Non-Parametric TestsHowever, non-parametric tests can be applied to most of the data that we usually encounter, including that from continuous data distributions.Hence, data that are normally distributed may also be analyzed using these methods.Disadvantage: less sensitive X 2Transforming the data is merely a change of units, like converting pounds to kilogramsAssess its normality again! Bad results? Use non-parametric testsNon-Parametric TestsDistribution-free statisticsRemember data types: nominal, ordinal, interval (no true zero), ratioMost efficient for nominal or ordinal (ranked) data Appropriate for continuous data not normally distributed Give examples!Data not normally distributed? Do transformation to achieve Normality!natural logarithm i.e. Other Common Probability DistributionsThe Poisson distributionThe Students t distributionThe chi-square (X2) distributionThe F distributionAssessing normality2 ways: with statistical tests or withoutWithout statistical test:In a statistical package, such as SPSS, look at:Histogram symmetric: goodBox plot symmetric: good, outliers?Normal Q-Q plot straight line: goodSkewness within -1 to 1, close to zero: good Kurtosis within -1 to 1, close to zero: good (in STATA: normal value is 3)Good results: normally distributed data parametric tests. Transformation of a value to a standard score(standardizing):The Normal Distributionstandard normal curve, standard score of Z Z: the number of SDs from the meanThe Normal Distributionstandard normal curve, standard score of Z The Normal Distributionstandard normal curve, standard score of Z Nevertheless, if real data conform reasonably well with the theoretical definition of the normal curve, adequate approximations, if not very accurate estimates of probability, can be computed based on normal curve theory.The Normal Distribution Scientific data from pharmaceutical experiments cannot possibly fit this definition. The Normal DistributionA continuous probability distribution and consists of an infinite number of values. The Binomial DistributionFour patients receiving antibiotics, p=0.75, q=.25
The Binomial DistributionThree patients receiving antibiotics possible results: N+1=4Three curesTwo cures and one failureTwo failures and one cureThree failures The Binomial DistributionTwo parameters: the probability of one or the other outcome, the number of trials or observations, NThe probability of the outcome of a binomial experiment consisting of N trials: (p+q)Np: the probability of successq: the probability of failureThe Binomial DistributionThree coin tosses possible results: N+1=4Three headsTwo heads and one tailTwo tails and one headThree tails Analisis Non-ParametrikAntonius NW PratamaMK Metodologi PenelitianBagian Farmasi Klinik dan KomunitasFakultas Farmasi Universitas JemberReferenceBolton, S., Bon, C., 2004, Pharmaceutical Statistics Practical and Clinical Applications, 4th ed, New York: Marcel Dekker, Inc.OutlineThe probability distributionBinomial and normal distributionNormality assessmentNon-parametric testsProbability DistributionA probability distribution is a mathematical representation (function) of the probabilities associated with the values of a random variable.For discrete, discontinuous, binary data: the binomial probability distributionFor continuous data: the normal distribution
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