Chapter 21 Hypothesis Testing
Hypothesis Test Basics: Testing covers three categories: testing whether the data you have fits the data model, comparing a statistic to a hypothesis about the data or population, and answering questions about whether something changed within the data
The type of data you have follows same guidelines: you begin with a statistic or criteria that you compute from sample data, you create a null and an alternate hypothesis, statistic or criteria compared again a reference criteria , and how the calculated stats compare to reference criteria whether you accept or reject the alternative hypothesis
Null Versus Alternative
Hypothesis tests: have a Null and alternative hypothesis
The null hypothesis is abbreviated as Ho and is a statement that refelects no effect or no difference
The alternative hypothesis is written as Ha and is a statement that is likely to be true if the null hypothesis is not true, typicall written as not equals, a greater than or less than statement, the mean of the new process is greater than the mean of the old process
The Risk of Hypothesis Testing Error
Type 1: Null hypothesis rejected when true, aka producer risk, probability of risk is measured by alpha where a is between 0 and 1
Type 2: Null hypothesis accepted when false, aka consumer risk, probability of risk if measured by beta where B is between 0 and 1
most common confidence level is used as 95% or a=.05
Selecting the Right Hypothesis Test
when selecting hypothesis test know: what type of data you have, number of levels of interest for input, distribution of data, what you are testing
Hypothesis Tests for Discrete Data
1-Proportion Test: used when there is one factor of x, one level of interest for x, comparing proportions
2-Proportion Test: used when one factor of x, two levels of intesrest for x, used when comparing proportions between samples of samples and a target
Hypothesis Tests for Continuous Normal Data
1-Sample T Test (Paired T-Test): used when comparing means, used when dealing with smaller samples or when standard deviation is known, compares mean of sample to target mean, compares mean of sample against mean of another sample for same factor of x
Chi Square Test (1-Variance Test): used when comparing standard deviation or variance, compares standard deviation or variation between two samples of same factor of x
2-Sample T Test: used when comparing means, compares means between two samples of different factors of x, requires noticing whether equal variances between two samples are assumed or not
Hypothesis Tests for Continuous Non-Normal Data
Chi-Square Test: used to compared standard deviation between sample and hypothesized standard deviation when data is not normal
One Sample Wilcox: used when comparing medians, compares medians between sample and hypothesized sample or a new sample to a previous sample before changes are made, used when data is somewhat symmetrical
Mann-Whitney Test: used when comparing medians, compares medians between samples of two factors of x
Why Run Hypothesis Tests: answer the question of number being statistically different that action can be taken on information
Running Hypothests Tests
- State null and alternative hypothesis
- Set confidence level for alpha
- Decide hypothesis test that is going to be used
- Decide whether sample size is fixed or can be selected based on beta setting
- Run test in Minitab
- Interpret p-value against alpha setting
- Translate statistical analysis in real-world, business-relevant language
Hypothesis Testing in Analyze Improve Control: hypothesis testing found in last 3 stages of DMAIC, mainly found in analyze phase
used in analyze to determine if inputs and factors fould be a root cause
used in improve phase to validate solutions being tested in beta environments or small batches