Z-scores and standard deviation

Z-scores are standard deviations, which are a measure of how many standard deviations away an element is from the mean. A z-score of 0 represents an element equal to the mean, while a score of +2.5 would indicate that the element is 2.5 standard deviations away. These scores can be positive or negative. We can also associate z-scores with confidence levels just like we saw with p-values. A z-score of less than -1.65 or greater than +1.65 equates to a 90% confidence level. A z-score of less than -1.96 or greater than +1.96 gives a confidence level of 95%, and a z-score of less than -2.58 or greater than +2.58 gives a confidence level of 99%:

Typically, the z-scores and p-values are analyzed together. In general, very high or low z-scores plus small p-values will allow us to consider rejecting the null hypothesis:

Rejecting the null hypothesis requires a subject judgment. You must determine what degree of risk you are willing to accept for being wrong. Before the pattern analysis tool is run, you will want to select a confidence value and not reject the null hypothesis unless the output matches or exceeds the confidence value. Typical confidence values include 90%, 95%, and 99% with 99% being the most conservative. In other words, if you selected a 99% confidence level, you would not reject the null hypothesis unless the probability that the pattern was created by random chance is less than 1%.