Chi-square Analysis For Attribute Data
Chi-square Analysis For Attribute Data
What Is A ChiSquare Test?
The probability density curve of a chisquare distribution is asymmetric curve stretching over the positive side of the line and having a long right tail.
The form of the curve depends on the value of the degrees of freedom.
Types of ChiSquare Analysis:
Chisquare Test for Association is a nonparametric therefore can be used for nominal data test of statistical significance widely used bivariate tabular association analysis.
Typically the hypothesis is whether or not two different populations are different enough in some characteristic or aspect of their behavior based on two random samples.
This test procedure is also known as the Pearson chisquare test.
Chisquare Goodnessoffit Test is used to test if an observed distribution conforms to any particular distribution. Calculation of this goodness of fit test is by comparison of observed data with data expected based on the particular distribution.
When to apply a ChiSquared Test:
ChiSquared test is used to determine if there is a statistically significant difference in the proportions for different groups. To accomplish this it breaks all outcomes into groups.
What the ChiSquared Test does:
It starts by determining how many defects for example would be expected in each group involved.
It does this by assuming that all groups have the same defect rate which Minitab approximates from the data provided.
Minitab then compares the expected counts with what was actually observed.
If the numbers are different by a large enough amount ChiSquare determines that the groups do not have the same proportion.
ChiSquare Requirements:
Data is typically attribute discrete. At the very least all data must be able to be categorized as being in some category or another.
Expected cell counts should not be low definitely not less than 1 and preferable not less than 5 as this could lead to a false positive indication that there is a difference when in fact none exists.
ChiSquare Hypotheses:
Ho: The null hypotheses PValue > 0.05 means the populations have the same proportions.
Ha: The alternate hypotheses PValue <= 0.05 means the populations do NOT have the same proportions.
Note: if the expected cell counts are below 5 Minitab will print a warning. The warning is generated because of the fact that with the expected count in the denominator a small value potentially creates an artificially large chisquare statistic. This is particularly troublesome if more than 20 of the cells have expected counts less than 5 and the contribution to the overall chisquare statistic is considerable.
Additionally if any of the expected cell counts are below 1 Minitab will not even produce a pvalue since the chisquare statistic is sure to be artificially inflated. In either of these cases the binomial distribution Minitab: Stat/ ANOVA/ Analysis of Means may be able to be used.
Lastly: Attribute Gage RR ARR or Kappa Test is needed with an acceptable level of measurement system error prior to running a ChiSquare Analysis
Tips:
Determine the subgroups and categories to be tested for variation differences in proportions as part of your data collection plan.
Define the operational definitions for success/defect the stratifications layers subgroups and the Cause Effect diagram fishbone to predetermine where the team believes differences in proportions may exist.
Continuous Variable data can usually be converted into Discrete Attribute data by using categories
Example: cycle time continuous 1 hr 1.5 hr 2 hr can be categorized into Cycle Time Met = 1 where success is cycle time 8 hrs.
Tricks
An MSA Attribute RR Kappa Analysis for discrete data or Gage RR for continuous variable data is used prior to calculating the ChiSquare Test to ensure that the measurement variation 10 then the variation you will see in the Chi Square Test is not valid as too much of the variation seen is coming from your measurement system 10 MSA error and not your process variation.
About the writer: Steven Bonacorsi is a Senior Master Black Belt instructor and coach. Steven Bonacorsi has trained hundreds of Master Black Belts Black Belts Green Belts and Project Sponsors and Excutive Leaders in Lean Six Sigma DMAIC and Design for Lean Six Sigma process improvement methodologies.
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