What methods did we employ in this experiment? On each trial, two circles were shown. Your task was to adjust the size of one circle until it appeared to match the size of the other target circle. The size of the target circle varied across trials.

The independent variable in this experiment is the size of the target circle. The dependent variable is the size of the matching circle.

What do we predict participants will do? Why? Not surprisingly, the mean size of the matching circle should be pretty close to the true physical size of the target circle. The mean is a good measure of the accuracy of someone matching the target circle.

What is more interesting is that the deviations from the mean tend to get bigger as the physical size of the target increases. This is a measure of the precision of someone matching the target. Precision and accuracy do not have to go together. Precision can be measured with the standard deviation.

The term "Weber's Law" refers to an empirical observation that the standard deviation tends to increase linearly with increases in the physical size of whatever is being measured. In this experiment, the standard deviation should be larger as the diameter of the target circle increases in size.

How robust is this effect? Are there limits to this effect? Weber's Law holds for many different stimuli, tasks, and conditions. You may not find the expected pattern of results if you do not really try to match the circle sizes. Not trying to do your best may introduce so much variability from trial to trial that the effects of Weber's Law will be impossible to detect.

Formulas To calculate the standard deviation we will use a formula that makes it clear that the standard deviation is similar to an average distance from the mean value. There are other formulas that are easier to calculate but are not as easy to understand. To begin, you need to calculate the mean value of a set of scores:

X=ni=1Xin, where n is the number of scores.

The mean is then used to compute the sum of squares, SS, which is the sum of the squared deviations for each score and the mean.

SS=i=1n(XiX)2. To compute the standard deviation, we divide the SS by n-1 and take the square root:

s=SSn1 You will use these formulas separately for each of the target size conditions. It is important to sort the trial-by-trial data according to the target size. If you mix together trials from different conditions, you will get incorrect answers.

The mean of matching circle radius values when the target is 10: (The difference between your answer and the correct value must be less than 0.01.) Sum of squares for when the target is 10: (The difference between your answer and the correct value must be less than 0.01.) The standard deviation of the matching circle radius when the target is 10: (The difference between your answer and the correct value must be less than 0.01.) The mean of matching circle radius values when the target is 30: (The difference between your answer and the correct value must be less than 0.01.) Sum of squares for when the target is 30: (The difference between your answer and the correct value must be less than 0.01.) The standard deviation of the matching circle radius when the target is 30: (The difference between your answer and the correct value must be less than 0.01.) The mean of matching circle radius values when the target is 50: (The difference between your answer and the correct value must be less than 0.01.) Sum of squares for when the target is 50: (The difference between your answer and the correct value must be less than 0.01.) The standard deviation of the matching circle radius when the target is 50: (The difference between your answer and the correct value must be less than 0.01.)

Trial	Target circle radius (pixels)	Matching circle radius (pixels)
1	10	11.1
2	30	30.4
3	30	31.4
4	50	50.9
5	50	53.5
6	50	55.3
7	50	52
8	10	10.2
9	30	34.9
10	50	49
11	10	11
12	50	52.5
13	50	52
14	10	11.7
15	10	10.3
16	10	11.4
17	10	10.5
18	30	34.5
19	10	11.6
20	30	29.3
21	10	12.2
22	50	46.4
23	30	32.8
24	30	31.1
25	50	53.4
26	50	53.1
27	30	34.8
28	30	33.9
29	10	13.3
30	30	30.6