Non parametric test
- 1. Non-Parametric Test Submitted By : Neeta Thakur
- 2. Introduction Researcher in the field of health sciences many times may not be aware about the nature of the distribution or other required population parametres . In addition sample may be too small to test the hypothesis and generalize the findings for the population from which the sample is drawn. furthermore, many times in the observations presented in numerical figures, the scale of measurements may not be really numerical, such as grading bedsores or ranks given to the analgesic’s drugs effectiveness in cancer patient management. In these situation, parametric test may not be suitable, and a researcher may need different types of tests to draw inferences , those test are known as non parametric tests.
- 3. Nonparametric tests • Non parametric test are applied under the circumstances where the population is not normally distributed based on fewer assumptions or no assumptions. • There are some situations when it is clear that the outcome does not follow a normal distribution. • .
- 4. Where we can use Non parametric test 1. Where the sample is selected using either probability or even may be non probability sampling technique. 2. where the population distribution is not known or even may not normally distributed 3. Where the measurement of data is generally in nominal or ordinal scale 4. Where the population of the study is not clearly defind or complete information about population is not known.
- 5. Non-parametric Methods • Chi Square Test • The sign test • Wilcoxon Signed-Rank Test • Mann-Whitney U- Test • Median test • Kruskal-Wallis Test
- 9. Sample for Chi –Square Test Preferably random sample. Sample size should be more than 30 Lowest expected frequency not less than 5
- 10. Chi Square Test • Simplest & Most Widely used non-parametric test in statistical work • Calculated using the formula - ꭓ2 • = ∑ 𝑶−𝑬 𝟐 𝑬 O- observed frequencies E- expected frequencies • Calculated value of ꭓ2 is compared with table value of ꭓ2 for given degrees of freedom.
- 16. Ranking Data • To rank data we must order a set of scores from smallest to largest. The smallest score is given rank 1, the second smallest score is given 2 and so on. It is purely the sample size that affects the ranks and not the actual numerical values of the scores. • Imagine you have collected a sample of ten students' exam scores (out of fifty) and wish to rank them. • You collect the following scores: 25,49,12,40,35,43,28,30,45,1825,49,12,40,35,43,2 8,30,45,18. • If we sort them into ascending order, we get: 12,18,25,28,30,35,40,45,4912,18,25,28,30,35,40,45,4 9 •
- 17. These are now in ranked order and we can put them into a table:
- 18. Sign test It is used as an alternate test to T-test where median is compared rather than mean. Uses of Signed test 1. Used to test null hypothesis about population median with single sample or paired data 2. Population parametres are not known or not normally distributed. 3. The data available are on ordinal scale rather than interval or rational scale
- 23. If a small size sample (n<30) is drawn from a grossly non- normally distributed population and t-test and Z test cannot be applied, then a best alternative non- parametric test is Wilcoxon- signed Rank test. Because sign test may be used when data consist of single sample or have a paired data .
- 24. FOLLOWING ASSUMPTIONS ARE CONSIDERED IN WILCOXON SIGNED RANK TEST : 1 The sample is random 2 The variable is continuous The population is symmetrically distributed about its mean The measurement scale is at least interval.
- 25. Methods of Wilcoxon sign test •First, delete any case where the scores are the same in both groups (so zero differences), they can be ignored in the sign test. •Subtract the second group's scores away from the first group's. Remember to include the sign of the difference (++ or −−). •Now count the number of differences which have a positive sign and then count the number of differences with a negative sign. •Take the smaller number. •Look up the significance of the smaller number in a significance table. look at the row containing the sum of the positive and negative signs (the total number of differences ignoring zero differences.) The value must be in the range specified in the table for it to be statistically significant. •Report the findings and form conclusion.
- 29. The Mann-Whitney U-test is the most common non-parametric test for unrelated samples of scores. We would use it when the two groups are independent of each other, for example i testing of two different groups of people in a conformity study. It can used when the two groups are different sizes and a.
- 31. •Method of Mann Whitney U test •First, we state our null and alternative hypotheses. •Next, we rank all of the scores (from both groups) from the smallest to largest. Equal scores are allocated the average of the ranks they would have if there was tiny differences between them. For example, say there are two scores of 13. If there was just one score of 13 it would have the rank 7 in this particular example. However, since there are two scores of 13, we instead assign the rank 7+8/2=7.5 to both scores. •Next we sum the ranks for each group. Then sum of the ranks for the larger group R1 and for the smaller sized group,R2. If both groups are equally sized then we can label them whichever way round we like.
- 39. Median test It is used to test the null hypothesis that two independent sample have drawn from population with equal median Follwing assumption are considered 1. The sample are selected independently and at random from population with equal mediun 2. The level of measurement must be at least ordinal 3. The sample don’t have to be equal in size 4. The population are of the same form and differ only in location
- 40. Kruskal WallisTest • Like the one-way analysis of variance, the Kruskal- Wallis test is used to determine whether c ≥3 samples come from the same or different populations. • The Kruskal-Wallis test is based on the assumption that the c groups are independent and that individual items are selected randomly. The hypotheses tested by the Kruskal-Wallis test follow. H0 :The c populations are identical. Ha: At least one of the c populations is different.
- 41. Advantages of Nonparametric Tests • Used with all scales • Easier to compute — Developed originally before wide computer use • Make fewer assumptions • Need not involve population parameters • Results may be as exact as parametric procedures .
- 42. Disadvantages of Nonparametric Tests • May waste information — If data permit using parametric procedures — Example: converting data from ratio to ordinal scale • Difficult to compute by hand for large samples • Tables not widely available .
- 43. Parametric Non-parametric Assumed distribution normal any Typical data Ratio or interval Nominal or ordinal Usual central measures mean Median Benefits Can draw many conclusions Simplicity less affected by outliers Independent measures, 2 groups Independent measures, >2 groups Repeated measures, 2 conditions Tests Independent measure t test One way independent measures ANOVA Matched pair t-test Mann- whitney test Kruskal wallis test Wilcoxon test parametric statistic
- 44. • Jarkko Isotalo, Basics of Statistics (Available online at: http://www.mv.helsinki.fi/home/jmisotal/BoS.pdf) • Ken Black, 6th edition, Business Statistics For Contemporary Decision Making • Lisa Sullivan, Non parametric statistics, Boston University School of Public Health (available online at: http://sphweb.bumc.bu.edu/otlt/MPHModules/BS/BS704_Nonpara metri c/BS704_Nonparametric_print.html) • Arora, P.N and Malhan P.K; Biostatistics, 2009 Edition • http://blog.minitab.com/blog/adventures-in-statistics/choosing- between-a-nonparametric-test-and-a-parametric-test