How to proceed Analyze phase? Hypothesis Testing – Part 11 ( Chi Square Test )

Chi Square Test is used to test proportions of > 2 sample data.

Following is a case study to illustrate it’s application.

The process engineer would like to know if different raw material ( type A, B & C ) give significant impact on the Yield. He run the experiment for 3 material types on similar production line. Below is the Yield data collected.


Material A

Material B

Material C









Total inspected




So, the practical question here was “Was there significant difference in Yield among the 3 material type?”

It was then translated to statistical question by means of Hypothesis Statement.

Ho : Null Hypothesis => pA = pB = pC

Ha : Alternate Hypothesis => At least one p is different than another.

Next, conduct Statistical Analysis. In Minitab, click Stat>Tables>Chi Square Test ( Two- way table in one worksheet ) and select relevant information.

image image

Click OK to view the analysis result from Minitab Session window below.

Chi-Square Test: A, B, C


Expected counts are printed below observed counts

Chi-Square contributions are printed below expected counts


           A      B      C  Total

    1     95     93     96    284

       94.67  94.67  94.67

       0.001  0.029  0.019


    2      5      7      4     16

        5.33   5.33   5.33

       0.021  0.521  0.333


Total    100    100    100    300


Chi-Sq = 0.924, DF = 2, P-Value = 0.630


The Pvalue was 0.630. Fail to reject Ho (assuming Alpha risk of 5% i.e. 0.05 )

Statistically, it was to say the material type did not have association with Yield.

Practically, it was concluded that No significant difference in Yield among the 3 material type.


About ssbblky

Six Sigma Professional
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