# Score Estimator Calculations

Updated: Nov 9, 2018

# The Short Version

In the Marzano True Score Estimator, Empower provides three different methods of calculating a student's present summative score. The difference between these calculations is how they take into account (or don't) when the evidence scores were received and what the expected score (MAS) was.

The methodology that under-girds this tool is based on Dr Marzano's research and is explained in full in context in his book __Making Classroom Assessments Reliable and Valid.__

## The Full(er) Version

There are three distinct methods of calculation Empower uses to determine how a student is trending on a given Learning Target: Linear, Power Law and Average. Empower then determines which of these methods has historically been the most accurate in predicting the actual observed scores and method's final calculation is suggested as the *True Score*.

## What is a Linear score?

The basic assumption of this model is that student learning occurs in equal steps or increments. If the assessments are spaced equally apart then the line representing the growth in true score will be a straight line gradually getting higher

## What is a Power Law score?

The assumption underlining this model is that learning begins with rather large increases but those increases get smaller and smaller as the learner develops greater levels of expertise.

To calculate the Power Law Score, Empower weights the later evidences more than earlier scores.

## What is an Average score?

The Average score in Empower is a simple mean score: the sum of the numbers/ quantity of numbers.

## How does Empower calculate the True Score?

Having drawn trend lines for each of the three methods, Empower next checks the difference between the predicted scores on those lines against the actual observed scores the student received. The method with the least total difference between prediction and observation is said to be the most accurate method of prediction in this case and is thus recommended (in green) as the True Score.

A teacher can click on that score to sync the Standard Score with the suggestion, or they can make their own determination. This tool simply provides research-backed, evidence-based suggestions for a summative score.