What are the Nonparametric tests?. Why we need nonparametric statistical analysis?

Parametric statistical methods are based on particular assumptions about the population in which the samples have been drawn. Particularly probability distribution, observation accuracy, outlier, etc….In most of the cases, parametric methods apply to continuous normal data like interval or ratio scales.

In most cases, if the assumption does not hold then does not meet parametric methods requirements. In this case, nonparametric methods are more appropriate. In the case of parametric methods inference made thorough mean value but in the case of a nonparametric approach, median values are used.

When nonparametric methods are more appropriate?

Based on the following cases occur nonparametric methods are ideal.

1) The hypothesis does not involve the parameter of the probability function of the population.

2) Observations are not accurate.

3) Observations are nominal or ordinal scales.

4) If the normality assumption violated.

5) If want to avoid complicated parametric methods.

6) Small number of observations and quick result generation

Advantage of nonparametric methods.

Advantageous over parametric methods are mentioned as below.

1) If the assumption does not hold good then the parametric analysis may be erroneous, such situation nonparametric methods can safely apply.

2) Nominal or ordinal scale non-parametric methods an be used.

3) Measurements are not accurate the parametric methods can apply.

4) In the case of a smaller number of observations, nonparametric methods are ideal.

5) If the sample data are continuous nonparametric methods can apply.

6) Who wants to do little computational works then nonparametric methods are ideal.

Disadvantageous of nonparametric methods

1) Based on simplicity nonparametric methods are not recommended because most of the cases powerful parametric methods are available.

2) Not possible to compute actual power, in this case, parametric methods are ideal.

Nonparametric methods are calculating based on ranks, in case of tied observations (like a round of or the same observational value multiple times) faces the problems in award ranking. To avoid the ranking issue, many approaches are available.

1) Midranks approach

Take the average of the ranks of tied values and assign the same average rank to the tied observations.

2) Average statistics approach

Need to calculate the test statistic, this test statistic will have the same mean and different variance. More calculation in this approach and not recommended.

3) Omitting tied observations

The simplest way, omit the tied observation and rank the observations. In case of fewer observations and affect the test result than not recommended.

4) Range of probability

This is based on test statistic fall under inside or outside of the rejection region

Assumptions of nonparametric methods

1) The random sample drawn from a population and median is unknown.

2) Observations need to independent.

3) Observations are continuous.

4) Observations are ordinal or nominal scale.

What are the nonparametric methods

One sample test

1) Kolmogorov Smirnov test

2) Ordinary sign test

3) Wilcoxon signed-rank test

4) Runs test

Major Two or more than two sample methods are mentioned below.

1) KS two-sample test

2) Sign test for paired observations

3) Wilcoxon paired signed-rank test

4) Median test

5) Mann Whitney u test

6) Mcnemar’s test

7) Cochran’s Q test

8) Kruskal Wallis test

9) Friedmann’s test

10) Spearman rank correlation

11) Kendal Correlation

In most cases, the sample size may be small and the ideal test is parametric because of less sample don’t go for nonparametric tests. If your hypothesis inference is suitable to mean standard deviation go with that instead of the nonparametric median approach. In the case of the t-test, one of the assumptions is sample is drawn from a normal population and one group contains a minimum of five observations use a t-test.

Conclusion

The majority of cases more than one test appear appropriate for the test of a hypothesis, such a situation needs to fix some criteria to choose the appropriate tests.1)