Parametric and Non Parametric methods

Parametric and Non Parametric methods

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  To determine the rangeof difference STATISTICAL INFERENCE Tests of hypotheses
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  French Latin Greek ParametreParametrum Para =beside + Metron=measure A value kept constant during an experiment, equation, calculation or similar, but varied over other versions of the experiment, equation, calculation, etc. Nonparametric methods is essentially concerned with the development of statistical inference procedures without making any explicit assumption regarding the functional form of the probability distribution of the sample observations. Parameter Parametric statistical test is one that makes assumptions about the parameters (defining properties) of the population distribution(s) from which one's data are drawn
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  J. Wolfowitz inthe 1942 The Annals of Mathematical Statistics THE ORIGIN OF THE WORD "NONPARAMETRIC" The Assumption That Populations Have Distributions Of Known Functional Form . . . [With] A Finite Number Of Parameters," While ". Methods ... That Did Not Require Such Specialized Assumptions . Became Known As Non-parametric" By 1967 The Predominant Spelling Had Changed To "Nonparametric," Which Had Meant
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  NONPARAMETRIC METHODS IN COMPARISONTO PARAMETRIC METHODS Submitted by Kishor Pujar First Ph.D. PALB 9014 Agricultural Entomology University of Agricultural Sciences Bangalore
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  SEQUENCE OF PRESENTATION Introduction Nonparametrictests Nonparametric methods Vs Parametric methods Advantages and dis advantages of Nonparametric methods Conclusion
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  Parametric Methods Set of fixed parameters Presumptionsof population Population is normal Mean Standard Deviation Introduction
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  Distribution- free method Probability law is unspecified Nofixed set of parameters Doesn’t depend on the population No assumption on probability distribution of sample Nonparametric methods
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  When to useNonparametric methods If data is not normal Look at the distribution of the data Normal Parametric Not Nonparametric Scale Nominal or ordinal Nonparametric Interval scales or ratio scales Parametric If you want to test median rather than the mean Look for scale
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  ONE SAMPLE TESTS TWO RELATED SAMPLE TESTS TWO INDEPENDENT SAMPLE TESTS KRELATED SAMPLE TESTS K INDEPENDENT SAMPLE TESTS Binomial test McNemar test Fishers Exact probability test Cochran Q test Chi-square test for k independent samples Chi square one sample test Sign test Chi square test for two independent samples Friedman’s Two- way ANOVA by ranks Extension of Median test Kolmogorov- Smirnov one sample test Wilcoxon’s * Matched pair Signed rank test Median test Kruskal-Wallis $ One-way ANOVA by ranks One sample runs test Mann-Whitney U test # Kolmogorov-Smirnov Two sample test Nonparametric tests Alternative = * Paired samples t test, # Independent samples t test, $ one way ANOVA
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  MEASURES OF CORRELATIONAND THEIR TESTS 1. CONTINGENCY COEFFICIENT (C ) 2. PHI (Φ) COEFFICIENT FOR 2X2 TABLE. 3. CRAMER’S V COEFFICIENT 4. MANN KENDALL TREND TEST 5. SPEARMAN’S RANK CORRELATION COEFFICIENT (RS) 6. KENDALL’S RANK CORRELATION COEFFICIENT (Τ) 7. KENDALL’S COEFFICIENT OF CONCORDANCE (W)
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  Nonparametric tests Parametrictests Applies to measurements such as nominal, ordinal. Require measurement equivalent to at least an interval scale Do not assume any parameters of the parent population. Assume some of the parameters of the parent population. Need more number of observations to achieve the same size α Need less number of observations to achieve the size of α Not systematic More systematic It is to test medians It is to test group means. It is applicable for both – Variable and Attribute It is applicable only for variables. Nonparametric methods Vs Parametric methods
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  Nonparametric tests Parametrictests It generally no assumptions about data. It always considers strong assumptions about data. Requires much more data. Require lesser data There is no assumed distribution Assumed to be a normal distribution. Handle original data Handles – Intervals data or ratio data. The result or outputs generated cannot be seriously affected by outliers The result or outputs generated can be easily affected by outliers. Its performance is at peak (top) when the spread of each group is the same. Its performance is at peak (top) when the spread of each group is different. Continued..
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  Provide exact probabilitystatements Useful when sample size is low (N=6) Treating samples made up of observations from several different populations. Available to treat data which are inherently in ranks as well as data whose numerical scores have the strength of ranks. Available to treat data which are in a nominal scale Advantages of Nonparametric tests . The complexity is very low
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  Not useful, ifthe measurement is of the required strength, • When all the assumptions of the parametric statistical model are in fact met in the data No Nonparametric methods for testing interactions in the analysis of variance model, • Unless special assumptions are made about additivity. Disadvantages of Nonparametric tests
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  CONCLUSION When we compareparametric and nonparametric methods, both are having own role, significance and unique power efficiency in deriving statistical inference.
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