Saturday, February 9, 2008

Chi-Square Test for Six Sigma

This interesting article addresses some of the key issues regarding Chi-Square Test. A careful reading of this material could make a big difference in how you think about Chi-Square Test.

It's really a good idea to probe a little deeper into the subject of Chi-Square Test. What you learn may give you the confidence you need to venture into new areas.

Chi-Square Test is one of the Six Sigma Tools.The Chi Square Test is a particular statistical test, generally used in Six Sigma methodology. This test comprises three different types of analysis. Those are as follows:
Goodness of fit
Test for Homogeneity
Test of Independence.

The Test for Goodness of fit ascertains if the sample under analysis was drawn from a population that follows some specified distribution. The Test for Homogeneity is conducted to prove the proposition whereby several populations are homogeneous in relation to some characteristic or other. On the other hand, the Test for independence is there to examine the null hypothesis that two criteria of classification, when applied to a population of subjects are independent. If they are not autonomous, then the test aids to make an association between them. Therefore, it is true, that, Chi-Square Test is the most popular distinct data hypothesis testing method.

Overview of the Chi Square Test

Chi Square tests, and contingency tables, are the responsible to answer several question related with Six Sigma methodology. Moreover, the test is used to check whether counts, or proportions, are consistent with some specified population distribution or not. Those frequently asked questions are as follows:

1.Whether the people, who have seen an advertisement, are more likely to purchase a product or not.
2.Whether the people of a particular type under, or over represented, are in a group or not.
3.Lastly, in both these examples, the tests would discover whether the differences could be explained by chance, or whether they indicate that the factor being investigated did affect the result.

Chi-Square Test The Chi-Square 'Goodness of Fit' examination is used to check, if a sample is depicted from a population that conforms to a specified distribution or not. Accordingly, the hypothesis is made as follows:

H0 the sample conforms to the specified distribution
H1 the sample does not conform to the distribution

The test can be explained by the example given below. Suppose, an organization has three categories of employees. They are categorized in 'A', 'B' and 'C'. What is the responsibility of Chi-Square Test is, to collect the following data first:
Category Employees Days Sick
A 100 10
B 60 12
C 40 14
Total 200 36

From the above mentioned data, form the table and though the Chi-Square Contribution 'Days Well' can be calculated.

In case the sample exactly conforms to the distribution, the days kept well and days kept sick would be shared out as shown in the expected column. Afterwards, the chi-square statistics are calculated by summing up chi-square contributions from each category: Where:

Ai actual value for category 'i'
Ei expected value for category 'i'

The freedom is in two degrees. The critical p-value is obtained from the tables, or the p-value can simply be calculated using Excel.

Contingency Tables
The Contingency Table is actually an application of chi-square test used specially when a relation is between two variables. For instance, if the organization decides to find out if there is any relationship between employees taking sick leave, and those taking full entitlement of annual leave, the hypothesis is:

H0 there is no relationship between taking leave and propensity for sickness
H1 there is a relationship between taking leave and sickness

Now that wasn't hard at all, was it? And you've earned a wealth of knowledge, just from taking some time to study an expert's word on Chi-Square Test.

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