to be confident their finding is correct. The significance level is given the Greek letter alpha and specified as the probability the researcher is willing to be incorrect. Generally, a researcher wants to be correct about their outcome 95% of the time, so the researcher is willing to be incorrect 5% of the time. Probabilities are decimals, with 1.0 being entirely positive (100%) and 0 being completely negative (0%). Thus, the researcher who wants to be 95% sure about the outcome of their study is willing to be wrong about the result 5% of the time. The alpha is the decimal expression of how much they are ready to be incorrect. For the current example, the alpha is 0.05. The level of uncertainty the researcher is willing to accept (alpha or significance level) is 0.05, or a 5% chance they are incorrect about the study's outcome.

Now, the researcher can perform the research. In this example, a prospective randomized controlled study is conducted in which the researcher gives some individuals the new medication and others a placebo. The researcher then evaluates the blood pressure of both groups after a specified time and performs a statistical analysis of the results to obtain a P value (probability value). Several different tests can be performed depending on the type of variable being studied and the number of subjects. The exact test is outside the scope of this review, but the output would be a P value. Using the correct statistical analysis tool when calculating the P value is imperative. If the researchers use the wrong test, the P value will not be accurate, and this result can mislead the researcher. A P value is a probability under a specified statistical model that a statistical summary of the data (eg, the sample mean difference between 2 compared groups) would be equal to or more extreme than its observed value.

In this example, the researcher hypothetically found blood pressure tended to decrease after taking the new medication, with an average decrease of 15 mm Hg in the group taking the new medication. The researcher then used the help of their statistician to perform the correct analysis and arrived at a P value of 0.02 for a decrease in blood pressure in those taking the new medication versus those not taking the new medication. This researcher now has the 3 required pieces of information to look at statistical significance: the null hypothesis, the significance level, and the P value.

The researcher can finally assess the statistical significance of the new medication. A study result is statistically significant if the P value of the data analysis is less than the prespecified alpha (significance level). In this example, the P value is 0.02, which is less than the prespecified alpha of 0.05, so the researcher rejects the null hypothesis, which has been determined within the predetermined confidence level to be disproven, and accepts the hypothesis, thus concluding there is statistical significance for the finding that the new medication lowers blood pressure.

What does this mean? The P value is not the probability of the null hypothesis itself. It is the probability that, if the study were repeated an infinite number of times, one would expect the findings to be as, or more extreme, than the one calculated in this test. Therefore, the P value of 0.02 would signify that 2% of the infinite tests would find a result at least as extreme as the one in this study. Given that the null hypothesis states that there is no significant change in blood pressure if the patient is or is not taking the new medication, we can assume that this statement is false, as 98% of the infinite studies would find that there was indeed a reduction in blood pressure. However, as the P value implies, there is a chance that this is false, and there truly is no effect of the medication on the blood pressure. However, as the researcher prespecified an acceptable confidence level with an alpha of 0.05, and the P value is 0.02, less than the acceptable alpha of 0.05, the researcher rejects the null hypothesis. By rejecting the null hypothesis, the researcher accepts the alternative hypothesis. The researcher rejects the idea that there is no difference in systolic blood pressure with the new medication and accepts a difference of at least 10 mm Hg in systolic blood pressure when taking the new medication.

If the researcher had prespecified an alpha of 0.01, implying they wanted to be 99% sure the new medication lowered the blood pressure by at least 10 mm Hg, the P value of 0.02 would be more significant than the prespecified alpha of 0.01. The researcher would conclude the study did not reach statistical significance as the P value is equal to or greater than the prespecified alpha. The research would then not be able to reject the null hypothesis.

## Function

A study is statistically significant if the P value is less than the pre-specified alpha. Stated succinctly:

• P value less than a predetermined alpha is considered a statistically significant result
• P value greater than or equal to alpha is not a statistically significant result.

## Issues of Concern

A few issues of concern when looking at statistical significance are evident. These issues include choosing the alpha, statistical analysis method, and clinical significance.

