# Effect of insignificant p-value on capability calculation?

#### Cailin

##### New Member
Hi,

I have a coworker who analyzed a data set with the goal of generating it's Cpk. Because the data set p-value was less than .05 for all calculated distributions and transformations, he selected a transform based on AD value and continued with the calculation. Understanding that the more appropriate next step would be to take a closer look at the data set and re-evaluate the analysis (might be binomial, etc.), mathematically what effect would the insignificant p-value have on the Cpk calculated? Does it invalidate the result?

Thank you!

#### hlsmith

##### Omega Contributor
Cpk = ?

I am guessing sample size is going to come into play with your question.

#### Cailin

##### New Member
Yes, it likely does. Most of the data sets he's looking at have 80-150 data points, which is low for capability.

For the one I'm currently looking at, the AD value was reported around 3 and the corresponding Cpk was .77. There are several data sets he used this same method on, all are similar to those values though the histograms themselves tell a variety of different stories. Some data sets are skewed, some bimodal.

Does having a particular level AD value negate the need for a significant p value? I'm not very familiar with using AD.

Cpk = ?

I am guessing sample size is going to come into play with your question.

#### hlsmith

##### Omega Contributor
Cpk = ?

Can you define these acronyms? Thanks.

#### Miner

##### TS Contributor
Cpk = ?

Can you define these acronyms? Thanks.
Cpk is a capability index. The lower of upper spec limit - mean or mean - lower spec limit divided by 3 * StDev.
AD is the Anderson Darling test statistic.

#### Miner

##### TS Contributor
Does having a particular level AD value negate the need for a significant p value? I'm not very familiar with using AD.
No. The AD test statistic has a distribution with a corresponding p-value. This is similar to the t distribution or F distribution having associate p-values.

If you have bimodal distributions, you probably have data from a process mixture, or an unstable process. In that case, the Cpk is irrelevant and meaningless as it assumes a single, stable process stream.