Non parametric test 8

Assistant Professor of Commerce um Government First Grade College for Women, Holenarasipura
7. May 2020
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Non parametric test 8

• 2. Non-parametric statistics test Non-parametric statistics is the branch of statistics. It refers to a statistical method in which the data is not required to fit a normal distribution. Nonparametric statistics uses data that is often ordinal, meaning it does not rely on numbers, but rather a ranking or order of sorts. For example: a survey conveying consumer preferences ranging from like to dislike would be considered ordinal data. Nonparametric statistics does not assume that data is drawn from a normal distribution. Instead, the shape of the distribution is estimated under this form of statistical measurements like descriptive statistics, statistical test, inference statistics and models. There is no assumption of sample size because it’s observed data is quantitative.
• 3. This type of statistics can be used without the mean, sample size, standard deviation or estimation of any other parameters. The non-parametric test are called as “distribution-free” test since they make no assumptions regarding the population distribution. It is test may be applied ranking test. They are easier to explain and easier to understand but one should not forget the fact that they usually less efficient/powerful as they are based on no assumptions. Non-parametric test is always valid, but not always efficient. Types of Non-parametric statistics test  Rank sum test  Chi-square test  Spearman’s rank correlation
• 4. Rank sum test Rank sum tests are U test (Wilcoxon-Mann-Whitney test) H test (Kruskal-Wallis test) U test: It is a non-parametric test. This test is determine whether two independent samples have been drawn from the same population. The data that can be ranked i.e., order from lowest to highest (ordinal data).
• 5. U test For example The values of one sample 53, 38, 69, 57, 46 The values of another sample 44, 40, 61, 53, 32 We assign the ranks to all observations, adopting low to high ranking process and given items belong to a single sample. Size of sample in ascending order Rank 32 1 38 2 40 3 44 4 46 5 53 6.5 53 6.5 57 8 61 9 69 10
• 6. Kruskal-Wallis H test  H test: The Kruskal-Wallis H test (also called as the “one- Way ANOVA on ranks”) is a rank-based non parametric test that can be used to determine if there are statistically significant difference between two or more groups of an independent variable on a continuous or ordinal dependent variable. For example: H test to understand whether exam performance, measured on a continuous scale from 0-100, differed based on test anxiety levels(i.e., dependent variable would be “exam performance” and independent variable would be “test axiety level”, which has three independent groups: students with “low”, “medium” and “high” test anxiety levels).
• 7. Chi square test The chi-square test is a non-parametric test. It is used mainly when dealing with a nominal variable. The chi-square test is mainly 2 methods.  Goodness of fit: Goodness of fit refers to whether a significant difference exists between an observed number and an expected number of responses, people or other objects. For example: suppose that we flip a coin 20 times and record the frequency of occurrence of heads and tails. Then we should expect 10 heads and 10 tails. Let us suppose our coin-flipping experiment yielded 12 heads and 8 tails. Our expected frequencies (10-10) and our observed frequencies (12-8).  Independence: the independence of test is difference between the frequencies of occurrence in two or more categories with two or more groups.
• 8. Spearman’s rank correlation test-In this method a measure of association that is based on the ranks of the observations and not on the numerical values of the data. It was developed by famous Charles spearman in the early 1990s and such it is also known as spearman’s rank correlation co-efficient. English (marks) Maths (marks) Rank (English) Rank (maths) Difference of ranks 56 66 9 4 5 75 70 3 2 1 45 40 10 10 0 71 60 4 7 3 62 65 6 5 1 64 56 5 9 16 58 59 8 8 0 80 77 1 1 0 76 67 2 3 1 61 63 7 6 1