Statistical tests are mind bogglers! Collection, organisation, interpretation and analysis of data and results constitutes an integral part of statistics. Statistical tests, are basically the medium through which we can approximate solutions when the processes are highly complex or unknown in their true forms.
Statistical tests are classified into
- parametric test, and
- non parametric test
Parametric test (conventional statistical procedure) are suitable for normally distributed data. The majority of elementary statistical methods are parametric, and parametric tests generally have higher statistical power.
- In the parametric test, the test statistic is based on distribution.
- The measurement of variables of interest is done on interval or ratio level.
- In general, measure of central tendency in the parametric test is mean.
- Parametric test can be applied only for the variables.
- This test provides you with complete information about the population.
Parametric Test for Independent Measures Between Two Groups: T-test- A t-test is used to compare between the means of two data sets, when the data is normally distributed. Here, the two groups of data must be independent from one another.
Parametric correlation test: Pearson test – A common parametric method of measuring correlation between two variables is the Pearson Product-Moment Correlation. In this test, the variables should be normally distributed.
Why should you use parametric test?
- Parametric tests can perform well with skewed and non normal distributions
- Parametric tests can perform well when the spread of each group is different
- Parametric tests usually have more statistical power than nonparametric tests
Non parametric test
Non parametric test (distribution free test), does not assume anything about the underlying distribution. Non parametric tests are used when the data isn’t normal.
- In the case of non parametric test, the test statistic is arbitrary.
- The variable of interest are measured on nominal or ordinal scale.
- The measure of central tendency is median in case of non parametric test.
- Non parametric test doesn’t consist any information regarding the population.
- This test can be applied to both variables as well as attributes.
Non Parametric Test for Independent Measures Between Two Groups: Mann-whitney test- This test is used to compare the means between two groups of ordinal data.
Non parametric correlation test: Spearman test- This test is used when data are ordinal rather than interval. This test works the same as the Pearson Correlation test, but the data here must first be ranked.
Reasons to use non parametric test
- Your area of study is better represented by the median
- Your sample size is too small to run a parametric test
- Your have ordinal/ ranked data or outliers that cannot be removed
Lastly, to use parametric test or nonparametric test often depends on whether the mean or median more accurately represents the center of the data set’s distribution. If the mean represents the center of the distribution of your data, and the sample size is large enough, use parametric test and if the median represents the center of the distribution of your data, use non parametric test.