# Can CGIs and CGPs be averaged, aggregated, or compared across grades, subjects, and seasons?

Document created by Community User on Jul 28, 2016Last modified by Community User on Jun 23, 2020
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Question
Can CGIs or CGPs be aggregated, averaged, or compared across test seasons? Can you aggregate the CGIs or CGPs for a mixed group of students across different grade levels?

## Can I compare the conditional growth index (CGI) or conditional growth percentile (CGP) across grades, seasons, and subjects?

Yes. Since the CGI and CGP are standardized scores, you can compare them across grades, seasons, and subjects. So if a 3rd grade student has a CGP of 25 in reading, and a 5th grade student has a 75 in math, we can fairly say that the 5th grade student had more growth in math compared to the norm group than the 3rd grade student did in reading.

## Can I average the students' CGI or CGP?

You can average the CGI (also known as a z-score or a standard score), however, you should not average the CGP. This is because students in the same percentile can have different growth, and the difference in growth between two adjacent percentiles can be different depending on whether the percentiles are towards the middle (50) or the extremes (1 or 99).

For example, let's say you have two students: one with a CGP of 50, and another with a CGP of 99. If you average their CGP, you get the 75th percentile. Now, let's look at their CGI. Let's say the student with a CGP at the 50th percentile has a CGI of 0 - meaning the student met their growth projection exactly - and the student with a CGP of 99 has a CGI of 2.3, which does fall within the 99th percentile. Their average CGI is 1.15, which falls in the 87th percentile - 12 percentile ranks higher than averaging their CGP. Let's say the student with a CGP of 99 has a CGI of 4, which is incredible growth, but also falls within the 99th percentile. In this case, the average CGI is 2, which falls in the 98th percentile - 22 percentile ranks higher than averaging the CGP. So we can see how averaging the CGP masks and flattens the difference between students between and within percentile ranks.

In summary, you can average the CGI for a group of students to get a valid CGI for the whole group. This is one of the advantages of the CGI, a standardized metric also known as a z-score. However, you should not average the CGP to get the CGP of a group.

## What types of groups would it make sense to average CGI for?

You could average CGI for any group for which you were interested in measuring and tracking student progress. For example, you can average the CGI for genders, racial or ethnic groups, high achievers, low achievers, etc. The smaller the number of students, the greater the variability will be, and your calculation will be more prone to outliers. A minimum of 10 students is necessary to draw conclusions from the average of a group, but we recommend that you use 20 or more students if possible.

## What is the best way to aggregate grade levels for a full school-wide CGI?

If you want to find the average growth for students in a school, then you can average the student CGI scores. For example, if your students have an average CGI of 0.5, you can say that on average, students in your school showed growth that was a half of a standard deviation above average (above the growth norms).

If you want to see how the growth of groups of students at a grade level compares to the growth of other groups of students, then you should use the school norms. In this instance, don't aggregate across grades; we recommend reporting this information at the grade-within-school level.

## How can I calculate the CGP for a group of students?

The Student Growth Summary report shows the CGI and CGP for groups of students based on the 2015 school norms.

To get the CGP based on the student norms, you can perform this calculation with help from Microsoft Excel:
1. Calculate the average CGI of the group of students.
2. In Excel, enter the following formula in a cell: =NORMSDIST(Average CGI from step 1)*100
3. Round the result to the nearest integer to get the CGP.