Research Non Parametric Statistics And its Application
- 1. Non-Parametric Statistics Presented by AroofaAfzal (S-20) PUNJAB UNIVERSITY,IER Advanced studies in Education PRESENTED TO PROF. DR. MUHAMMAD SHAHID FAROOQ
- 2. Table of Content Whatis Non-parametric statistics ? Why Non-parametric statistics is used ? How Non-parametric statistics is conducted? Types of Non-parametric
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- 4. What is non-parametric statistic? Non-parametricstatistical techniques are distribution free test. In other words, these tests are not based on data that is normally distributed or any such assumption (as is the case with parametric statistical techniques). Non-parametric statistics can also be described as tests that do not involve testing of hypotheses related to population parameters (King and Minium, 2013).
- 5. What is non-parametric statistic? Salkind(2014, page 46) described non- parametric statistics as “distribution free statistics that do not require the same assumptions as do parametric statistics”.
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- 7. Why non-Parametric statistics isused? When assumptions for parametric tests are violated: Dependent variable is not interval/ratio- scaled. Dependent variable is not normally distributed. Ideal for small sample sizes or ordinal data. (Cronk, 2018, p. 99)
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- 9. How non-Parametric statistics isused? Non-parametric tests are typically used when the data violate the assumptions required for parametric tests (e.g., normality or homogeneity of variance). Below is the step-by-step guide to conducting non-parametric tests: Formulate Hypotheses • Null Hypothesis ( 0H 0 ): 𝐻 Generally, the null hypothesis assumes that there is no difference or no relationship between the groups being compared or the variables being correlated. • Alternative Hypothesis ( H a ): 𝐻𝑎 This is the hypothesis that suggests there is a difference or a relationship
- 10. How non-Parametric statistics isused? Choose the Appropriate Test Select the appropriate non-parametric test based on the following factors: Type of data (ordinal, continuous, categorical). Number of groups (two independent groups, two related groups, more than two groups). Data structure (independent observations or repeated measures).
- 11. Types of Non-ParametricStatistic Wilcoxon Signed Rank test Sign test Mann Whitney U- Test Kruskal Wallis H- Test Friedman Test Two Dependent Samples Two Independent Samples Three or more dependent Samples Three or more Independen t Samples Chi-Square
- 12. Core Principle Compare Frequencies Expected Frequencies: What we predict under no difference. Obtained Frequencies: Actual data observed. Interpretation of Results No Significant Difference: If expected ≈ obtained frequencies. Significant Difference: If expected ≠ obtained frequencies. Chi-Square Test Chi-square ( 2) is a 𝜒 nonparametric test used to analyze nominal data in the form of frequency counts, percentages, or proportions. (Gay,2012 pg.365) Purpose: It compares observed frequencies in different categories to expected frequencies to determine if the differences are statistically significant
- 13. Chi-Square Test - Thebasic contingency table displays the distribution of males and females across three reading levels. - The goal is to determine if the distribution patterns for males and females differ significantly. - Observations: ReadLevel 1: 1 female vs. 18 males. ReadLevel 3: 44 females vs. 7 males. - Initial data suggests noticeable differences in reading level distribution by gender. - A chi-square analysis is needed to assess whether these differences are statistically significant. - A significant chi-square result would indicate that the variables (gender and reading level) are not independent.
- 14. Chi- Square testof independence The chi-square test of independence is a non parametric test design to determine whether two nominal variables are independent or related. . The chi-square test of independence tests whether or not two variables are independent of each other(Cronk, 2018 page 103). Chi-Square Test Chi-square test for goodness of fit. compare the proportion of cases from a sample with hypothesized values or those obtained previously from a comparison population. (Pallant, 2012)
- 15. Chi-square test forgoodness of it - A chi-square goodness-of-fi t test indicates there was no significant difference in the proportion of smokers identified in the current sample (19.5%) as compared with the value of 20% that was obtained in a previous nationwide study, χ2 (1, n = 436) = .07, p < .79.
- 16. Wilcoxon Signed Rank test The Wilcoxon rank-sum test is similar to the independent-groups t test It uses ordinal data rather than interval-ratio data and compares medians rather than means The wilcoxon Rank test is an alternative form of the Mann- Whitney test that is used when samples are dependent The purpose of the Wilcoxon test is to compare mean rank differences between two groups with related scores. The Wilcoxon test is the nonparametric alternative to the dependent t-test. (Martin & Bridgmon, 2012 p,71 ) It is used to test the difference between two independent variables.
- 17. The Mann-Whitney U Test. Definition: TheMann-Whitney U Test is used to test for differences between two independent groups on a continuous measure Purpose: Compares medians of two groups instead of means. Process: Converts continuous variable scores into ranks across the two groups. Evaluates whether the ranks differ significantly between the groups
- 18. Kruskal Wallis H-test Definition: Non-parametric alternative to a one-way between-groups ANOVA. Purpose: Compares scores of a continuous variable across three or more groups. Key Features: Similar to the Mann-Whitney U Test but for more than two groups. Converts scores to ranks and compares mean ranks between group.
- 19. Sign Test Sign Test: Non-parametric test for analyzing two related samples. Purpose: Compare paired or matched groups, such as: Matched samples (e.g., groups equalized by IQ, age, gender). Pre-test and post-test data from the same group. Process: Line up paired scores and count how often one group scores higher than the other. If totals are significantly unequal, the difference may be statistically significant.
- 20. Friedman Test Friedman Test: Non-parametric test for more than two related groups. Purpose: Compares scores across multiple matched groups (e.g., 4 groups). Key Feature: Suitable for repeated measures or matched-group designs.
- 21. References • Creswell, J.W. (2011). Educational research: Planning, conducting, and evaluating quantitative and qualitative research (4th ed.). Pearson. • Cronk, B. C. (2019). How to use SPSS®: A step-by-step guide to analysis and interpretation (10th ed.). Routledge. • Fraenkel, J. R., & Wallen, N. E. (2009). How to design and evaluate research in education (7th ed.). McGraw-Hill Education. • Gay, L. R., Mills, G. E., & Airasian, P. W. (2012). Educational research: Competencies for analysis and applications (10th ed.). Pearson. • Pallant, J. (2010). SPSS survival manual: A step by step guide to data analysis using SPSS (4th ed.). McGraw-Hill Education.
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