PARAMETRIC TEST

Parametric statistics assume more about the quality of the data, but in return they can tell us more about what is going on with those data.  The most common parametric statistics assume the “General Linear Model”—that is, they assume that the “true,” underlying distribution of the data can be described by a straight line (or one of its variants).A parametric test is one which specifies certain conditions about the parameter of the population from which the sample is taken. Such statistical test are considered more powerful statistical test and should be used if there basic requirements and assumptions are made. The assumptions for the test are given as follows:

1.   The observations must be independent that means the selection of one test must be dependent upon the selection of any other test.

2.   The observation must be drawn from a normally distributed population. The samples drawn from a population must have equal variance if particularly the sample size is small.

3.   Variance must be expressed in interval or ratio scale. Nominal measures are ordinal measures do not qualify for a parametric statistical test.

4.   The variables under study should be continuous.

The examples of parametric test are Z-test, f-test, t-test, correlation and ANOVA.

Correlation and Analysis of Variance (ANOVA) are among the most powerful of the parametric statistics.  Both test for the presence of a relationship between two characteristics, and are based on an assumption that is called the “general linear model.”  This assumption states that the relationship between characteristics (or “variables”), in its ideal form, can be described as a straight line.  In other words, a change in one variable always produces a change in other variables and that change is always in a certain direction (greater or less) and at the same strength.  For many relationships, this makes sense. For example, the harder we swing a hammer, the bigger the dent we make in the wood.  The harder we push on the gas pedal, the faster we go.  The harder we work in school, the better the grades we get.  And so on.  As long as we can reasonably make this assumption (that there is a relationship, and that it is “linear”), then we can apply the linear model.  Correlation requires the additional assumption that both variables are “normally” distributed; ANOVA only requires that one of the variables be normally distributed. The parametric tests are commonly applied in behavioral research.