a) Touch the blue words, "Discrepancy Calculator" to switch views.

b) Slide the report screen to convenient locations if you are cramped for viewing space.

c) Notice how selecting a test changes its position in the list. The most recent selections appear at the top of the list.

d) Be aware, if you change a reliability coefficient, it will affect the reporting. Changes you make will be permanent.

e) Use the slider as an alternative to the keyboard for inputting test scores.

f) Touch the Android action menu icon at the bottom of the screen (the icon made up of several short parallel horizontal lines, or little gray squares, depending on whether you use the ice cream sandwich version or jellybean version of android) to choose the 'Reynolds method' or the 'Modified Reynolds method' for calculating the severity of the discrepancy. The default is the 'Reynolds method.' Both are explained in greater detail in the mathematics section.

Reliability Numbers and How to Change and Save Them

Decimal numbers  appear in editable boxes to the right of where you tap in the student's cognitive and achievement standard scores. The numbers that appear are called split-half reliability coefficients and they are some fraction less than 1.00. These numbers are saved in the test lists and generally should not be changed unless you have good reason to do so. Each test has a statistical reliability, indicating the probability that a particular score for a test is actually a real indication of what the test measures, and not just random chance. These probabilities are used in computing the regression formula and determining if the difference in two scores is significant. You might change values if you find better data in a test manual, or if a test publisher reports changes. You can do this easily by tapping in the box and typing in the same way you enter student scores. When you do this, the little red square next to the Calculate button lights up and the word, "Save" appears. This is the new SAVE button introduced in v7 and when you press it, all the current reliability coefficients get permanently saved. If you dont save changes, when you power up your tablet you will revert back to the previous values.

Restore Default Reliability Values

If you start playing around with reliability values you will affect the reporting of severe discrepancies. If you get them really messed up, you can restore the original default values by going to the Android Action Menu (see item f, above) and choosing "Reset Test Lists." This action also initializes new tests that have been added in program updates.

How to Interpret Results

After pressing 'Calculate' the Discrepancy Calculator will tell you if the difference in scores between cognitive and achievement is statistically significant. In other words, is the difference in score real, or could it be better explained by chance? If Discrepancy Calculator says the discrepancy is significant it means you can be at least 95% certain the difference is not due to chance.

If a discrepancy is NOT significant we are unable to discern anything meaningful from the test scores about the possibility of a learning disability. There is just not enough difference in the scores to be able to say the difference wasn't caused by random chance.

If a discrepancy IS significant, then the app computes an expected achievement score based on the reported IQ score. The app takes regression, or deviation to the mean into account when computing an expected score.

Here is a brief explanation. Suppose Jenna scores really high on her IQ test, 120, for instance. She is way above average! Suppose Mary scores really low on her IQ test, 80, for instance. Mary really struggles in school. The odds are if Jenna and Mary took the IQ test again, Mary would do a little better, and Jenna would do a little worse. In other words, their scores would 'deviate' somewhat, and both scores would be a little closer to the mean, or average score of 100.

That deviation is what Discrepancy Calculator takes into account when it computes an expected achievement score. In a perfect world, if Jenna scored 120 on her IQ test, she would also score 120 on an achievement test, but it is not a perfect world. When we take regression to the mean into account, we expect that Jenna's achievement score will probably be a little lower than her above average IQ score. Mary's achievement score, on the other hand, would be expected to be a little higher than her IQ score, which was below average. The 'farther away' a score is from the mean, the more deviation there will be.

Next, Discrepancy Calculator computes a 'critical threshold score.' This is the achievement score below which a child would be deemed to show a 'severe' discrepancy. The critical threshold is based upon the expected achievement score and test unreliability, or the margin of error within a test. Taking test unreliability into account increases our confidence that we do not mistakenly rule out a severe discrepancy because of error in our measures. The Discrepancy Calculator is set to a confidence level of 95%.

If the actual achievement score is less than the computed critical threshold, then we have a severe discrepancy. Discrepancy Calculator displays a message to this effect and it is printed in red. You will also see the student's IQ and achievement scores fit onto a bell curve if you tap on the blue words, "Discrepancy Calculator" to switch views. The IQ score will appear as a vertical blue line. The achievement score will be shown as the 'lowest nth percentile.' 

A percentile is a ranking showing where the student would fit in comparison to other students. If a child is in the 38^th percentile, it means the student's performance is better than 38 percent of his or her peers. 50^th percentile would be perfectly average – 50 percent of peers scored higher, 50 percent scored lower. A percentile rank of 98 would mean that the student performed better than 98 percent of all others in the peer group.

