# Statistical Significance: Definition, Levels & Critical Regions

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• 0:06 Definition
• 1:53 P-Value
• 3:19 Critical Regions
• 4:52 Error
• 6:13 Lesson Summary
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Lesson Transcript
Instructor: Devin Kowalczyk

Devin has taught psychology and has a master's degree in clinical forensic psychology. He is working on his PhD.

This lesson explores the basic principle of statistical significance and why it is important to understand when performing nearly any statistical test.

## Definition

There was a big hubbub some years ago that accused vaccines of causing autism. (Vaccines are a weak form of an infection given to people to prevent them from getting the full infection. Autism is a pervasive developmental disorder that is characterized by difficulties with socializing and communication, and it is believed to affect over 1 in 100 people.) This is, of course, ridiculous since it has been found that the brain structure of those with autism is different than those of other people. No simple shot could alter a person's brain like that. However, some people still didn't know this and freaked out.

My reason for bringing this up is to show you how understanding significance tests, along with your statistical tests, is necessary. Statistically significant means the relationship in the results did not occur by random chance. Most researchers work with samples, defined as a section of the population. A population is defined as the complete collection to be studied. Since a researcher is not looking at everyone, there is a possibility that they will collect, by accident, a sample that will lead them to erroneous conclusions. To avoid this, nearly all statistical tests look for statistical significance.

Using our autism and vaccine example, after several tests had been conducted, the researchers found that there was no relationship. They could make this assertion with confidence because their results were statistically significant despite using a sample. So, even though they didn't test every person who had a vaccine, the researchers found no relationship between those who had the vaccine and those who were diagnosed with autism.

## P-Value

When you run a statistical test, you will compute a p-value, which is defined as the significance level value. This value will be represented by a decimal, anywhere between 1.0 to below .01. This value will inform you how likely the null hypothesis, or the prediction that there is no relationship, is true.

The commonly accepted level of the p-value for the relationship to be statistically significant is .05. This means that 1 in 20 times your results will be positive despite there being no actual relationship. In our autism example, there will be some studies that find significant connections between autism and vaccines. This means that 1 in 20 times the results will be positive based on pure probability and not because there is a statistical relationship.

Where does this .05 come from? What is the p-value? It is derived from looking at the bell curve and examining the strength of the relationship and the likelihood that there is no relationship. Back to our autism/vaccine example - if I were to make up some of the p-values, they might be .03, .001, and .5. I listed three, and they are all made up. The first two, .03 and .001, would be statistically significant. The .5 would not be statistically significant.

## Critical Regions

Statistical significance comes from the bell curve. In a statistical test, you are looking to see if there is a relationship between the numbers. This relationship can be in the form of scores being similar, like a correlation, or different, like a t-test. When testing for significance, you are testing your data to see if your value falls in the critical region, defined as the statistical value that will allow you to reject the null hypothesis.

What this means is when you perform a statistical test, you will end up with a p-value. If the number falls in the critical regions area, then your relationship is statistically significant, and you are able to reject the null hypothesis. This is because in the critical regions, you are testing to see if the relationship between your scores is strong enough. If the relationship is weak, then your score will fall in the null hypothesis area and not be statistically significant.

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