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Parameters
Parameters are characteristics of populations—they describe the population. In research design, one is often interested in estimating certain parameters of a defined population or testing hypotheses on them. A clear understanding of the objectives of the study will influence the parameter(s) of importance. Consider the situation of environmental pollution in a certain city or region. Suppose that a measure of environmental pollution is the level of carbon monoxide in the air. A parameter could be the mean level of carbon monoxide per specified unit volume. This entry describes the types and categories of parameters; discusses the use of parameters in probability distributions, estimation, and hypothesis testing; and suggests a focus for future research.
Types of Parameters
In general, parameters are either discrete or continuous. For the example considered previously (mean level of carbon monoxide per unit volume), the parameter is continuous. It can take on an infinite number of values on a continuum scale. On the other hand, consider a binomial distribution, where each person is asked whether he or she prefers a given product or not. In this situation, there are two parameters. The first represents the number of persons selected (n), and the second is the proportion of people who prefer the product (p). The parameter n is discrete, whereas the parameter p is continuous.
Different categories of parameters may define different features associated with the population. Consider, for example, the location parameter—three common ones are mean, median, and mode. The population mean, μ, is a measure of location or central tendency of the elements in the population. It is one of the most widely used parameters of interest in research designs. Typically, when an experiment is conducted based on a design, one is interested in determining if a treatment has any effect on the population mean response. The median could be of interest in applications of nonparametric tests, where the assumption of normality of the response variable may not hold. The mode is used very infrequently in research design as a parameter.
Another category of parameters is that associated with variability in a population. Examples are the range, standard deviation, variance, and interquartile range. Of these, the standard deviation and variance are widely used. The population standard deviation is usually denoted by σ2 and the population variance by σ2. In a majority of research design problems, even if the population dispersion parameter, σ2, is not directly of interest, it does show up indirectly in assumptions pertaining to statistical hypothesis tests on the population means. A common assumption in these tests is that of homogeneity of population variances, which assumes that the variances of the population distributions associated with each treatment are equal.
Probability Distribution Parameters
Parameters that completely specify the probability distribution of a certain random variable are known as probability distribution parameters. The most commonly used one in practice relates to the normal probability distribution, whose density function is given by
The two parameters in Equation 1 are the population mean, μ, and the population standard deviation, σ. Knowledge of these two parameters gives us complete information about the nature of the distribution. Hence, it is of interest to estimate these parameters or test hypotheses on them.
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- Descriptive Statistics
- Distributions
- Graphical Displays of Data
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- “Coefficient Alpha and the Internal Structure of Tests”
- “Convergent and Discriminant Validation by the Multitrait-Multimethod Matrix”
- “Meta-Analysis of Psychotherapy Outcome Studies”
- “On the Theory of Scales of Measurement”
- “Probable Error of a Mean, The”
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- Theory
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- Weber-Fechner Law
- Types of Variables
- Validity of Scores
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