6 January 2012

## Should students calculate?

At an NCTM conference session on teaching statistics I suggested that there was no point in teaching how to calculate a standard deviation. It caused a somewhat heated response, mostly in opposition, but it did get us thinking. Similarly I have suggested that using the graphical method of Linear Programming is not helpful for most students, with similarly mixed response. The paper was rejected by reviewers. Each of those issues can have a post all of their own. What I want to discuss here is when calculation is useful, and when it isn’t. Type of student and purpose of the […]
3 January 2012

## The meaning of the mean

Here is an exercise you might like to try on a class or individual, when introducing the mean. I have found it interesting and enlightening for all parties, especially those who think they know everything. Dr Nic: Tell me what a mean is, as if explaining it to someone who doesn’t know about statistics. Student: It’s an average. Dr Nic: Correct, however you haven’t really increased my understanding with that description. Student: It is what you get when you add all the numbers together and divide by the number of numbers. Dr Nic: That is a correct description of how to calculate a mean. Still […]
28 December 2011

## Re Solutions

In this time of New Year resolutions I will post re solutions. ;)* In mathematics the solution is the answer. Examples: x=42. Theta is 57 degrees. The price has increased by 15%. In statistics a solution provides something we can be reasonably sure of. Examples: We are 95% confident that the price of a house increases by between \$5,000 and \$7,000 for each extra bathroom, all other things being equal. The margin of error is 3 percent. There is evidence that more men prefer milk chocolate than dark chocolate. What is called a solution in operations research could be called an […]
27 December 2011

## Templates for statistical reports – spoon-feeding?

Here is the poll for today. Indicate what you think, then read what I think. Reporting the outputs of statistical analysis is tricky. It is not easy to be both correct and readable. There are so many nuances that can make a seemingly correct statement incorrect. For example when reporting the R-sq value from a regression analysis, I have seen it written that “temperature explains 63% of sales.” This is almost correct, but should read “temperature explains 63% of the variation in sales.” There is a subtle but important difference (which can be the subject of another post!) For many […]
21 December 2011
Understanding
Mathematical understanding is not the only kind of understanding. Cobb and Moore (1997)
20 December 2011

## Statistics for all

Let’s start with a question. Please answer it now before you read any further! Statistics, like Operations Research, is a mathematical science. However people can be intelligent consumers of statistical analysis without having to use mathematics. The statement in the box above is false. Often statistics is taught by mathematics teachers, who understand the mathematical aspects of statistics, but may never have dirtied their hands with real data. They teach the mechanics of calculating the values of standard deviations and confidence intervals, intending that this will lead to understanding. Unfortunately many of their pupils do not gain understanding from the application […]