# Talk:Resources

### From Panamath

## Contents |

#### How Size Controlling Works

Size control changes the average size of the dots in relation to the number of dots of each color.

Without size control, it would be possible to get most of the trials correct by simply noting which color fills up more area on the screen. A size control of 0, Non Size-Controlled, creates dots with the same average size for both sets of dots, while a negative size control creates smaller dots for the set with more dots, and a positive size control creates larger dots for the set with more dots.

A size control of -1,Size-Controlled, changes the average size of each dot set so that the area of the screen filled by each dot set is approximately equal.

If all the trials in a test used the same size control, it would be possible to get most of the trials correct by paying attention to either the average sizes of the dots or the area of the screen filled with each color. By using a combination of different size controls, we can ensure that the area and size of the dots will not reveal the correct answer. The size control number, which can be adjusted from -3 to 1 in the customize panel of the advanced settings panel, is the exponent to which the ratio of the number of dots is raised to obtain the ratio of the average sizes of dots.

### Non Size-Controlled

In a non size-controlled experiment, size control is 0. The ratio of the average sizes of the dots is calculated to be (numerosity ratio)^{0}, which means that the ratio of the average sizes of the two dot sets is 1 for any numerosity ratio. This results in total area of each color being proportional to the number of dots.\\
Sizecontrol0.png?600x400

### Size-Controlled

In a size-controlled experiment, size control is -1. The ratio of the average sizes of the dots is (numerosity ratio)^{-1}. With this setting, the total area that a one dot set fills will be the same as the other dot set, pixel ratio of the two colors is approximately 1:1.\\
In the example below, there are 5 yellow dots and 20 blue dots. The ratio of the sizes of dots is (1/4)^{-1} or (4/1). The yellow dots to blue dots average size ratio is 4:1.\\
Sizecontrol-1.png?600x400

In an anti-correlated experiment, size control is -2. The ratio of the average sizes of the dots is (numerosity ratio)^{-2}. With this setting, the total area that the dot set with less dots fills will be more than the area of the dot set with more dots.\\
In the example below, there are 5 yellow dots and 20 blue dots. The ratio of the sizes of dots is (1/4)^{-2} or (16/1). The yellow dots to blue dots average size ratio is 16:1.\\
Sizecontrol-2.png?600x400