Six Sigma Discrete Data Tools

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Discrete Data Tools


The analysis of continuous data is dominated by ANOVA and DOE. Chi-Square and contingency table analysis play an equally important role in the analysis of discrete data.

Six Sigma discrete data tools include cross-tabulation and contingency tables. These list variables and their levels or categories in a matrix form together with the frequency of occurrence in each cell.

A Chi-Square analysis is used to test for independence of the variables and their levels or categories. The degrees of freedom for such an analysis is equal to (number of rows – 1) (number of columns – 1).

Chi-Square is also an extremely powerful tool to test how well measured discrete data fit an assumed distribution.


If product or process yield is measured by discrete data, different conditions can be treated as levels of a variable and a Chi-Square test of Homogeneity performed in a contingency table. Rejection of the null hypothesis implies that different conditions have an effect on process yield.


If discrete data is measured in terms of a proportion, the binomial distribution parameters can be used to calculate the standard deviation and hence confidence interval for a proportion. This can, in turn, be used for a hypothesis test about proportions.

When discrete data are measured in terms of a proportion, the standard deviation can be calculated using the binomial distribution parameters.

Then, providing the values of np and n(1-p) are both greater than five, the confidence on the measured properties can be calculated and interpreted in the usual manner.


Discrete data tools include surveys which are an important source of discrete data for analyses. Such surveys typically have three sections, which deal with demographics, customer CTs, and factors, which can be linked to CTPs. The survey results can be analysed by using cross-tabulation and contingency tables.

If the metric used is defects or Defects Per Unit, the effect on process yield can be calculated. The Chi-Square Goodness of Fit Test is used to decide whether or not discrete data follow an expected or assumed distribution. In such a test the null hypothesis is that the data do follow the distribution.


When a CTX has two or more variables, which are categorical, and each has two or more levels, these categories and levels are cross-tabulated in a table and the cells are populated by the frequency of joint occurrence of the variable/level combinations.

A test of homogeneity checks for independence of variables and levels. If the variables are determined not to be independent then the degree of association can be calculated using the contingency coefficient.

From Six Sigma Discrete Data Tools to Six Sigma Tools.

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