ALL PARAMETRIC TESTS| ECONOMETRICS|L-9|

A parametric test is a statistical test which makes certain assumptions about the distribution of the unknown parameter of interest and thus the test statistic is valid under these assumptions. A significance test under a Simple Normal Model for example has the assumption that the parameter has a normal distribution, behaves like an independent variable is the result of an independent process is identically distributed and has a constant mean and variance. Therefore, an integral part of applying such a test is making sure it is adequate vis-a-vis the observed data. This process is called mis-specification testing.The parametric test make certain assumptions about a data set; namely that the data are drawn from a population with a specific or normal distribution. It is further assumed in parametric test that the variables in the population are measured based on an interval scale.When parametric tests are usedWhen the data has a normal distribution.When the measurement scale is interval or ratioTypes of Parametric test,Twosample t-test,Paired t-test,Analysis of variance (ANOVA),Pearson coefficient of correlation

Z-test, F-test, and T-test

A z-test is used for testing the mean of a population versus a standard, or comparing the means of two populations, with large (n ≥ 30) samples whether you know the population standard deviation or not. It is also used for testing the proportion of some characteristic versus a standard proportion, or comparing the proportions of two populations.

Example:Comparing the average engineering salaries of men versus women.

Example: Comparing the fraction defectives from 2 production lines.

A t-test is used for testing the mean of one population against a standard or comparing the means of two populations if you do not know the populations’ standard deviation and when you have a limited sample . If you know the populations’ standard deviation, you may use a z-test.

Example:Measuring the average diameter of shafts from a certain machine when you have a small sample.

An F-test is used to compare 2 populations’ variances. The samples can be any size. It is the basis of ANOVA.

Example: Comparing the variability of bolt diameters from two machines.

Matched pair test is used to compare the means before and after something is done to the samples. A t-test is often used because the samples are often small. However, a z-test is used when the samples are large. The variable is the difference between the before and after measurements.

Example: The average weight of subjects before and after following a diet for 6 weeks