Hypothesis Testing is a statistical tool, that allows the resemblance of two or more process attributes – mean, median and standard deviation. It provides with a method to determine differences.

• Important part of a conclusion reached on the basis of random sampling (statistical inference)
• A hypothesis is a statement that we want to verify using data
• is there are difference?
• has there been a change?
• Null and Alternative hypotheses are formed
• Level of risk and confidence required
• Experimentation is conducted and interpret the results
• Fail to reject the null hypothesis
• No change. No difference, or…
• Reject the null hypothesis
• There is a change, a difference

## What might we “Test” for?

We will be testing for a Change or Difference in Process…

• Central Tendency
• Mean, Median, Mode
• Variation
• Variance, Standard Deviation
• Proportion
• % (ratio, proportion)
• Frequency (of occurrence)
• Distribution of count/frequency

## Testing Protocol

• Null” hypothesis (H0)
• This is a statement validating the status quo – there will be no change of significance observed. Any differences detected are purely due to chance and not a change in the process.
• Symbols:
• = (equals)
• < (not less than)
• > (not greater than)
• Alternative” hypothesis (H1)
• This is a statement that there will be a difference of statistical significance detected, there has been a change.
• Symbols:
• <> (doesn’t equal)
• < (is less than)
• > (is greater than)

The hypotheses are complementary to each other. If one is true, other is not true, and vice versa.

## If the p is low, the null must go!

When performing any statistical test, outcome is based on sampling from population, therefore there is a room for an error. Most statistical tests are run with a 95% confidence level, indicating that there is a 5% chance of making an error.

The decision of whether to simply accept or reject the null hypothesis is predicated on the calculated p value. If the p value is a smaller amount than or adequate to a preassigned significance level (normally set at 5%), then we reject the null hypothesis and accept the alternative.

A p value are going to be calculated by the statistical software when running a hypothesis test.

## Types of Hypothesis Testing

There are many different types of hypothesis tests, they can be divided into two main categories:

• Parametric tests
• Makes inferences about parameters like mean and variance
• Based on assumptions of specific distributions (ex. “normal” or “t” distributions)
• Non-parametric tests
• Makes inferences about frequency distribution like median, distribution type
• Usually include sign and rank tests (type of “math” used)
• Do not require assumptions of normality (but do have some assumptions… always check them!)

Depending on the type of data you have collected, as well if it’s normal or non-normal, there are several hypothesis tests available for comparing process characteristics.