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# Principles, Properties and Assumptions of Statistical methods

## Results are only as good as the assumptions

The pages (listed left)These pages  summarize the properties and assumptions of various statistical methods, ranging from simple summary statistics, statistical tests & intervals, to use of appropriate study designs, and generalized linear modelling. These short summaries were extracted from our statistics for biologists course.

Each of these online pages summarizes the purpose of a statistical procedure, and the circumstances under which its use would be appropriate.

These pages also list the assumptions made by each procedure, ranging from sampling assumptions, and independence of errors, to the distribution of errors - and the additivity of effects. How these assumptions are tested for each procedure is covered in the 'how to do' pages, via the How To  link at the top of each page.

Those 'how to' pages are, in essence, the bare bones of those statistical procedures. You may decide that this is all you need to know to design your research and analyse your data - those procedures and formulae are what conventional statistics courses teach biologists. Unfortunately, those conventional courses teach you nothing about how those statistics can mislead when their assumptions are unreasonable, nor do they teach you what to do about it.

 "Almost every student of probability and statistics simply memorizes the rules. Most ... select their methods blindly, understanding little or nothing of the basis for choosing one method rather than another. This often leads to wildly inappropriate practices, and contributes to the damnation of statistics." Julian Simon and Peter Bruce (1999) Probability and Statistics the Resampling Way: Stats for Poets, Politicians - and Statisticians.

There are few experiences more frustrating than having your research rubbished by statistical referees. Which is why it is important to know what lies behind those formulae, to understand the underlying models, and predict their behaviour when applied to real situations.

Instead of simply memorizing the rules and recommendations listed in these summaries, we can strongly recommend using simulation models - the so-called resampling approach to statistics. They are probably the only way you really will understand what a P-value is all about, and what a confidence interval really means, and why some conventional rules produce horribly misleading results.

Lastly, we must emphasize, these online pages only summarise the key points. Our book looks, in rather more depth than usual, into the principles and practice of study design. We cannot claim to illuminate you on all the various approaches and philosophies involved in statistical design and analysis - but at least we make it clear when there are differing views, and assess the strengths and weaknesses of the different approaches.

For full details see: Dransfield R.D., Brightwell R. (2012)   How to Get On Top of Statistics: Design & Analysis for Biologists, with R. InfluentialPoints, UK. [full text]