homeresearch servicesdata analysisdiscriminant analysis

Discriminant Analysis:

Throughout the course of our various market research projects we often find data certain key variables are made up of distinct groups. Example of such groups could be customers (satisfied versus non satisfied), products (successful versus unsuccessful), stores (profitable versus unprofitable), or any other object that can be evaluated. By understanding the dynamics of group membership one can focus the business accordingly. Correctly implementing solutions based on these findings should reap increases in revenue and profitability.

Discriminant Analysis is used in situations where you want to build a predictive model of group membership based on observed data - characteristics, attitudes, and demographic data. It is an a priori technique in that the groups are defined beforehand (the opposite of cluster analysis where we use the methodology to form the groups).

The analysis produces a linear equation that can be used to explain which variables best discriminates between two or more groups, and consequently, builds a predictive model that can be used for future classification.

Case Study
A company wished to investigate the characteristics of those customers that would definitely recommend the company to their friends compared to those that would not. They wished to identify those features of service that distinguish between the two groups.

The study involved the collection of attitudinal information on a range of service issues within the business. Generally, the discriminant analysis procedure does not use all of the available data. The use of all the available data would result in a data with much error. Parsimony allows for a clear picture to be painted and more a coherent message to be given to the client. A Stepwise methodology was employed during the selection process to ensure that those variables that are included are significantly contributing to the discriminant function.

A number of the available attitudinal variables with sufficient sample sizes were entered into the stepwise procedure and below is a list of those that were found to be significant with respect to the discriminant function:

It is important to assess the relative importance of the factor questions included in the discriminant function. The standardised canonical coefficients allow one to compare the relative contribution of each variable to the overall discriminant function. Standardised coefficients are useful to look at each factor relative to the others. Therefore, if one coefficient is twice as large as another, it is twice as good a discriminator as the other.

Looking at the coefficients below, factors Automated telephone answering service, Ease of connection and Helpfulness of person appear to be the most important factors within the discriminant function. This information is displayed graphical below:



When placed into a commercial context, it is clear that the issues of Automated telephone answering service, Ease of connection and Helpfulness of person dealing with the call are at the forefront of the customers mind when using the service. Therefore, it is these areas that should be concentrated on when trying to improve customer satisfaction and recommendation rates. Accuracy of Information and the Callback Process are more marginal issues, but significant ones not be dismissed.

The next step is to assess the model itself. The primary tool here is Wilks' Lambda test. The Wilks' Lambda test tests the hypothesis that the means of the functions listed are equal across groups, Wilks' lambda being the proportion of the total variance in the discriminant scores not explained by differences among the groups. A significance value less than 0.05 indicates that the group means differ, and therefore the function is a significant discriminator. This is clearly the case in this study and one can conclude that the function is a valid discriminator.

Wilks' Lambda
Test of Function(s)	Wilks' Lambda	Chi-square	df	Sig.
1	.691	205.147	5	.000

The ultimate test of the function's discriminatory power is the rate of correct classification. The performance of the discriminant function is given in the subsequent matrix. It can be seen that 75.3% of original grouped cases have been correctly classified. This appears to be a satisfactory rate of correct classification. This can be tested using a t-test (p<0.01).

Classification Results(a)
			Predicted Group Membership		Total
	RECOM2	1.00	2.00
Original	Count	1.00	259	133	392
		75	376	451
	%	1.00	66.1	33.9	100.0
		2.00	16.6	83.4	100.0
a 75.3% of original grouped cases correctly classified.

Hopefully, you have realised the power of Discriminant Analysis as an aid to strategic planning, allowing the explanation and prediction of customer behaviour. This information can help in the understanding of group dynamics leading to more focused business development.

« Analysis for Target Setting

back to data analysis