Parameter Estimation, Inferences, and Tests of Difference The benefits of parameter estimation are that the measurement gives you a sense of which customers are buying which products, what the production costs are, and how the profits will look. Essentially it allows one to use sample data to gauge the parameters of the distribution. By performing a type of test, the statistical analysis will tell you more about the population with a fitted distribution line curve depicting true values. This is a statistical way to evaluate or project one's profit-making potential based on the evidence or data available.

Types of parameters that marketing decision-makers would use would include location parameter, dispersion or scale parameter and shape parameter. Concentration parameter could also be of interest along with statistical parameters such as regression coefficients.

Examples of parameter methods that might be of interest to decision-makers in areas such as marketing would be probability plotting, which is not very dependent upon mathematical skills and consists of basic plotting of data and allows one to see a visual representation of the parameter in a linear way.

Another example would be maximum likelihood estimation, which consists of a rather strong technique with complete data usage with large sample properties and consistency that add to its attractiveness. It does depend, however, on a large sample size -- but for a marketing team this should not be a problem, as it will most likely want to draw from a large sample size in the first place.

A third example would be the Bayesian parameter estimation method, which is separate from the classical statistics models discussed above in that it uses prior knowledge plus present observational data to produce results. Prior sets of data can consists of information recorded during past operations or from sets of observations already conducted in the past. Building on prior knowledge can be a good way to project forward looking expectations. Prior distributions play a major role in the execution of...

The quality of the decisions made on this type of analysis would be solidly based not on qualitative assessment or opinion but rather on quantitative data that could be tested and re-tested and evaluated by others under the same circumstances in order to verify accounts. Far from being subjective and uncertain, these parameters help to define and concretely visualize the objective data that supports decision-making.
The business benefits of drawing inferences -- specifically when it is advantageous to rely on inferences and what is required to ascertain the correctness of inferences -- are that it allows the firm to better understand the customer and then appeal to the customer by giving him or her what he/she wants. Advantageous times to rely on inferences could be when a survey is conducted of customer satisfaction, when one examines the records of customer complaints -- how frequently they come, how severe they are, etc., or when a focus group study is conducted, or what customer turnover rates are. Each of these instances would be grounds for making inferences about a consumer base. Essentially what is required to make a solid inference is verifiable data, whether quantitative or qualitative that is based in fact and not in assumption.

The relationship between tests of difference and hypothesis testing in the context of designing marketing promotions is that in a paired difference test (a location test), measurements can be taken to see if the means of the populations are different; while in a hypothesis test is used to see if ample evidence is available to make an inference about a variable (for example to see if it applies to the whole or just…