Home | Clinical Café Archive | February 2003

Clinical Café by Tina Radichel, M.S., CCC-SLP, with the able help of Dr. Tsuey-Hwa Chen, Associate Director of Research

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Age and Grade Equivalents-Truly Equivalent?

February 2003 Clinical Café by Tina Radichel, M.S., CCC-SLP, with the able help of Dr. Tsuey-Hwa Chen, Associate Director of Research

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Just when you thought last month's Clinical Café column provided "all you needed to know" about normative scores, now we are telling you, "No, wait—there's more!" This month's "espresso shot" (you may need one to get through all of this!) drills into two particular normative score types—age and grade equivalents. Read on because there's more here than meets the eye!

How Age & Grade Equivalents Differ from Other Norms

Low         High	Levels of Measurement
	Nominal	Categorical
	Ordinal	Sequential
	Interval	Equal units
	Ratio	True "zero point"
Figure 1.

Age and grade equivalents are very different from other types of normative scores (e.g., standard scores) commonly available for standardized tests such as OWLS. Remember that age and grade equivalent scores are not on an equal-interval scale. (see Figure 1 for a refresher on the levels of measurement) They are at most ordinal in nature when there is a developmental sequence consistent with age/grade because they are derived from aggregated or group data with a certain degree of added subjectivity. Therefore, age and grade equivalents lack the desired psychometric properties for statistical manipulations—they are not built to add, subtract, multiply, or divide.

Age and grade equivalents provide a frame of reference for growth based on the "typical" performance (usually indicated by mean or median scores) of individuals across different ages or grades. In other words, the reference is based on aggregated information without regard to individual differences within the groups. In contrast, standard scores are transformations (linear or normalized) of individual obtained (raw) scores. Unlike age and grade equivalents, standard scores provide a frame of reference for an individual's performance with respect to his/her same age or grade peers in the sample. In other words, the reference takes into account individual differences (variation) within each age group or grade level. Here's a quick view of both types of scores:

You can see how different these two types of normative scores really are and how differently they are developed. Use normative scores such as standard scores as a measure of performance. Do not use age and grade equivalents alone for any interpretation or decision-making purposes.

How Skill Acquisition Impacts Norms Development

It is vital when developing normative data to understand how the target population (in this case, school-aged students) acquires the skills you are measuring. The rate of growth, as indicated by age or grade equivalents, then depends on that particular skill area. As an example:

In the Oral and Written Language Scales-Written Expression (OWLS WE), the acquisition of writing skills occurs most rapidly from the early ages through about age 12 or Grade 6 because writing mechanics are taught in the primary grades. However, after age 12 and Grade 6, the acquisition of writing skills occurs at a slower rate, causing the growth curve to level off. Differences in writing performance for these upper ages/grades are reflected in content, complexity, sophistication of topics, etc. See the plots below for the OWLS WE test: In Figure 2, Age Group #26 corresponds to ages 12-0 to 12-3; In Figure 3, Grade Group #12 corresponds to Fall of Grade 6. The straight lines on the graphs indicate the cutoff points for the age- and grade-equivalency norms development in OWLS WE.

Figure 2.

Figure 3.

When the growth curve plateaus, the age and grade equivalents become less discriminating. Therefore, a small amount of gain in a individual's raw score would lead to a disproportional leap in the age and grade equivalents, causing the growth in the upper extreme of the scale to be inflated (exaggerated). For this reason, the OWLS age equivalents are provided only for ages 4-0 to 12-0 and grade equivalents are provided only for Grades K to 6.0.

What This All Means

The range restriction of the equivalents does not in any way lower the validity of any other OWLS normative scores (standard scores, percentiles, stanines, and NCEs). In fact, the restriction of these age- and grade-equivalent norms adds to the validity of the test. Even though the age and/or grade growth slows down at the upper levels, individuals within each age or grade level (high or low) learn and develop at different paces. These individual differences (variation) provide a sufficient basis for deriving valid standard scores within, as opposed to between, groups throughout the entire age/grade span. Thus, you can see that age and grade equivalents are not "truly equivalent" to other normative scores that you might use on a test.

Summary

It is important to know how your norms were created! We realize that you don't get the joy (really, joy!) of working with these statistics at this depth every day, so we hope to answer some of the questions you have asked us over the years in an understandable way. Please let us know what other questions you have.

As always, we'd like to thank you for your ongoing service to people with communication needs and to remind you that we are here to support you with that effort. If you'd like to discuss this topic further, please feel free to use the SLP Discussion Center as the vehicle for an ongoing discussion with your colleagues. Should you have questions regarding these or other Pearson Speech and Language products, we welcome your phone calls at 800-627-7271 or use our web site at http://ags.pearsonassessments.com.

Here's to spring testing!