## Ratios smart and simple

June 25, 2018

Your survey asked quantities as absolute counts. But now you need to report them as percentages. Here's how to calculate ratios and correctly preserve percentages, frequencies and means:

## A simple example

Let's say you have four respondents. For each respondent, the survey asks the number of patients treated overall, and on a certain therapy specifically:

ID | S8 | Q1 | S8/Q1 |
---|---|---|---|

Respondent Id | # pts treated | # pts on GA | % pts on GA |

#1 | 10 | 10 | 100% |

#2 | 30 | 15 | 50% |

#3 | 60 | 20 | 33% |

#4 | 100 | 15 | 15% |

## Simple average percent

A simple average weights each respondent equally:

(100% + 60% + 33% + 15%) / 4 = 50%

## Ratio average percent

A ratio average weights each respondent by their denominator. It's the same as the sum of numerators divided by the sum of denominators :

(10 + 15 + 20 + 15) / (10 + 30 + 60 + 100) = 30%

## Why are they different?

In this toy example, doctors who treat more patients treat fewer patients with GA. The simple average treats each respondent equally. The simple average weights respondents by their denominator.

## Which way to go?

In this toy example the difference between the two is substantial. In practice the two are typically closer, but still you want to choose carefully.

A simple average is appropriate when you want to project to the sample of respondents. E.g. "The average respondent in our sample reported treating 50% of their Condition X patients with GA".

A ratio average is appropriate when you want to refer to the patients. E.g. "Physicians in our sample reported treating 30% of their patients with GA on average."

## See how

Protobi can calculate ratios either way, but it's especially simple to create smart ratio averages. See how in this tutorial: Calculate ratios in Protobi