Statistics Assignment #9 (additional pages+payment) - Speech or Presentation Example

Often, the experiment is carried out as a double blind test where both the doctors and patients do not know whether the given drug is actually a placebo or not. A simplified approach to this type of experiment may result in the table seen below. From this table, the problem can actually be handled as a chi square problem. Specifically, the Test of Homogeneity may be used in such a case. In such a case, the null hypothesis is that the ratio of effective against non-effective cases for both the new drug and the placebo must be equal.

If the drug is to be considered for use, there must be a high probability of rejecting the null hypothesis hence indicating a significant difference between the control group (placebo group) and the trial group. In contrast, the lack of a control group would simply result to a measure of whether the new drug was effective or not. Since the testers are bound to think that the new drug would cure their complaints, the placebo effect takes place and the results of the experiment will no longer be reliable.

The chi square approach establishes a framework for testing with non-parametric probability distributions. That is, the distribution is not defined by parameters such as the mean and standard deviation in the case of the normal distribution. Instead, the frequency or probabilities of certain observations are necessary to describe a model. Three applications of the chi square paradigm are the Goodness of Fit, Test of Independence, and Test of Homogeneity. While the three revolve around the same approach, they differ slightly in terms of interpretation.

The Goodness of Fit testing approach is used when the expected probability of certain observations are known. This test compares the actual observations from the expected values and determines whether there is a significant deviation from the expected probabilities. An example for this would be a die roll. Each side of the die is supposed to appear as often as