extensive and the stronger the assumptions, the more powerful the statistical test. That is,
the test is more likely to detect a true difference should one exist. (The statistical test is
more likely to lead to rejection of the null hypothesis when it is false.)
What do we do if the general assumptions of the parametric model and or
specific conditions of particular statistical tests are not met?In the first instance we have to recognize when test assumptions are violated and be
aware of the severity of the consequences of violating particular assumptions. This
problem is dealt with in the sections describing particular test procedures. Assuming we
believe distributional assumptions for a particular parametric test are not met then we can
use other statistical test procedures called NONPARAMETRIC TESTS. These tests are
sometimes called distribution-free tests because they do not make assumptions about the
probability distribution of errors. These nonparametric tests have fewer and less
restrictive assumptions. For example, when the underlying population distribution of a
key variable is thought to be non-normal (i.e., when data is very skewed), or when
measurement assumptions are not met, then a non-parametric test should be considered.
The terms ‘parametric’ and ‘nonparametric’ are used in inconsistent ways (even among
‘experts’). Nonparametric may refer to the use of statistical tests which make no
assumptions about the distribution of errors (hence the term ‘distribution free’) or to the
procedure of hypothesis testing based on distribution free inference (a hypothesis which
does not make an assertion about a parameter). However, nonparametric test procedures
are generally less powerful than comparable parametric tests (on average about 10–20 per
cent less powerful). An alternative strategy to using nonparametric tests is to transform
data to make it more normal. Procedures for checking normality of data distributions and
transforming variables are discussed at the end of this chapter.
5.2 From IDA to Inferential AnalysisA quantitative study is often based on previous empirical studies and or theoretical
considerations, either of which may suggest a possible class of statistical models for your
data. The choice for the new researcher conducting his or her first study in education or
psychology, is usually limited to three classes of models: the general parametric model
based on the normal probability distribution, (associated parametric statistical tests might
include t, F, Pearson r); the binomial model based on the binomial distribution
(associated tests might include binomial and sign tests); and distribution free
procedures (associated with nonparametric statistical tests). Other classes of models less
frequently encountered include Poisson, Hypergeometric (discrete distributions) and
Exponential, Gamma and Weibull (continuous distribution) models. These distributions
and other complex multivariate and time series designs are beyond the scope of this text.
The reader is referred to Manley (1986) for a non-mathematical introduction to
multivariate statistical analysis and the text by Tabachnich & Fidell (1989) is an excellent
practical guide to the use of multivariate analysis. A general introduction to time series
designs is given by Chatfield (1984).
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