# Hypothesis Testing

Hypothesis testing and selecting the correct test can be challenging especially in the learning stages. A Six Sigma project manager should understand the formulas and computations within the most commonly applied tests.

In hypothesis testing, samples represent a subset of the population which are used to infer conclusions about the population. There's always a chance or risk (known as alpha-risk and beta-risk) that the selected sample is not representative of the population and one could infer the incorrect conclusion. Assumptions are inferred that allows the estimation of the probability (known as p-value) of getting a wrong conclusion.

Statistical software has simplified the work to the point where comprehension of these tests is convenient to overlook.

CAUTION: A statistical difference doesn't always imply a practical difference, numbers don't always reflect reality.

Parametric Tests are used when:

Nonparametric tests are used when:

• The above criteria are not met or if distribution is unknown
• These test are used when analyzing nominal or ordinal data
• Nonparametric test can also analyze interval or ratio data

In general, the power of standard parametric tests are greater than the power of the alternative nonparametric test. As the sample size increases and becomes very large the power of the nonparametric test approaches its parametric alternative.

Nonparametric tests also assume that the underlying distributions are symmetric but not necessarily normal. When the choice exist on whether to use the parametric or nonparametric, if the distribution is fairly symmetric, the standard parametric tests are better choices than the nonparametric alternatives.

### Comparison of Means using Parametric Tests Six-Sigma-Material.com

### Comparison of Variances

For 1 sample: Use Chi-square

For 2 samples: Use the F-Test or ANOVA for >2 variances. The F-test assumes the data is normal.

Levene's test is an option to compare variances of non-parametric data.

For >2 samples: Use Bartlett's Test for parametric data and Levene's Test for nonparametric data

## Hypothesis Testing Steps

1. Define the Problem
2. State the Objectives
3. Establish the Hypothesis (left-tailed, right-tailed, or two tailed test).
4. State the Null Hypothesis (HO)
5. State the Alternative Hypothesis (HA)
6. Select the appropriate statistical test
7. State the alpha-risk (α) level
8. State the beta-risk (β) level
9. Establish the Effect Size
10. Create Sampling Plan, determine sample size
11. Gather samples
12. Collect and record data
13. Calculate the test statistic
14. Determine the p-value

If p-value < α, reject Ho and accept HA

If p-value > α, fail to reject the Null, HO

Try to re-run the test (if practical) to further confirm results. The next step is to take the statistical results and translate it to a practical solution.

It is also possible to determine the critical value of the test and use to calculated test statistic to determine the results. Either way, using the p-value approach or critical value should provide the same result.

### Statistical Power

The statistical power is 1 minus the beta-risk chosen. Usually the beta-risk is between 10-20% so Power typically range from 80-90%.

This is the likelihood of finding an effect when there is actually an effect. This is the chance of rejecting the null hypothesis when the null hypothesis is actually false. ### Detectable Difference (δ)

A minimum detectable difference, δ, can also be specified. This detectable difference is used to examine a desired difference among:

• Target (or given) value and a sample mean - using 1 sample t test
• Two sample means - using Paired t or 2 sample t tests
• > 2 sample means in ANOVA
• Target (or given) value and a sample proportion
• Two proportions

### Sensitivity

The minimum detectable difference desired relative to the standard deviation is the sensitivity of the test. It is the size of the difference expressed in standard deviations.

Similar to the Coefficient of Variation in that the mean is expressed as relative magnitude in standard deviations. The numerator itself doesn't provide much information, it is when it (or the δ) are expressed in terms of standard deviations are you able to compare two or more values with more meaning. ## Create a Visual Aid of the Test

To simplify the testing process, break down the process into four small steps.

Create a table similar to the one below and begin by completing the top two quadrants. The bottom-left contains the results from the test and then converting those numbers into meaning is the practical result which belongs in the bottom-right quadrant.

## Null Hypothesis & Alternative Hypothesis

Null Hypothesis characteristics:

• Denoted as "HO"
• Assumed to be true until proven otherwise
• Represents "no difference" or "no change"
• Factor is not statistically significant
• Population follows a normal distribution
• Variation is from random, inherent sources.

This is the hypothesis being tested or the claim being tested. The null hypothesis is either "rejected" or "failed to reject". Rejecting the null hypothesis means accepting the alternative hypothesis.

The null hypothesis is valid until it is proven wrong. The burden of truth rest with the alternative hypothesis. This is done by collecting data and using statistics with a specified amount of certainty. The more samples of data usually equates as more evidence and reduces the risk of an improper decision.

The null hypothesis is never accepted, it can be "failed to reject" due to lack of evidence, just as a defendant is not proven guilty due to lack of evidence. The defendant is not necessarily innocent but is determined (based on the evidence) "not guilty".

There is simply not enough evidence and the decision is made that no change exists so the defendant started the trial as not guilty and leaves the trial not guilty.

Alternative Hypothesis characteristics:

• Denoted as "HA"
• Has the burden of proof
• Represents "a difference" or "a change"
• Factor is statistically significant
• Population does not follow a normal distribution
• Variation is from non-random sources.

## Examples of Testing Claims

The shape of a distribution is normally distributed

Ho = Data is Normal

HA = Data is not Normal

There is a relationship between sales of a toy and placing it on the ends of aisles

HO: Slope = 0

HA: Slope does not equal 0

Supplier ABC’s Part # 34565 weight is not the same as Supplier XYZ’s

Ho= Mean ABC = Mean XYZ

HA =Mean ABC does not equal the Mean XYZ

People that eat carrots have better eyesight

Ho = eating carrots and eyesight are independent

H = eating carrots and eyesight are dependent

Running more tests allows you to hone in on the differences and conclude more information that can lead to more effective improvements. There are ways to improve the accuracy of results such as being more specific with testing.

For example, testing for specific numerical differences or looking for differences (or lack of) within a gender, a region, an industry, an age group, a religion, an affiliation, or combination of them.

If you detect a change from large group of people from another that is helpful.....but what about more detail?

Therefore, if possible, test the data by gender, by age group, by hair color, by religion, by political party affiliation, by region, etc. You will begin to identify more meaningful information and generate new discussion.

## Selecting the Hypothesis Test

Several hypothesis test flowcharts are available to subscibers at no additional charge along with other free downloads and tools to help a Green Belt or Black Belt. A couple generic visual aids are shown below.

### If you have One X and One Y variable and...... ### If you have >1 X and One Y variable and......  This module in provides lessons and more detail about commonly used hypothesis tests. This is often a new area of study for those learning about the Six Sigma methodology and represents a significant challenge on certification exams and in real-life application.Click here to purchase the Hypothesis Test module and view others that are available.

## Hypothesis Testing Guide ### Hypothesis Testing on TI-83 or TI-84 Calculator

Continue to the IMPROVE phase

Search active job openings related to Six Sigma

Review Six Sigma certification options

Custom Search

Six Sigma

Templates, Tables & Calculators

Six Sigma Certification Six Sigma Modules

Green Belt Program (1,000+ Slides)

Basic Statistics

SPC

Process Mapping

Capability Studies

MSA

Cause & Effect Matrix

FMEA

Multivariate Analysis

Central Limit Theorem

Confidence Intervals

Hypothesis Testing

T Tests

1-Way Anova Test

Chi-Square Test

Correlation and Regression

Control Plan

Kaizen

Error Proofing

## Need a Gantt Chart? 