## Check Reducibility

The CheckReducibility Class in Quorum implements suitability checks that are needed before factor analysis to reduce the dimensionality of large datasets. It checks that the correlation between variables are about equal or the sphericity of it.

The Goodness of Fit tests if the frequency distribution was different from the expected frequency distribution. The Test of Independence tests if two variables are related to each other.

Formal Test | Action in CheckReducibility Class |
---|---|

Bartlett's Test of Sphericity | CheckReducibility |

### Check if Variables are Correlated

#### Technical Test Name: Bartlett's Test of Sphericity

A Bartlett's Test of Sphericity is used to determine if the correlation matrix is significantly different from the identity matrix. Essentially, if the correlation matrix is the identity matrix, then a Principal Component Analysis cannot be run to reduce the dataset since the variables will be uncorrelated.

Let's say we have a lot of different things like fruit and you want to put them all together based on their characteristics. We can group apples, bananas, and oranges together because they are sweet. Then we can group zucchini, cucumbers, and peppers together because they are vegetables.

Let's say we have a lot of different things like fruit and you want to put them all together based on their characteristics. We can group apples, bananas, and oranges together because they are sweet. Then we can group zucchini, cucumbers, and peppers together because they are vegetables.

This test checks if our data is suitable for factor analysis. Factor analysis is trying to group things together that are similar to each other. But before we can do that, we have to check if our data is good enough which is where Barlett's Test comes in.

It checks if our data is spherical or if all of our data is equally related to each other. If our data is not spherical, then that means some data is more related to others and is not really good enough for factor analysis. Below is an example of how to run this test in Quorum.

Example of Bartlett's Test of Sphericity

## Code Area

## Output Area

## Next Tutorial

In the next tutorial, we will discuss Check Reducibility Strength, which describes how to check the reducibility strength of your data.