Angular analysis...

Here are our data from our blind spot measurements

We can look at these in a Histogram - we sort the angles into size ranges and plot how many are in each range. If we make a sensible choice for the size ranges we can see where most of the measurements lie and how spread out they are (too many small size ranges and we just see the individual measurements like in the list: too few and they all end up in the same range and it doesn't illuminate our data...)

This looks like there is a typical value in the 15-20 degree group and some spread about that value. This is quite normal for many properties measured in nature where values are 'randomly' spread around a central value. The spread can be due to natural variation (like for example peoples height) and also due to measurement error.

We can fit a Normal distribution - a mathematical characterisation of the variation - which gives a mean and a standard deviation parameter. The mean is the average value and the value we would Expect to find if we measure someone new. The standard deviation is a measure of how spread out the measurements are. Most (about 95%) values are within two times the standard deviation of the mean value. In the next figure you can see the red curve which is the fitted distribution showing the relative Likelihood of a given value being measured.

Of course, the more measurements we make, the more Confident we can be about these values. In fact we have quite a small Sample (only 9 of you recorded measurements) and so the mean value is uncertain. We can estimate how uncertain the estimate of the mean is (!), and the green curve shows the likelihood of the true mean angle taking different values.

The mean angle of our blind spot is therefore found (with 95% confidence) to lie between 16.2 and 21.5 degrees horizontally from the line of central fixation.

This is bigger than Wikipedia tells us (if you look up blind spot on Wikipedia it gives 12-15 degrees. Why are our numbers different?)

If you look closely, the wikipedia entry comes from a US military spec document for the design of optical displays and equipment that needs to be viewed so is a rather specific source for the angle. Another reference (http://www.ncbi.nlm.nih.gov/books/NBK220/ - also US) gives 12-17 degrees.

Possible reasons why our number is different include...

1) Errors (did we measure it badly?)

2) Bias due to not considering how big the blind spot is (ie did we always measure the outer limit of the blind spot which is about 5 degrees wide?)

3) Random discrepancy due to our small sample size (we just happened to measure eyes with big angles to the blind spot...)

4) Wikipedia's source reference is wrong or untypical?

5) We are both right but UK children's eyes have a bigger angle that US soldiers eyes (they are changing as we grow? or US soldiers exclude people who can't see perfectly so form a biased sample? or US soldiers are mostly men whereas we are fairly equally boys and girls? or ...)

We could test some of these ideas by measuring a bigger sample of eyes, perhaps improving our techniques, sampling boys and girls separately, and also recording how old the eye is that we measure...