Statistics II: Interpreting Results

In one sense, the meaning of the tests is given in their definitions. Descriptive statistics describe characteristics of the distribution of data. Inductive statistics allow you to draw conclusions about the relationship between variables: whether there is one, how strong it is, and sometimes even what it looks like.

In another sense, you have been told nothing about these statistics. Each of these tools has been developed in a context of statistical theory, very little of which has been transmitted here. This unit is no substitute for a course in statistics. To really understand parametric statistics, you should study the “normal curve” and its characteristics. To really understand significance testing, you should study probability theory. Analysis of variance and correlation are complicated enough that an entire course could easily be offered on the variations commonly used with either one of them. For example, this unit has not touched on curve-fitting, multiple regression, causal modeling, factor analysis, canonical correlation, or analysis of covariance.

There is another sense in which the discussion here is lacking: I have presented the statistics in their basic form. Almost all of them have corrections which must be applied in special circumstances. Correlation requires that the data be normally distributed; there are some techniques for loosening that requirement. Adjustments like these are the topics of courses in statistics.

The purpose of these two units on statistics is to provide you with a basic framework for doing statistical analysis. If you have already taken a course in statistics, you can make the adjustments in the formulas in the template as circumstances dictate. If you have not studied statistics yet, there are several good references listed in the bibliography.

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