While I agree with the issues that Max Taub raises, I don't think that relying on statistics is the answer. First of all, it is certainly true that variation is important. In fact, a colleague of mine used to argue that understand the variability of natural phenomena is more important than knowing the mean values. If students look at scatter plots or histograms they can see and discuss variability and try to interpret it. But if they know their statistics they find it difficult to do this - they automatically assume that all error distributions are normal and consider only the standard deviation, no matter what the distribution looks like. In the published literature you often see serious discussions of the variance of highly skewed or bimodal distributions.
A particularly pernicious example of this is the use of normal distributions to describe data where the numbers have to be positive, like lengths or concentrations - what does it mean to use a normal distribution to describe such a variable when the distribution gives a 20% probability that the value is negative? As for correlation, do you really need a statistics course to see a relationship in a scatter plot? Max, your students will see a strong negative correlation if you show it to them. But if they know their statistics they will only be able to see a linear correlation - in fact, I earlier posted an example of a scientist who presented a clearly nonlinear correlation to a meeting and not only claimed it was linear, but used an incorrect statistical test to prove that it was linear! Statistics has the strange effect of making people blind to the obvious. Bill Silvert ----- Original Message ----- From: "Max Taub" <[EMAIL PROTECTED]> To: <ECOLOG-L@LISTSERV.UMD.EDU> Sent: Wednesday, November 02, 2005 11:32 PM Subject: Re: curriculum question > While statistical (hypothesis) testing may be overused or misused among > professional ecologists, I think that a strong introduction to > statistics is essential for undergraduates. Few undergraduates, prior to > taking a statistics course have thought about how important variation > is, or are aware that there are ways to quantitatively describe > variability in measurements. Students are also naively inclined to take > ANY difference among the means of experimental groups as meaningful. > Hypothesis testing can help break them of this habit, and this, I would > say, is a mighty important lesson to learn about interpreting > experimental (or observational) results. > I also value being able to use the vocabulary of statistics in my > classes; I want it to mean something to students if I say there is a > strong negative correlation between two variables. So I am one who is > strongly in favor of statistics in the undergradute curriculum- early > and often. > > Max Taub
