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

  1. State null and alternative hypothesis
  1. Set confidence level for alpha
  1. Decide hypothesis test that is going to be used
  1. Decide whether sample size is fixed or can be selected based on beta setting
  1. Run test in Minitab
  1. Interpret p-value against alpha setting
  1. 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