What methods did we employ in this experiment?

On each trial, you adjusted the size of an isolated green circle so that it appeared to be the same size as another circle that was surrounded by larger circles.

What do we predict participants will do? Why?

The presence of the larger surrounding circles often introduces a size illusion, so that the surrounded circle appears smaller than it would by itself. As a result, we expect participants will adjust the isolated circle to be physically smaller than the true size of the surrounded circle. By adjusting the isolated circle to be physically smaller, it will perceptually look the same size as the surrounded circle.

In the statistical analysis of the data, you carry out a one-tailed hypothesis test to determine whether you have evidence for the illusion. That is, you are looking to see if you have evidence that the matching sizes are smaller (on average) than the true physical size (20 pixels in radius). The null hypothesis is

H0: = 20.

and the alternative hypothesis is

Ha: < 20.

A one-tailed test is appropriate here because we know the illusion exists in most situations.

How robust is this effect? Are there limits to this effect?

Most people will probably reject the null hypothesis, but it will depend on how strong the illusion is for you personally and how much variability is in your responses.

Formulas

To calculate the t test statistic, you need to first calculate the mean and standard deviation of the matching circle radius scores. This is done in the first three questions.

The standard deviation is used to calculate the standard error of the mean

sX=sn.

Now compute the t test statistic

t=X20sX,

which has degrees of freedom df=n-1.

The number of trials:

(Your answer must exactly equal the correct value.)

The mean matching circle radius:

(The difference between your answer and the correct value must be less than 0.01.)

The standard deviation of the matching circle radius:

(The difference between your answer and the correct value must be less than 0.01.)

Standard error of the mean:

(The difference between your answer and the correct value must be less than 0.01.)

t test statistic:

(The difference between your answer and the correct value must be less than 0.01.)

degrees of freedom:

(The difference between your answer and the correct value must be less than 0.01.)

p-value for a one-tailed test:

(The difference between your answer and the correct value must be less than 0.01.)

Do you reject the null hypothesis?:

Trial Matching circle radius (pixels)

1 22.8

2 26.0

3 24.3

4 22.4

5 25.8

6 19.8

7 26.7

8 22.0

9 21.3

10 18.9

11 22.4

12 22.2

13 23.2

14 18.6

15 24.2

16 21.8

17 19.8

18 22.5

19 22.4

20 22.7