Many current research articles specify an alpha of 0.05 for their significance level. It cannot be stated strongly enough that there is nothing special, mathematical, or certain about picking an alpha of 0.05. Historically, the originators concluded that for many applications, an alpha of 0.05, or a one in 20 chance of being incorrect, was good enough. The researcher must consider what the confidence level should genuinely be for the research question being asked. A smaller alpha, say 0.01, may be more appropriate.

When creating a study, the alpha, or confidence level, should be specified before any intervention or collection of data. It is easy for a researcher to "see what the data shows" and then pick an alpha to give a statistically significant result. Such approaches compromise the data and results as the researcher is more likely to be lax on confidence level selection to obtain a result that looks statistically significant.

A second important issue is selecting the correct statistical analysis method. There are numerous methods for obtaining a P value. The method chosen depends on the type of data, the number of data points, and the question being asked. It is essential to consider these questions during the study design so the statistical analysis can be correctly identified before the research. The statistical analysis method can help determine how to collect the data correctly and the number of data points needed. If the wrong statistical method is used, the results may be meaningless, as an incorrect P value would be calculated.

## Clinical Significance

A key distinction between statistical significance and clinical significance is evident. Statistical significance determines if there is mathematical significance to the analysis of the results. Clinical significance means the difference is vital to the patient and the clinician. This study's statistical significance would be present as the P value was less than the prespecified alpha. The clinical significance would be the 10 mmHg drop in systolic blood pressure.[6]

Two studies can have a similar statistical significance but vastly differ in clinical significance. In a hypothetical example of 2 new chemotherapy agents for treating cancer, Drug A increased survival by at least 10 years with a P value of 0.01 and an alpha for the study of 0.05. Thus, this study has statistical significance (P value less than alpha) and clinical significance (increased survival by 10 years). A second chemotherapy agent, Drug B, increases survival by at least 10 minutes with a P value of 0.01 and alpha for the study of 0.05. The study for Drug B also found statistical significance (P value less than alpha) but no clinical significance (a 10-minute increase in life expectancy is not clinically significant). In a separate study, those taking Drug A lived an average of 8 years after starting the medication versus living for only 2 more years for those not taking Drug A, with a P value of 0.08 and alpha for this second study of Drug A of 0.05. In this second study of Drug A, there is no statistical significance (P value greater than or equal to alpha).

## Enhancing Healthcare Team Outcomes

Each healthcare team member needs a basic understanding of statistical significance. All members of the care continuum, including nurses, physicians, advanced practitioners, social workers, and pharmacists, peruse copious literature and consider conclusions based on statistical significance. Suppose team members do not have a cohesive and harmonious understanding of the statistical significance and its implications for research studies and findings. In that case, various members may draw opposing conclusions from the same research.

## References

1.
Hayat MJ. Understanding statistical significance. Nurs Res. 2010 May-Jun;59(3):219-23. [PubMed: 20445438]
2.
Mondal H, Mondal S. Statistical Significance is Prerequisite in Study. J Clin Diagn Res. 2017 Sep;11(9):CL01. [PMC free article: PMC5713722] [PubMed: 29207700]
3.
Heston TF, King JM. Predictive power of statistical significance. World J Methodol. 2017 Dec 26;7(4):112-116. [PMC free article: PMC5746664] [PubMed: 29354483]
4.
Nakagawa S, Cuthill IC. Effect size, confidence interval and statistical significance: a practical guide for biologists. Biol Rev Camb Philos Soc. 2007 Nov;82(4):591-605. [PubMed: 17944619]
5.
Haig BD. Tests of Statistical Significance Made Sound. Educ Psychol Meas. 2017 Jun;77(3):489-506. [PMC free article: PMC5965554] [PubMed: 29795925]
6.
Jiménez-Paneque R. The questioned p value: clinical, practical and statistical significance. Medwave. 2016 Sep 09;16(8):e6534. [PubMed: 27636600]
7.
Mariani AW, Pêgo-Fernandes PM. Statistical significance and clinical significance. Sao Paulo Med J. 2014;132(2):71-2. [PubMed: 24714985]

Disclosure: Steven Tenny declares no relevant financial relationships with ineligible companies.

Disclosure: Ibrahim Abdelgawad declares no relevant financial relationships with ineligible companies.

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Bookshelf ID: NBK459346PMID: 29083828

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