# Conversion Tables

Select the links below to see commonly referenced tables. Within the links are explanations and examples of how to apply them.

## Z-distribution (Normal Distribution Table)

The tables assumes the data set is normally distributed and the process is stable.

## t-distribution

t-Distribution: Critical values from the t-Distribution

For the t-distribution, dF = n-1, represents the degrees of freedom. If you have 29 samples, then dF = 28.

The t-distribution is used instead of the z-distribution (standard normal distribution) when the:

• Population standard deviation is unknown
• Population is normally distributed

The t-distribution is a series of distributions, a unique distribution exist for each sample size. As the sample size increases it becomes taller and narrower and exhibits more characteristics of the normal curve. Generally applied with sample sizes <30.

## F-distribution

NIST table with the most common levels of significance and degrees of freedom.

## Chi-Squared distribution

The Chi-square distribution is most often used in many cases for the critical regions for hypothesis tests and in determining confidence intervals.

1) Chi-square test for independence in an "Row x Column" contingency table

2) Chi-square test to determine if the standard deviation of a population is equal to a specified value.

BE CAREFUL when using tables, there are many varieties out there and all can be correct but only when used and interpreted correctly. Some tables are for one-tailed test and others cover two-tailed test.

### Short Term Sigma Conversion Table ## Statistical Evaluation Tools ### Long Term Sigma / PPM / Cpk Table

The conversion table below is similar to the one above but lets discuss the differences.

It is very important to remember that DPMO and PPM may or may not be the same.

Lets use an exaggerated example to try an illustrate a point.

If ONE part has 1,000,000 opportunities for a defect, and one defect is found that makes the entire PART a defective PART.

So it is possible that you could have 1 PPM with a DPMO of 0.000001.

Also, Cpk is estimated from the sigma level and it isn't always an exact match since the Cpk calculation takes the better of the USL or LSL and doesn't consider the tail of the opposite tail.

It is most important to understand the basic relationships and memorize the most common levels of sigma, Cpk, and yield for normal distributions.

Also, if a process is CENTERED, then Cp = Cpk. Link to the new Six Sigma material

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