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
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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