# Z Value Calculation Two Sample T Test

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- June 15, 2005 at 10:58 am #39719
Hello, Everybody,

My name is Frank and I am doing one GB project for my customer now. Some questions need expert to help clarify.Thanks in advance!

My data is continous data and have lower specific limits. I did normality test before doing process capabity analysis.Confirmed that the data is not normal distributed. I also tried to transfer the data through box-cox, but failed. Because my data includes positive data, 0 and negative data.

Question1: Can I transfer data through other tools?

if not, I have to take the data as defective data to calculate base capability, right?

My improved process data are available now. They are positive and normal distribute. To compare before and after process difference, I have below questions:

1.Can I use two sample T test to compare the before and after process mean? (before process data: not normal distribution. After process data: normal distribution)

2. If can not use T sample T test, I have to use Chi-Square, right?

Many Thanks and Best RegardsFrank0June 15, 2005 at 11:12 am #121439Frank,

People being taught to transform non normal without an understanding of why is wrong. that said, when dealing with 0 and negative values, you have to do a transform of your own before using a box cox type utility. Just add barely enough to every value to make all vallues positive. For example if your lowest value is -9, add 10 to all values. Box Cox is nothing magic, it is just taking all values to a power greater than 1 to extend the right side of a distribution that is skewed left or taking all values to a power less than 1 to pull in the right side of a distribution that is skewed right. If you look at a histogram of your untransformed data and is a somewhat smooth distribution but either skewed left or skewed right, you have a very good posibility of transformation. Otherwise, you are wasting your time.

An example of this is the famous “shift”. Taken to its extreme a normal distribution that is constantly shifting will never transform and looks almost like a uniform distribution. Look at the picture and make sense of it. There is more information in a non normal distribution that will not transform than there is in one that will.

For analysis, do histograms of the before and after on both the same x and same y scale. Look at the pictures and you will know if you have an improvment. You will also know how to defend your conclusion, You don’t need no stinking t-test.0June 15, 2005 at 12:30 pm #121445Stan, thanks a lot for the help.

Let’s asssuming scenario as this: lowest negative value -9, my project lower specific limit is 5. To calculate Z value I need to do below:

1. Add 10 to my all data to transform data to be positive

2. Box Cox transform data to normal distribution….. transformed data available.

3. Use step 2 transformed data to calculate Z value.

Question: because I add 10 to transform my original data to be positive. When performing step 3, what is my lower specific limit? still 5, or 15 (5+10)?

You are right Histogram is another tool to compare before and after process. Still curious if I can use two sample T test? If yes, my after process data are all positive and normal distribute. I need to compare my new data to step 2 transformed dat, right?

P value is really a good sign to show statistical difference.0June 15, 2005 at 12:45 pm #121447Transformed spec is 15 and when you do the Box Cox apply the very same transform to the spec of 15.

To fully answer your question of the t test, I would really like to see the histogram of the non normal data. Most of the time, you will wind up overestimating Standard Deviation with the non normal so your risk with two sample t is not finding a difference if one exists. If the t test says there is a difference, you are safe. It’s no difference you need to worry about.

0June 15, 2005 at 1:16 pm #121453Got it! Will do both histogram and T test to see the difference. Really appreciate your help. :o)

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