# Statistical Significance: What It Is, How It Works, and Examples

> **Definition**
>
> Statistical significance is a determination that a relationship between two or more variables is caused by something other than chance.

## What Is Statistical Significance?

Statistical significance is a determination made by an analyst that the results in data aren't explainable by chance alone. An analyst makes this determination by using statistical [hypothesis testing](https://www.investopedia.com/terms/h/hypothesistesting.asp). The test provides a [p-value](https://www.investopedia.com/terms/p/p-value.asp), which is the probability of observing results as extreme as those in the data assuming the results are truly due to chance alone.

A p-value of 5% or lower is often considered to be statistically significant.

### Key Takeaways

*   Statistical significance is a determination that a relationship between two or more variables is caused by something other than chance.
*   It's used to provide evidence concerning the plausibility of the null hypothesis that hypothesizes that there's nothing more than random chance at work in the data.
*   Statistical hypothesis testing is used to determine whether the result of a data set is statistically significant.
*   A p-value of 5% or lower is generally considered statistically significant.

![Statistical Significance: A determination made by an analyst that the results in the data are not explainable by chance alone.](https://www.investopedia.com/thmb/Fxbn5Ahjyq9-mVgoQ0WjPsUhAQM=/1500x0/filters:no_upscale():max_bytes(150000):strip_icc()/StatSignificance_Final_4188628-592d4b5107e6473bacab46e107bfdfd3.jpg)

*— Investopedia / Paige McLaughlin*

## Understanding Statistical Significance

Statistical significance is a determination of the [null hypothesis](https://www.investopedia.com/terms/n/null_hypothesis.asp), which suggests that the results are due to chance alone. A data set provides statistical significance when the p-value is sufficiently small.

The results in the data are explainable by chance alone when the p-value is large and the data are deemed consistent with the null hypothesis (although they don't prove it).

The results aren't easily explained by chance alone when the p-value is sufficiently small, typically 5% or less, and the data are deemed inconsistent with the null hypothesis. In this case, the null hypothesis of chance alone is rejected as an explanation of the data in favor of a more systematic explanation.

> **Important**
>
> Statistical significance is often used for new pharmaceutical drug trials, to test vaccines, and in the study of pathology for effectiveness testing. It can inform investors on how successful a company is at releasing new products.

## Examples of Statistical Significance

Suppose Alex, a financial analyst, is curious as to whether some investors had advance knowledge of a company's sudden failure. Alex decides to compare the average of [daily market returns](https://www.investopedia.com/terms/i/intraday-return.asp) before the company's failure with those after to see if there's a statistically significant difference between the two averages.

The study's p-value was 28% (>5%), indicating that a difference as large as the observed (-0.0033 to +0.0007) isn't unusual under the chance-only explanation. The data therefore didn't provide compelling evidence of advance knowledge of the failure.

The observed difference would be very unusual under the chance-only explanation if the p-value was 0.01%, much less than 5%. Alex might decide to reject the null hypothesis in this case and further investigate whether some traders had advance knowledge.

Statistical significance is also used to test new medical products including drugs, devices, and vaccines. Publicly available reports of statistical significance also inform investors about how successful a company is at releasing new products.

Suppose a pharmaceutical leader in diabetes medications reported that there was a statistically significant reduction in diabetes when it tested its new insulin. The test consisted of 26 weeks of randomized therapy among diabetes patients and the data gave a p-value of 4%. This signifies to investors and regulatory agencies that the data show a statistically significant reduction in diabetes.

Stock prices of pharmaceutical companies are often affected by announcements of the statistical significance of their new products.  

## How Is Statistical Significance Determined?

Statistical hypothesis testing is used to determine whether data is statistically significant and whether a phenomenon can be explained as a byproduct of chance alone. Statistical significance is a determination of the null hypothesis which posits that the results are due to chance alone. The rejection of the null hypothesis is necessary for the data to be deemed statistically significant.

## What Is P-Value?

A p-value is a measure of the probability that an observed difference could have occurred just by random chance. The results are not easily explained by chance alone and the null hypothesis can be rejected when the p-value is sufficiently small—5% or less. When the p-value is greater than 5%, the results in the data are explainable by chance alone and the data is deemed consistent, proving the null hypothesis.

## How Is Statistical Significance Used?

Statistical significance is often used to test the effectiveness of new medical products, including drugs, devices, and vaccines. Publicly available reports of statistical significance also inform investors as to how successfully a company releases new products. Stock prices of pharmaceutical companies are often affected strongly by announcements of the statistical significance of their new products.

## The Bottom Line

Statistical significance is a result of hypothesis testing that arrives at a p-value or likelihood that two or more variables are caused by something other than chance. A 5% p-value tends to be the dividing line. The lower the value, the more statistically significant the result of the data set is considered to be.

This form of testing is frequently used to assess pharmaceutical drug trials but it can be helpful for investors as well, particularly those who want to assess a company that’s releasing a new product.

> **Article Sources**
>
> 1.  Steven Tenny and Ibrahim Abdelgawad. "[Statistical Significance](https://www.ncbi.nlm.nih.gov/books/NBK459346/)." StatPearls Publishing, 2023.
>     
> 2.  American Diabetes Association. "[Efficacy and Safety of Fast-Acting Aspart Compared With Insulin Aspart, Both in Combination With Insulin Degludec, in Children and Adolescents With Type 1 Diabetes: The Onset 7 Trial](https://care.diabetesjournals.org/content/42/7/1255)."
>     
> 3.  Hwang, Thomas J. "[Stock Market Returns and Clinical Trial Results of Investigational Compounds: An Event Study Analysis of Large Biopharmaceutical Companies](https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3737210/)." _PLoS One_, vol. 8. no. 8, August 2013.
>     
> 4.  Rothenstein, Jeffrey, et al. "[Company Stock Prices Before and After Public Announcements Related to Oncology Drugs](https://academic.oup.com/jnci/article/103/20/1507/904625)." _Journal of the National Cancer Institute,_ vol. 103, no. 20, October 2011, pp. 1507-1512.