Selecting the appropriate comparison test can be challenging especially in the learning stages. A Six Sigma project manager should understand the formulas and computations within the commonly applied tests.
In hypothesis testing, samples represents a small subset of the population which are used to infer conclusions about the population. There is 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:
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.
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
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.
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.
A minimum detectable difference, δ, can also be specified. This detectable difference is used to examine a desired difference among:
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.
To simplify the 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 characteristics:
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:
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
HA = eating carrots and eyesight are dependent
There are ways to improve results such as being more specific with testing such as 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.
This module in PowerPoint 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.
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Green Belt Program (1,000+ Slides)
Cause & Effect Matrix
Central Limit Theorem
1-Way Anova Test
Correlation and Regression