bodmas blog

http://www.openquals.org.uk/

• Central Limit Theorem – you can roll up to 5 dice up to 10000 times and plot the frequency distribution of the total score. As you ‘roll the dice’ a second and third time, the cumulative score is shown so that the Normal distribution can emerge through repeated samples. Nice touch – imagine using this on an interactive whiteboard while asking questions from a well-primed group…
• Confidence Interval of the mean – you get multiple samples of 20 drawn from the same normal distribution. The applet then plots the data and the confidence interval. See how many CIs don’t overlap…. You get a choice of probability level (90%, 95% and 99%).

Jutta Degener’s What is good hypertext writing essay is still relevant 7 years later, even though Web pages tend to look more like interfaces and less like documents.

The rest of her homepage looks sort of antique but still interesting. I like the paintings.

” It never occurred to me that the techies writing the software would try to use the computer to simulate paper Ôø? actually not even paper, but paper under glass. ” quoted in Grand Text Auto blog

Ted Nelson suffered character assasination in a well known Wired article about Xanadu. Anyone who can dismiss Word / MS Xp as a Paper Simulator is fine in my book. When you think about it, modern PCs and application software do spend a lot of time emulating paper! I have always preferred MS Excel’s tabbed worksheets as an interface to Word’s Kerouac like scrolling teletype roll.

The image above is quite deliberately deep-linked to a server that Nelson has specified as a ‘Transquoting’ source. Nice idea, but alas the official server is dead, so I cheated and linked to a server that really does have the picture.

Ted Nelson’s four maxims…

• most people are fools
• most authority is malignant
• God does not exist
• and everything is wrong

” The distribution of an average tends to be Normal, even when the distribution from which the average is computed is decidedly non-Normal “.

“Thus, the Central Limit theorem is the foundation for many statistical procedures, including Quality Control Charts, because the distribution of the phenomenon under study does not have to be Normal because it’s average will be.”

From Charles Annis’ page on the central limit theorem

A nice simple illustration of the distribution of the means of samples of 2, 3, 4 and so on for a variable drawn from a uniform distribution with an animated gif at the bottom of the page to make the point.

Take on the world with a stack of 5 by 3 index cards – one way to get Web sites sorted before clicking on the Dreamweaver icon when building a moderately complex Web site.

This page describes card sorting techniques to help plan Web sites. Ideally card sorting can help define content – not so much functionality. You need to use a consistent granularity (does each card stand for a page, small section or main division of a Web site). You need between 30 and 100 cards – quite a large site.

Once the cards have been sorted, you might want to ask the sorters to walk through a typical task to verify the information domains.

All of this lends itself admirably to a lesson on information architecture for 16-19 student who are reluctant to summarise and write information.

Histograms are meaningless for datasets smaller than about 500 items – you will be better off using a dotplot. I think that the ‘error bar’ for each bar of the histogram can be approximated by the square root of the frequency so that a bar with a frequency of 36 could have a standard deviation of ±6 and so could be within a range of 24 to 48 two thirds of the time if a series of different samples were taken.

A simulation of the histogram (and frequency distribution) for samples of 100 and 1000 drawn from a normal distribution can show how the bars bounce around much less with the larger frequency. Excel has functions (rand(), countif()) that make it possible to make a spreadsheet that will display a new histogram each time you press F9. I cheated by approximating a normal distribution by adding together 10 lots of the RAND function for each cell. I then picked a scaling that gave me a mean of 160 and a standard deviation of 8 or so. This approximates to female height but with rather a high standard deviation.

• Download the Excel 98 spreadsheet (52 Kb) Works on Excel 97 upwards and OpenOffice
• There is a very useful Java applet that allows you to vary the sample size over a larger range, and vary the mean and SD dynamically.
• There is a nice Javascript page where you can copy and paste data into a form, click a button, and calculate a range of summary statistics. One for the intranet!