Friday, 2 March 2018

Parametric Tests in Statistics - When to Use Which

This is an easy topic to understand if you understand the basic concepts I am going to present in this article. So read carefully as I will make the explanation very simple. This article would serve as a guide on how to choose a parametric test.

As you know, in statistics, there are two categories of tests that can be carried out:
  • Parametric Tests
  • Non-Parametric Tests
The difference between parametric test and non-parametric test is that parametric tests assume that the  data follows a normal distribution while parametric test does not.We would focus our attention on Parametric test in this article.

Figure 1 illustrates the basic parametric tests and the summary

Figure 1:Basic Parametric Tests

PARAMTERIC TESTS
The various parametric tests that can be carried out are listed below

1. One-sample z-test (u-test): This is a hypothesis test that is used to test the mean of a sample against an already specified value. The z-test is used when the standard deviation of the distribution is known or when the sample size is large (usually 30 and above). And of curse the pupulation must be assumed to follow a normal distribution.


2. Independent-samples z-test: This is like the z-test, but in this case we are working with two samples and trying to find a relatioship(if any exists) between the two samples.

3. One-sample t-test: The one-sample t-test is a hypothesis test used to test the mean of a small sample taken from a population against a given value. The formular for calculating the t statistic is given below:
4. Independent-samples t-test: This is like the t-test, but in this case we are working with two samples and trying to find a relatioship(if any exists) between the two samples.

5. F-test: The F Test is adopted to compare the variances of two different samples to test the hypothesis that the samples are drawn from population that have different variances.The F-test value is based on the ratio of the variances of the two samples.

6. Paired-sample t-test: This is like the t-test, but in this case we have a sample that have pairs of values. For example, a measurement taken before is paired with a measurement taken after.

7. One-way ANOVA: The Analysis of Variace test is a statistical test used to compare if samples taken from populations have the same mean, or whether the population means are significantly different. An example is that of six different  suppliers that supplies steel to a company and the strenght of the steel is critical to the application which it is used for. ANOVA could be peformed to check if the average strenght of steel from the six suppliers are the same.

8. Bartlett test: This is also called test for homogenity of variance. It is a test to test whether the variances of samples drawn from different populations are equal.

9. Chi-Square Test: This is also called 'Goodness of Fit' test. It is used to test if a sample is taken from a population that conforms to a specified distribution.