The Implementation of Statistical Techniques in Business

Statistics underwrite the validity of decisions in business. Statistics offers the best tool for predicting, analysis, and forecasting and as such forms a valid basis on which to base business logic. Business decisions are probabilistic as there is always an element of uncertainty in most of the choices that a manager makes. Even in the cases where the manager is absolutely certain of a result, in which case he is a certainty operator, statistics is used to reinforce the validity of the belief. Statistics forms a basis for making the right decisions which will ensure the business remains productive and profitable.

Statistics finds wide application in business, but one of the most critical use cases lies in market research. Central to a business money making objective is intimate knowledge of their market. Such statistics as customer’s preferences, past buying trends, and where the customer demographic prove very useful in marketing strategy. One particular tool that is useful in market research, particularly in analyzing the relationship between any two factors relevant to the quality of a decision is the Chi-square (X²) technique. For our purposes, we will look at how it is used to test for goodness of fit and to test for independence of factors as well. Say we want to introduce a product into the market and are probing customers to identify the best option to use in branding. In this particular instance, we want to identify the preferred color for our product. A quick survey yields the following result

Package Color	Consumer Preference
Red	35
Black	53
Green	40
Yellow	35
Blue	37
Total	200

A reasonable assumption would point to black being the preferred customer choice for product branding. However, this fails to account for the probability that black was chosen merely out of chance. To ensure the choice was not arbitrary, we can employ the Chi-square test. We use a series of steps in this analysis. First, we formulate a null hypothesis, and an alternative hypothesis that must be true if our null hypothesis is not. Second, we select the level of significance [one tail], in this case 5% (0.05) is reasonable. The level of significance sets the probability that a true Null Hypothesis is rejected. Third, we select a test statistic that follows Chi-square distribution. Then we formulate a decision rule to ensure that the decision falls within the accepted range and then use Chi-square to calculate if the preference is arbitrary or not.

Null Hypothesis: All colors are equally preferred.

Alternative Hypothesis:They are not equally preferred.

Chi-Square will then be calculated as:

The application of the test on the sampling data yields

Package Color	Observed Frequencies (O)	Expected Frequencies (E)	(O-E)2
Red	35	40	25	0.625
Black	53	40	169	4.225
Green	40	40	0	0
Yellow	35	40	25	0.625
Orange	37	40	9	0.225
Total	200	200		5.7

The computed value of Chi-Square distribution (X²) is 5.7 .  

There are five categories in the distribution, implying the degree of freedom will be 4 (k-1=5-1=4). The critical value of (X²) at 5% level of significance and 4 degrees of freedom is 9.488 .

The decision rule is to reject the null hypothesis if the computed value of Chi-square is greater than 7.815. If it is less than or equal to 7.815, we fail to reject the null hypothesis. We can surmise that the null hypothesis is not true, therefore, the preference for the different colors is not the same.

To conclude, statistics is an essential tool in decision making in business. It helps us predict, analyze, forecast and make sense of data. Like in the example above, the manager is able to validate the accuracy of his decision before putting a product to market. Evidently, statistics is a great tool in taking the guesswork out of decision making. As a result, the overall quality of decisions is greatly improved, assuring the profitability and posterity of an enterprise.

References

Keller, G., & Warrack, B. (2000). Statistics for management and economics. Pacific Grove: Duxbury Press.

Lind, D., Marchal, W., & Wathen, S. (2005). Statistical techniques in business & economics. Boston: McGraw-Hill Irwin.