Vol. 8, No. 6

June 2006

PQ Systems
 
Contents

In-depth on dashboards

Quality Quiz: With a video!

Six Sigma

Data in everyday life

Bytes and pieces

FYI: Current releases

 

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Software

 

   

Quality Quiz from Professor Cleary

Congratulations:
"Yes" is correct.

Click here for a more complete video explanation

Walker Runn was actually right this time with his guess about Type I error. Of course he will be expecting a promotion.

Walker actually did a two-way analysis of variance. The two factors he considered were plant and shift. This type of analysis answers three questions:

1. Is there a significant difference among outputs in the three plants?

2. Is there a significant difference between outputs of the day and night shifts?

3. Are there combinations of shift and plant that are significantly different from other combinations?

Walker was looking at the second question above, whether significance differences emerged in the two shifts. The data below demonstrates that the day shift average is 8.9 and the night shift average is 13.7.

Of course, these numbers are different from one another, but hypothesis testing will indicate whether that difference is statistically significant and make a statement about one's confidence in the conclusion. The steps in hypothesis testing are:

Step 1:

Interpretation for H0: The day shift and the night shift produce the same amount of output. This is a null hypothesis.

Step 2:

Interpretation : An alpha value of .01 suggests a willingness to accept a 1 percent chance of rejecting the null when it is actually true. This is known as a Type I error.

(Note: Walker continues to confuse the alpha value with a famous Italian car, such as the one that is garaged in the PQ Systems basement. See the photo below of my other Alfa.)

Step 3:

Calculate the statistical F value to test this hypothesis:

Walker uses DOEpack EZ, so he does not require a calculator. As indicated, the F value for shift is 38.52.

Step 4:

Compare the calculated F value to the tabular F value, found in any statistics textbook.

For this case, the tabular F value is 9.33. Since the calculated F is greater than the tabular F value, the null that the output of the day and night shifts is the same can be rejected. The figure below illustrates this:

A second way to answer this question is to explain what the P-value of <0.001 means. Walker correctly saw this as a probability of a Type I error. In that this is smaller than the alpha value of .01 chosen in Step 2, you would conclude that the null that the day and night shifts produce the same outputs can be rejected.

Stay tuned to see what guesses Walker Runn makes next month.

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