## Wednesday, 31 August 2011

### Discriminant Analysis

Discriminant Analysis is a Predictive method used to determine which continuous variables discriminate between two or more naturally occurring groups. Linear discriminant analysis divide the variables into two groups. For example a researcher may want to find out which people would likely to yes to some particular question and which people would likely to say no to that particular question. Discriminant analysis thus helps to predict the responses of people to that particular question that have missed to answer it. The prediction is done on the basis of various parameters on which the response would be dependent on. Those parameters will be called as independent variables while the answer to the question will be called as dependent variable.

Thus discriminant analysis is a regression analysis when only 2 groups are involved. A transfer function is formed on the basis of dependent and independent variables as shown below:

Y = aX1 + bX2 + c X3 + dX4 + …….. +nXm

Where: Y = output score

X1, X2,X3…Xm = Independent variables

a, b, c ….n = co-efficients of Xs which are actually the weights of various independent variables (or predictor variables)

These co-efficients are also called as standardized co-efficients. However, these coefficients do not tell us between which of the groups the respective functions discriminate. We can identify the nature of the discrimination for each discriminant function by looking at the means for the functions across groups.

Data of this type may be represented in any number of different forms: scatterplots, tables of means and standard deviations, and overlapping frequency polygons.

As previously mentioned, DA is usually used to predict membership in naturally occurring groups. It answers the question: can a combination of variables be used to predict group membership? Usually, several variables are included in a study to see which ones contribute to the discrimination between groups. The means for the significant discriminant functions are examined in order to determine between which groups the respective functions seem to discriminate.

DA can be used for Research and Development, Consumer and market research, quality control and quality assurance across a range of industries such as food and beverage, paint, pharmaceuticals, chemicals, energy, telecommunications, and others. It can generate data models not only for prediction but for faster product and process optimization for application in Product Development and Quality Control. Apart from this, DA is used in speech recognition software.

DA can be extensively used in the Six Sigma projects. Inside the Improve phase of Six Sigma, while identifying and testing various solutions we need to develop transfer function to establish a relationship between the project output variables and various input variables. Once we plot the variables on scatter diagrams, pareto charts we could be able to draw the cause and effect diagrams identifying the various Xs and Ys. Once we verify the various root causes in the Analyse phase of the six sigma project, we could conduct design of experiments (DoE) and regression analysis to predict the output (Y).

Author - Siddhartha Sabale

Group 2 _ Operations