Power of Statistical Analysis Term Paper

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[. . .] The mean, median and mode are all equal in this type of measurement, and the scores at either end of the distribution, those which are extremely high, or extremely low, occur less often. For example, a curve representing the results of an intelligence test would have the highest number of people in the middle, or measuring within the 'average' intelligence range. The number of people decreases as the scores get farther away on either side of the average, thus creating a bell shape curve. Once the parameters are defined, the sampling process is used to test a hypothesis, or determine the actual frequency of given behavior or event.

Confidence intervals are developed from an estimate using a range of values (an interval) to predict the expected value of an unknown parameter. The confidence interval is identified as a specific level of confidence, or probability, that the estimate will be correct (i.e. that the hypothesized interval will in fact contain the true value of the parameter).

Regarding calculating and interpreting data, the Mean of the tar quantities in the above cigarette date is 22.216 mg, the Variance is 113, and the Standard deviation is 10.64.

The chi squared test of Association allows for the comparison of two attributes in a sample of data in order to determine if there is any relationship between them. The purpose behind this test is to compare the observed frequencies with the frequencies that would be expected if a hypothesis of no association / statistical independence were true. By assuming the variables are independent, we can also predict an expected frequency for each cell in the contingency table. For the cigarette data above, the null hypothesis is that there is no relationship between the tar and nicotine quantities in any given cigarette. Since these elements are individual elements in the tobacco, we could hypothesis that the quantities would not be related. However, by making a paired data set out of the tar and nicotine quantities for each brand measured, and plotting the, we come up with the following graph.

Similar results are attained by plotting the tar vs. Carbon monoxide content, and the nicotine vs. carbon monoxide content.

Regarding a linear regression analysis of this relationship, we find that the slope of the line is close to 0.5, and the relationship is a direct linear relationship between the amount of tar in a cigarette and the amount of nicotine.

Nonlinear trends in statistical data can be the most challenging to work with. When non-linear relationships exist, there may be a mathematical relationship which is based on a logarithm, or other multi-factor influence. However, true non-linear relationship, such as the height and weight of a specific person who shops in a given department store may leave the statistician without any relationship whatsoever. Non-linear data can also be the result of data which is being acted on by an artificial, outside force. In this case, the statistician is able to verify the existence of an outside force, and then approach the process of identifying the force.

An example of this situation is the expected relationship between supply and demand, and company profit based on the sales of a given product in the market place. In the early 1980's, the Coleco company produces a product called "Cabbage Patch dolls." The typical lifecycle of a new toy product is one to two years, but Coleco was able to extend the life of their product for four to five Christmas seasons by artificially affecting the relationship between supply and demand. The company had the production capacity to produce 4-5 times the amount of dolls which it shipped to the market during the first three years of the dolls life cycle. This would have produced a typical bell shaped curve, plotting a rising demand, and increasing profits which gave way to a declining demand and declining profits in a short period. However the company did not produce product equal to their capacity, nor equal to the demand. As a result, the company was able to continue a high level of demand, and an inflated retail based on the high demand for an extended period. The result was that the doll stayed popular for almost a decade, and the company was able to reap ongoing higher levels of profits. The longer bell curve, identified by an irregular and nonlinear relation between time and supply and demand was created… [END OF PREVIEW]

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