Statistical Significance

If the observed p-value is less than alpha (a threshold which is usually 0.05 or 5%), then the results are statistically significant.

Whether or not the result can be called statistically significant depends on the p-value (known as alpha), we establish for significance before we begin the experiment.

Statistical significance is built on a few simple ideas: hypothesis testing, the normal distribution, and p values.

If the observed p-value is less than alpha, then the results are statistically significant. We need to choose alpha before the experiment because if we waited until after, we could just select a number that proves our results are significant no matter what the data shows!

The choice of alpha depends on the situation and the field of study, but the most commonly used value is 0.05, corresponding to a 5% chance the results occurred at random.

From Z-score to P-value

To get from a z-score on the normal distribution to a p-value, we can use a table or any statistical software. The result will show us the probability of a z-score lower than the calculated value. For example, with a z-score of 2, the p-value is 0.977, which means there is only a 2.3% probability we observe a z-score higher than 2 at random (because of random noise).

The percentage of the distribution below a z-score of 2 is 97.7%

Note: In the above example, we are considering all of the left side up to 2 SD to the right side of the mean. Hence, its 50+34.1+13.6 = 97.7

An example statement - There is statistically significant evidence our students get less sleep on average than college students in the US at a significance level of 0.05. The p-value shows, there is a 2.12% chance that our results occurred because of random noise.