# Z-Score Equating Calculator

Welcome to the Z-Score Equating Calculator! Follow the steps below to equate your test scores based on the first test as the reference.

**Download the example file:**Click here to download the example file and follow these steps to prepare your data:- Open your dataset in Excel.
- Ensure that each test score is in its own column, with the first column being the reference test, and each participant's scores are in a separate row.
- Save your file as a CSV (Comma delimited) (*.csv).
- Open the saved CSV file in Notepad to copy the comma-separated values.

**Paste Your Data:**After copying your comma-separated values, paste them into the textarea below.**Generate Table:**Click the "Generate Table" button to view your data in tabular form.**Calculate Equated Scores:**After generating the table, click the "Calculate Equated Scores" button to get the result. The resultant equated scores will then be presented in a new table format, where all test scores have been adjusted in relation to the reference test.

## Z-Score Equating

Z-Score Equating is a statistical method used to standardize scores from different assessments to a common scale, allowing for direct comparison (Kolen & Brennan, 2004). This technique is often used in educational testing when equating test scores from different versions of an assessment.

Equating adjusts for any differences in difficulty across tests, ensuring that scores represent the same level of ability regardless of the test form. Z-Score equating involves transforming the scores into a distribution with a mean of 0 and a standard deviation of 1, also known as standard scores or Z-scores.

It is crucial in educational settings to ensure fairness and accuracy when comparing results from different test forms, especially when the tests have multiple forms or are administered at different times.

The formula for calculating a Z-score (\( Z \)) for a given raw score (\( X \)) is expressed as:

\[ Z = \frac{X - \mu}{\sigma} \]Where:

- \( X \) is the raw score to be equated
- \( \mu \) is the mean of the distribution of scores
- \( \sigma \) is the standard deviation of the distribution of scores

Z-score equating transforms raw scores so that they can be directly compared or aggregated across different test forms or administrations.

## References

Kolen, M. J., & Brennan, R. L. (2004). *Test equating, scaling, and linking: Methods and practices* (2nd ed.). Springer.