Basic Statistics for dentists

Really, really basic stats. Enough to let you interpret data and perhaps to think about how to present your own data. These notes are intended only as a guide. Understanding statistics is your responsibility.

Daily Mail headline MMR killed my daughterWhy do dentists need stats at all? Because data without statistics are meaningless. Consider the word meaningless: MEANING LESS; devoid of meaning. To say that a drug or intervention caused a 50% increase in survival rate of a disease sounds fantastic and is perfect for a tabloid headline but, without any statistical indication of how good the data are, the statement is worthless. The MMR "scandal" in which a link was made between immunisation and autism is a perfect example of a poorly designed study that yielded meaningless results that nevertheless caused great alarm when the data were reported in the press in the complete absence of objective statistical analysis. Nobody with any biomedical or statistical understanding would have been in the least impressed or worried by the original paper. Tragically, this argument still rumbles on and the impact of the misinformation from newspapers and elsewhere on vaccination programmes have effectively reintroduced measles into this country.

What follows are (almost) maths-free definitions of all the key statistical terms that I think you might need, plus a few others that you need to know about in order to make sense of the rest. Writing in this way is always a compromise between giving too much information (and so losing the message) and missing things out or simplifying to the point of nonsense. Please let me know if you think I have missed anything or generated too much nonsense. Links are provided to relevant articles in Wikipedia and elsewhere for anyone who wants to know more.

Definitions: Data, Probability and the Null Hypothesis

The Normal Distribution (and friends)

Presenting Data

Data should be presented in such a way as to make clear the observation and the degree of statistical certainty of the observation. there are various ways in which this may be achieved. Mean +/- SEM (n=number of observations) is one common way. Odds Ratios and confidence intervals are another. The important thing is to use the most appropriate technique for the data.

Statistical Tests

How to perform statistical calculations and tests

If you are really interested in what underlies this brief run through elementary statistics then follow any of the links into Wikipedia and go from there. The people writing these articles know far more about statistical processes than I do. So far as calculating Standard Deviation etc. from data..... look closely at your calculator.... the σ and σ-1 buttons will calculate Standard Deviation based on normal or t distributions respectively. Better yet, use MS Excel (the spreadsheet...). Enter data into (for example) column A and then use the basic statistical tools. To calculate the mean of data contained in rows 1-20 enter "=average(A1:A20)" into any empty cell. Similarly "=stdev(A1:A20)" returns standard deviation and "=count(A1:A20)" returns the number of observations..... Always start a formula in Excel with "=". Excel will calculate (some) probabilities for you if you ask it nicely. A simpler alternative are the on-line statistical testing packages. The one offered by GraphPad is particularly good. If all you want is a simple t-test then try my home-grown software. I've compiled the most commonly used formulae in a simple spreadsheet.

Laboratory based experimental biologists (and physicists) are suspicious of complex statistics because a) we don't understand them and b), to paraphrase Ernest Rutherford, "If your experiment needs (complex) statistics, then you ought to have done a better experiment". Non laboratory based disciplines (most social sciences, epidemiologists etc.) depend more heavily on statistical analyses because they can't easily perform experiments.

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