Non Parametric Statistics Workshop by fgYY1y

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									                    Non Parametric Statistics Workshop

The Aims of the Workshop are to Cover the Following Main Themes and to
Provide Research-Based Exercises Which Support Blended Learning

   1. non-parametric statistics to validate and explore a non-random sample
      based dataset
         a. You compare the data you have with the data that come from a
            much larger data set, without assuming that your data follow a
            normal distribution (t-test with heterogeneous dispersion)
         b. You compare the data you have with the data from another data
            set that is a random sample (Kolmogorov Smirnov test) without
            assuming either yours or their following a normal distribution
         c. You compare your sample distribution with another sample
            distribution using a small-numbers test (Fishers exact test and
            then permutation logic)
         d. You set up weights to adjust your small sample to the
            proportions found in a much larger sample, and these weights
            follow a set of three or four variates rather than being simply sex
            or age adjusted. (the logic of weighting for misrepresentation)
         e. You acquire data for an augmented sample to compensate for
            weaknesses in your sampling method, and you use weights to
            adjust the augmented sample cases down to their appropriate
            overall population [or sample] weight (weighting for
            underrepresentation)

   2. non-parametric statistics to compare sub-groups using a multi-variate
      substitute for regression in contexts where variables are predominantly
      not randomly distributed
         a. Regression with a logistic dependent variable compensates for
             the absence of normal distribution of the error term or of the
             dependent variable
         b. Regression with a multinomial dependent variable compensates
             for the absence of ordinality of the dependent variable
         c. Regression using ordered probit compensates for absence of a
             normal distribution for an ordinal dependent variable
         d. If none of these will work because of small sample sizes or
             poorly behaved sub-groups [technically known as the zero-cell
             problem, see Menard, Ref*’], then you can use those tests
             below…

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3. comparison of the distribution or the mean of the distribution in cases
   where the variable is not normally distributed or has no parameters to
   its distribution

      a. cases of a single sample: is it normally distributed or not?
      b. cases of two samples or two sub-groups, i.e. t-statistic but
         without normal distribution: is the median or mode really
         different? Are the distributions different?
      c. cases of multiple samples, can we say that either
              i. there is a pattern upward in the median or mode along an
                 ordinal scale, moving along some other variable which is
                 also ordinal in its measurement? (Kruskal – Wallis test)
             ii. there is a difference in the patterning of the distribution
                 of a multinomial variate, moving along some other
                 variable which is also ordinal in its measurement?
            iii. There is a difference in the patterning of the distribution
                 of one multinomial variate when compared with the
                 distribution of another m ultinomial variate – this is the
                 Chi Squared situation
                     1. with small numbers of cases in all cells (!) –
                        permutation logic, crisp-set comparative analysis
                        or fuzzy set comparative analysis
                            a. the degree of consistency
                            b. the degree of coherence
                     2. with small numbers of cases in some cells (Fishers
                        exact test)
                     3. with large numbers of expected cases in all cells




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