# Understanding Estimated Relationship

## Estimating Score Conversions for ACT Composite and SAT CR+M+W Scores

Two concordance tables are jointly available from ACT and the College Board. These concordance tables only relate the ACT Composite Score to the SAT sum of Critical Reading and Mathematics scores and the ACT Combined English/Writing Score to the SAT Writing Score.

ACT recognizes the fact that some institutions may want to relate the ACT Composite score and the SAT total score (Critical Reading+Math+Writing). As a further service to educators, ACT has developed an Estimated Relationship Table which addresses this need. There are several advantages institutions should consider in using this table instead of other methods that require a two-table approach:

1. ACT's Estimated Relationship Table is simple and easy to use. While other methods require the user to refer to two separate tables and calculate the sum, the Estimation Table requires look up of only a single table.
2. ACT's Estimated Relationship Table will work for all institutions and students. Because the ACT Writing Test is optional, other methods that are dependent upon the availability of an ACT Writing Test score will not work for all students since many students with an ACT Composite score may not have an ACT English/Writing score.
3. ACT's Estimated Relationship Table is more accurate. A two-table approach may involve double counting or double weighting the ACT English test. In addition, since all concordances have error associated with them, it is generally better to utilize a single table. Since ACT's Estimated Relationship Table is based on a single table, it contains only the error associated with that concordance relationship. Methods that involve two distinct concordance tables contain the errors in both relationships. The amount of error in the score conversion will undoubtedly be larger than that based on a single concordance relationship.

The SAT CR+M+W total score can be related to the ACT Composite using the following equation:

Estimated SAT CR+M score = (SAT CR+M+W score +15) / 1.5

Round this value to the nearest 10, and then use the concordance table to get the estimated ACT Composite score.

The ACT Composite can be related to the SAT CR+M+W scale by first converting the ACT Composite score to the SAT CR+M scale using the concordance table, and then using the following equation:

Estimated SAT CR+M+W score = (1.5 x SAT CR+M score) – 15

This number is rounded to the nearest 10.

Multiplying by 1.5 puts the value on the correct scale. The subtraction of 15 points is done because SAT W scores are lower, on average, than the SAT CR and SAT M scores. For example, in the 2007 College Board National Report, the average SAT W score is 494, while the average SAT CR score is 502 and the average SAT M score is 515. The average difference is about 15.

For example, suppose a student has an SAT CR+M+W score of 1500. Adding 15 and dividing by 1.5 gives an estimated SAT CR+M score of 1010. Using the table, we get an estimated ACT Composite score of 21.

Alternatively, suppose a student has an ACT Composite score of 21. Using the concordance table, the comparable SAT CR+M score is 990. Multiplying by 1.5 and subtracting 15, we get 1470.

The extent to which this conversion is accurate depends on the extent to which the SAT CR+M score can be used to predict the SAT CR+M+W score. The College Board Total Group Profile Report: 2007 College Bound Seniors (The College Board, 2007) can be used to get the standard deviations for each test, and correlations between tests are given in the report Validity of the SAT for Predicting First-Year College Grade Point Averages (Kobrin, et al., 2008). Using these values, the correlation between the SAT CR+M score and the SAT CR+M+W score is about .98, indicating that the conversion should be quite accurate.

References:

• Dobrins, J. Patterson, B., Shaw, E. Mattern, K, and Barbuti, S. (2008) Validity of the SAT for Predicting First-Year College Grade Point Averages. (College Board Research Report No. 2008-5). New York: The College Board
• The College Board. (2007) Total Group Profile Report: 2007 College Bound Seniors.