Chi-Square Model
A chi-square model is a statistical method used to analyze the results of certain types of experiments. It involves a comparison of the deviation of real observations from expected values, and helps determine whether a result is significant or not. It has been a particularly useful model in the development of new drugs.
The chi-square function was first proposed in 1900 by a British statistician, Karl Pearson. He developed a formula which takes in consideration the squares of the deviations of each observation from the expected value and weighs them accordingly. By using this distribution, he was able to show whether or not the results from a certain data set matched the expected results from the total population. In this way he developed a measure of the"goodness of fit" for a data set. He also developed a method for comparing the relationship between two data parameters.
Many biological experiments involve enumerative data in which subjects from a population are counted and classified. These type of experiments involve a reasonable degree of approximation and they are defined as multinomial experiments. For example, if a mouse were put in a maze and made to go through one of three doors depending on the stimulus, its response could be classified into one of three values. To determine whether the mouse's choice of door were random or a result of the specific stimuli given, a chi-square model is typically employed.
Chi square models are known as non-parametric statistical tests. This means that the data sets they measure do not necessarily follow a normal distribution about a mean. For an experiment to be valid by a chi square model it typically has the following restrictions. First, it consists of a set amount of identical trials. Second, the outcome of each trial falls into one of a set number of specific classes. Next, the probability that an observation falls in a certain class does not change over the course of the experiment. And finally, the trials are independent.
Since chi-square models can show whether there is a relationship between two data parameters, they have become important tools in the development of new drugs. In this type of research, a test and a control group of people are given a different treatments. Their conditions are monitored for a specified amount of time and data is collected. The incidences of recovery in the test and control groups are compared using a chi-square model to determine whether the treatment is truly effective or a result of random chance. It should be noted that while they are a powerful statistical tool, chi-square models never give a definitive answer and they must be interpreted by the experimenter.
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