Section VI.
Your Results: How To Analyze, Interpret, and Report Your Observations
Results
Provide thorough description of data (in terms of level of measurement, quality, etc.)
The application of statistical procedures to answer research questions and/or test
hypotheses
Statistics
Basic uses of statistics:
To
Describe
- Statistics can be used to describe the results of tests on a sample in terms
of central tendency (mean, median, mode), dispersion (standard deviation, variance),
relationships among or between variables (correlation coefficients), predictions
(regression, LISREL analysis), or differences between treatment groups (chi-square, t-
tests, anovas, etc.
.
To
Infer
- These same statistics can be used to make inferences from the sample to a
larger population, the difference being that inference introduces a random sampling error
band around all estimates (means, proportions, standard deviations, correlations, beta
weights, etc.).
Which statistical test should be used depends on the purpose (to describe or infer) and the
assumptions that can be met (the level of data and normalcy of distribution). Application of the
wrong test will produce uninterpretable and incorrect results. There are also ethical
considerations.
Parametric statistics:
Have a greater statistical power than non-parametric at a fixed sample size, i.e., they are
more sensitive to differences than non-parametric
Three assumptions must be met before applying parametric statistics to data: the data
must be interval or ratio level, population distributions must be normal and variances in
populations must be homogeneous. In other words, assumptions are made about
population parameters; hence the term parametric statistics
Non-parametric statistics:
Non-parametric statistics do not make assumptions about population parameters. They
are also called "distribution-free" statistics since no assumption of normality is made.