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  • Why the Supreme Court Needs to Know Standard Error

    Can you be completely sure that someone is “mentally disabled”?  This is what the Supreme Court must decide for the case that was presented this past Monday March 3rd.  The case involves Freddie Lee Hall of Florida who is sentenced to die for raping and killing a 21 year old woman who was seven months pregnant. In 1978, he was arrested and sentenced to death penalty.

    In 2002 Supreme Court, in Atkins v. Virginia case, ruled that executing "mentally disabled" people is unconstitutionally cruel and unusual punishment. However, the court didn’t specify who is legally “mentally disabled”.  Attorneys for Hall are using this ruling as the basis of their appeal to overturn Hall’s death sentence.

    The Supreme Court left the decision about how to define someone as “mentally disabled” to individual states.  State of Florida, where Hall was sentenced, only considers the IQ test score for declaring a person as “mentally disabled”. Specifically, Florida has a hard cutoff of 70, which means anyone scoring less than 70 on their IQ test is considered “mentally disabled”.  Hall average score for the IQ tests he has taken is more than 70 but less than 75.

    Florida’s exclusive use of the IQ test and its hard cut off of 70 are the basis of the appeal to the Supreme Court.  IQ tests, like all standardized tests, are usually good predictors but not 100% accurate - there is always a margin of error – about 5 points (according to Diagnostic and Statistical Manual of Mental Disorders, the authoritative manual of the American Psychiatric Association). Using this margin of error, then Hall whose average score is less 75 is “mentally disabled”.

    In a way the Supreme Court has to deliberate on the concepts of standard error and confidence intervals. If certainty is what you are looking for, then you will be hard-pressed to find it in averages.  Statistics will be able to tell you how likely you are to be making the right decision but it will be based on an interval and not a single number and even then, there is probability that you have made the wrong conclusion (significance level).  I hope the justices at the Supreme Court remember their confidence intervals, standard error, and margin of error – or their aides have their work cut out for them. 

    The larger issue here is that when you set a threshold (i.e. IQ test score of 70, or even 75) you are still likely to be wrong for some samples. How the Supreme Court should deal with this has very little to do with the validity of IQ score of 70 and more to do with how else we can minimize the risk of getting it wrong, a question that clearly was left alone in 2012 when making a ruling in Atkins v. Virginia case.

    Fataneh Taghaboni-Dutta
    Clinical Professor of Business Administration
    EMBA Professor of Statistics, Data Analysis and Decision Making