# Parametric and Non Parametric Statistics in Sport Research

Parametric Tests are based on the assumption that the population data follows a particular Probability distribution and satisfy certain properties or assumptions. The Emphasis in parametric test lies in estimating the population parameters using ‘statistics’ calculated from the sample, where as Non Parametric tests does not have any assumptions regarding the data and are very much handful when the data is ordinal. Both these tests are used widely in sports research, Researchers make a selection of these tests as per the data and arrive at conclusions.

Parametric Tests Parametric tests are based on certain assumptions. They are based on the assumption that the data follows a particular probability distribution. These tests are called as Parametric as most of the assumptions are regarding the parameters of the population. Parameter: Any measure computed for the entire population is called a parameter. Ex: Population means, Population variance etc…. Statistics: Any measure computed for the Sample is called as a statistic. Ex: Sample means, Sample Variance.

These tests assume that if the data set satisfies a set of assumptions, then the result will be accurate. For example t – test and ANOVA need to satisfy the assumptions that the data is Normal & the observations are independent etc…. These tests yield accurate results and are effective as long as the underlying assumptions are satisfied, but fail when the data is not normal, especially in cases where the data is ordinal, i. e in terms of ranking rather than scores. Non Parametric Tests

When the data is ordinal (ranks) rather than scores, we have a range of tests which can be effectively used Known as Non Parametric tests or ‘Distribution free tests. ’ These are so called because they do not depend on any on the parametric assumptions. These are very widely used when the data is not quantitative. Though there are numerous advantages of the Non Parametric tests, there are few disadvantages too. Parametric and Non Parametric Statistics 3 The following are some of the Non Parametric Tests

Sign Test: The sign test can be used with paired data to test the hypothesis that differences are equally likely to be positive or negative. For Example the Coach of national Volley ball team wants his team to get trained in a new fitness program for two months, after the training program the coach wants to test whether the performance of the players increased with the new fitness program when compared with the fitness prior to the Program, He can use the Sign test. Median Test: The median test is used to test whether two samples are drawn from populations with the same median.

Run test: Used to test whether the data is random. If we take the number of Goals scored by a particular Foot Ball team in the last 10 matches then by using the nonparametric tests we can test whether the team is getting goals consistently or just randomly. Rank test: Used to test the data which contains Ranks. Mann-Whitney U test: Used to test whether the two independent samples are equal, it is also alternative to independent t-test when the data is non parametric.

In Medical research if we want to test the efficiency of a new drug on Youngsters and Middle aged persons, we can test whether the drug works equally with the two age groups. Also in Sports research we can test whether a particular training program yields equal results for players belonging to two different sub continents, as their fitness, food habits, climate etc.. Varies largely. Wilcoxon rank-sum test, one of the significant Non parametric test . Wilcoxon matched pairs signed-rank test: it Provides an alternative for students t – test for matched paired data when the data is not normal.

We can test the significant difference between the pretest and post test scores for a group of athletics. When the data is ordinal and you want to find out if there is any significant difference between the two scores of the same individual we can use Wilcoxon matched pairs signed ranks test. Spearman rank correlation coefficient: The most efficient way to find out whether the variables or attributes are correlated when the data is qualitative. Also for finding relationships between groups we can use spearman’s rank correlation. Parametric and Non Parametric Statistics 4

Other important tests are Kruskal-Wallis analysis of variance by ranks and Friedman Two way analysis of variance. Chi square test is also a NP test for non parametric nominal data. (sports vary as per gender) Chi square test is used to assess the significance of the discrepancy between results that were actually achieved and the results excepted. Parametric and Non Parametric Statistics 5 References VK Kapoor & S. C. Gupta(2000) ,Fundamentals of Mathematical statistics A. M. Gun,M. K. Gupta,B. Das Gupta, Fudamentals of statistics

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