One method an education team uses to decide if a student has a learning disability is to look at a discrepancy that may occur between IQ and achievement scores. If it is severe, the team might suspect a learning disability if team members cannot account for the discrepancy through other factors. It is important to note that a discrepancy alone does not mean there is a learning disability. It is an essential component, but the education team must rule out other factors such as other types of disabilities or the possibility that a student has not received adequate instruction. 

In addition, eligibility for special services also depends on there being what is called an adverse effect. That is, in addition to there being a disability, does Mary also do poorly in school? A percentile rank on individually administered, nationally normed achievement tests is one gauge used by school districts to confirm an adverse effect. State special education regulations define the performance level below which it would be considered an adverse effect. The state in which I teach defines the level as being 15th percentile or less, or one standard deviation below the mean.

New in Version 6 of Discrepancy Calculator is a choice of two methods for calculating discrepancy. The original 'Reynolds' formula was developed by the US Department of Education, Special Education Programs Workgroup on Measurement in 1983. This formula was later modified by the Utah State Office of Education and Utah State University. Their 'Modified Reynolds' formula is offered as an alternative to the original. Which formula should you use? The Reynolds formula is the original proposed by the US Dept. of Education. The modified form uses a one-tailed test of significance for the difference in scores instead of the original's two-tailed test, making the modified Reynolds formula a more appropriate choice for your analyses.

A Note About Correlation Estimates

One piece of information that is vital to Discrepancy Calculator in order for it to decide if there is a severe discrepancy between IQ and achievement is the correlation between the two tests. A correlation is a measure of how likely one test score will predict the second score. A perfect correlation would mean the two scores would always be perfectly equal. A less than perfect correlation means there is a probability the second score will be somewhat different from the first. 

Test publishers sometimes provide correlations with other tests, which they obtain by analyzing the scores of people who take both tests. Lacking a publisher's correlation (which sadly is often the case), it is possible to estimate a correlation  if you know the reliability of each test. Accurate correlations -- or estimates -- are important to Discrepancy Calculator because they affect the computation of the expected achievement score and the critical threshold score used to determine if a discrepancy is severe.  This becomes especially critical when a student's scores are borderline between a severe discrepancy or not. 

There have been a few different methods offered by mathematicians for estimating correlation. Discrepancy Calculator lets you choose from among five different methods that employ different formulas.

Select a Correlation Method

Tap the cog wheel or gear icon in the upper left corner to open a selection menu for the different estimation methods. Discrepancy Calculator names the methods by referring to the actual mathematical formula used in the app to calculate the correlation coefficient between the two tests.

To select an estimation method, tap on the desired formula. Which one should you use? The formulas, 

Sqrt((r1 * r2)/2) 

and 

(r1 + r2)/(1+r1+r2) 

produce correlations that are close to publisher's correlations. They produce results that are generally very close to the results obtained when a publisher's correlation is entered.

Be aware that any value you type in the correlation entry box will make Discrepancy Calculator use that value as the test correlation and NOT estimate one for you. Since it is so easy to jump back and forth between estimated and publisher's correlations, you can sometimes lose track of which one you are using. Any report generated by Discrepancy Calculator will tell you what the correlation is and whether it is input -- typed by you -- or estimated -- calculated by the app.

When Making Important Decisions About a Student

Small variations in the results obtained using different correlation methods do not become problematic unless the student's scores place him or her on the boundary between severe discrepancy and no severe discrepancy. At these times, If you are using an estimated correlation, Discrepancy Calculator will tell you there is a narrow range between the actual achievement and the expected achievement. It will ask you type in a publisher's correlation if it is available. As any seasoned special education evaluator will tell you, these times when a student is on the borderline are the hardest. Discrepancy Calculator cannot make the decision for you. When making decisions for these students, don't rely on just one indicator. To borrow a judicial term, look for a preponderance of the evidence. Consider all other aspects of the student's learning, not just a borderline discrepancy. You can have higher confidence using a published correlation in Discrepancy Calculator, over an estimated one. You can likely also have higher confidence if Discrepancy Calculator's report using an estimated correlation agrees with a report using a published correlation.  Agreement using more than one method of estimation likewise raises your confidence level over using just one method of estimation. 

Please...

Please contact me if you need different tests added, if you have questions, to report bugs, or have a wish list of new features. Thank you for your purchase!

How Discrepancy Calculator Works: go to the mathematics page

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