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[null,"Hall v. Florida"]
[null,null,null,null,null,null,null,null,"Test Scores"]
[null,"From a purely statistical perspective, how strong is the",null,null,null,null,null,null,71]
[null,"evidence that Hall does not have an IQ of 70 or less? Take as",null,null,null,null,null,null,73]
[null,"the null hypothesis that his true mean score across IQ tests is",null,null,null,null,null,null,80]
[null,"indeed less than or equal to 70."]
[null,null,null,null,null,null,null,null,"Univariate statistics"]
[null,"We interpret the significance level of 11.47% as saying that",null,null,null,null,null,null,null,"Test"]
[null,"the data provides only a bit of evidence against the null",null,null,null,null,null,null,"mean",{"$f":"AVERAGE(I3:I5)","v":74.666666666666671},{"$f":"showformula(J9)","v":"=AVERAGE(I3:I5)"}]
[null,"hypothesis: Certainly not strong enough evidence on which",null,null,null,null,null,null,"standard deviation",{"$f":"STDEV(I3:I5)","v":4.7258156262526079},{"$f":"showformula(J10)","v":"=STDEV(I3:I5)"}]
[null,"to base an execution!",null,null,null,null,null,null,"standard error of the mean",{"$f":"J10/SQRT(J13)","v":2.728450923957483},{"$f":"showformula(J11)","v":"=J10/SQRT(J13)"}]
[]
[null,"Justice Kennedy was spot on:",null,null,null,null,null,null,"number of observations",{"$f":"COUNT(I3:I5)","v":3},{"$f":"showformula(J13)","v":"=COUNT(I3:I5)"}]
[]
[null,"That approach, Justice Kennedy wrote, had at least two flaws.",null,null,null,null,null,null,"t-statistic for computing"]
[null,"One was that it failed to take account of standard errors of",null,null,null,null,null,null,"95%-confidence intervals",{"$f":"_xlfn.T.INV(0.975,J13-1)","v":4.3026527297494619},{"$f":"showformula(J16)","v":"=T.INV(0.975,J13-1)"}]
[null,"measurement. “An individual’s score is best understood as a",null,null,null,null,null,null,null,null,null,null,null,"Hypothesis testing tool"]
[null,"range of scores on either side of the recorded scores,” he",null,null,null,null,null,null,"From the sample data, fill in the yellow boxes below:"]
[null,"wrote."]
[null,null,null,null,null,null,null,null,{"$f":"J9","v":74.666666666666671},"estimate/prediction of unknown quantity"]
[null,"Note: At the top of the second page, the newswriter says that",null,null,null,null,null,null,{"$f":"J11","v":2.728450923957483},"standard error of the estimate/prediction (i.e., one standard-deviation's-worth of exposure to error"]
[null,"the Florida law required proof that a defendant's IQ was 70 or",null,null,null,null,null,null,{"$f":"J13","v":3},"sample size",null,null,"                       in the making of the estimate or prediction)"]
[null,"below in order to avert execution. Were this the truth, the",null,null,null,null,null,null,0,"number of explanatory variables in regression, or"]
[null,"defense would need to show that evidence SUPPORTED the",null,null,null,null,null,null,null,"0 if dealing with a population mean"]
[null,"statement: \"IQ ≤ 70.\"  In that case, three test scores of 69, 67,"]
[null,"and 60 would only weakly contradict the null hypothesis that",null,null,null,null,null,null,null,null,null,null,null,null,"significance level of data with respect to null hypothesis"]
[null,"\"IQ ≥ 70\" (we'd have the same significance level of 11.47%),",null,null,null,null,null,null,"Null hypothesis:"]
[null,"and therefore even three scores that low would not be",null,null,null,null,null,null,null,null,null,"≥",null,null,null,{"$f":"IF(I20>=M29,1,TDIST((M29-I20)/I21,I22-1-I23,TRUE))","v":1}]
[null,"enough to save a defendant.",null,null,null,null,null,null,null,null,"true value   ","=",70,null,null,{"$f":"2*TDIST(ABS(M29-I20)/I21,I22-1-I23,TRUE)","v":0.22932536441154727}]
[null,null,null,null,null,null,null,null,null,null,null,"≤",null,null,null,{"$f":"IF(M29>=I20,1,TDIST((I20-M29)/I21,I22-1-I23,TRUE))","v":0.11466268220577364}]
[null,"In fact, the Florida law required that prosecutors provide",null,null,null,null,null,null,null,null,null,null,null,null,null,{"$f":"\"(from t-distribution with \"&TEXT(I22-1-I23,\"0\")&\" degrees of freedom)\"","v":"(from t-distribution with 2 degrees of freedom)"}]
[null,"evidence supporting the statement that \"IQ ≥ 70,\" and we've"]
[null,"seen here that three scores of 71, 73, and 80 don't provide"]
[null,"much support. "]
[]
[null,"The difference between placing the burden of proof on the"]
[null,"prosecution, versus placing it on the defense, is dramatic!"]