## What Is Statistical Significance?

Statistical significance is a determination made by an analyst that the results in the data are not explainable by chance alone. Statistical hypothesis testing is the method by which the analyst makes this determination. This test provides a p-value, 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.
- Statistical significance is used to provide evidence concerning the plausibility of the null hypothesis, which hypothesizes that there is 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.
- Generally, a p-value of 5% or lower is considered statistically significant.

#### Statistically Significant

## Understanding Statistical Significance

Statistical significance is a determination about the null hypothesis, which suggests that the results are due to chance alone. A data set provides statistical significance when the p-value is sufficiently small.

When the p-value is large, then the results in the data are explainable by chance alone, and the data are deemed consistent with (while not proving) the null hypothesis.

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

Statistical significance is often used for new pharmaceutical drug trials, to test vaccines, and in the study of pathology for effectiveness testing and to inform investors on how successful the 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 prior to the company's failure with those after to see if there is 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) is not unusual under the chance-only explanation. Thus, the data did not provide compelling evidence of advance knowledge of the failure. On the other hand, if the p-value were 0.01% (much less than 5%), then the observed difference would be very unusual under the chance-only explanation. In this case, Alex may decide to reject the null hypothesis and to investigate further 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 on how successful the company is at releasing new products.

Say, for example, a pharmaceutical leader in diabetes medication reported that there was a statistically significant reduction in type 1 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 type 1 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 the data is statistically significant. In other words, whether or not the phenomenon can be explained as a byproduct of chance alone. Statistical significance is a determination about the null hypothesis, which posits that the results are due to chance alone. The rejection of the null hypothesis is needed 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. When the p-value is sufficiently small (e.g., 5% or less), then the results are not easily explained by chance alone and the null hypothesis can be rejected. When the p-value is large, then the results in the data are explainable by chance alone, and the data is deemed consistent with (while 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 on how successful the company is at releasing new products. Stock prices of pharmaceutical companies are often affected strongly by announcements of the statistical significance of their new products.