A-N-OVA, ANO-VA! (#35)

ANOVA stands for Analysis of Variance and is a statistical approach that observes the variation between two different values. The ANOVA F Ratio is the value you get when you perform a regression analysis to determine if the means between groups of data are statistically significantly different. A Null Hypothesis means that the collected data is likely to happen by chance. If this is correct, your F Value should be 1.0, or extremely close to that number. The further away from 1.0, the less likely that variation is to happen by chance.

Example ANOVA F Ratio:
Skinny Pop makes several different flavors of popped popcorn. Their customers stated that their “Critical to Quality Requirement” is having the smallest amount of popcorn kernels that are un-popped in each bag. We gathered data from four different vendors of Skinny Pop to discover if we can find a variation between the group of vendors ratio of un-popped popcorn kernels.

Hypothesis Test Settings:
Single Variable (Kernel Type)
4 Settings (Different Vendors)
N= Sample Size (25/vendor; 100 total samples)
Degrees of Freedom of Variable= Settings -1 (4-1=3)
Total Degrees of Freedom= N-1 (25-1=24)
Degrees of Freedom of Error= Total Degrees of Freedom – Degrees of Freedom of Variable
(24-3=21)
F-Statistic:
Degrees of Freedom of Variable/Degrees of Freedom of Error= Critical F Statistic (3/21)

Refer to the table at http://www.statsoft.com/textbook/distribution-tables/#f05
This is a table of Critical F- Statistic Values. Our test needs to have a significance value of 0.05 (which is a 95% Confidence); this means that we will only allow for a 5% or less risk of being wrong. The table also states that the Critical F-Statistic Reference value is 3.44. If your calculated F-Value is less than 3.44, we will “accept the Null Hypothesis.”

Null Hypothesis (HO): We have found low statistical difference in the amount of un-popped popcorn kernels between our group of vendors
Alternative Hypothesis (Ha): We have found a statistical difference in the amount of un-popped popcorn kernels between our group of vendors
Alpha: 0.05


The F-Statistic has to be combined with the P-Value in order for you to determine if the results of your testing are significant or not. If your F-Statistic is deemed significant, other variables may or may not be significant. Your F-Statistic may just indicate one variable is different from the others; though the difference may not be significant enough for the Statistical Validity of the testing be questioned. 


About Six Sigma Development Solutions, Inc.
We are Certified as an Accredited Training Organization with the International Association of Six Sigma Certification (IASSC)
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We Provide Onsite Lean Six Sigma Certification Training. Some of the training's we provide are: Lean Six Sigma Black Belt, Lean Six Sigma Green Belt, Lean Six Sigma Yellow Belt, Lean Six Sigma Champions Training and Lean Certifications for Healthcare, Finance, I.T, Manufacturing, Processing, Logistics, Retail Sales and Government.
SSDSI will come to your site to train for your choice of the Lean Six Sigma Certification Levels. Onsite training is more cost effective than open enrollment training when training larger groups of team members.
Benefits of Onsite Training:
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Call Kevin Clay at 214-731-3176 or email at kclay@sixsigmadsi.com for more information

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