To achieve order in this chaos, statisticians have developed probability models. As such, they can never be known except in the mind of the mathematical statistician. If an infinite number of infinitely precise scores were taken, the resulting distribution would be a probability model of the population. The two graphs below illustrate two types of probability models, the uniform distribution and the normal curve. As discussed earlier in the chapter on the normal curve, probability distributions are described by mathematical equations that contain parameters.
Parameters are variables that change the shape of the probability model.
By setting these parameters equal to numbers, a member of that probability model family of models results. A critical aspect of statistics is the estimation of parameters with sample statistics . Sample statistics are used as estimators of the corresponding parameters in the population model. For example, the mean and standard deviation of the sample are used as estimates of the corresponding population parameters m and d . Mathematical statistics texts devote considerable effort to defining what is a good or poor parameter estimation procedure.