THIS IS A READONLY ARCHIVE FROM THE SORABJI.COM MESSAGE BOARDS (19952016). 

I'm taking a quiz right now. It's due in an hour. I'm almost done, except for one problem, and you're going to hear about it since I have no one else to complain to. Here it is: 5. Tom gets a 650 on verbal SAT and a 750 on math SAT. Assume the standard error of measurement is 30 for the first test and 40 for the second. a) Would we be justified (certain at the .05 level) in concluding that Tom is more able in Math than in Verbal ability? b) What is the reliability (splithalf, Spearman Brown corrected) of the Math test? What is the reliability (splithalf, uncorrected) of the Math test? Well, fine and good, but A) we never learned how to do a splithalf test, B) I'm looking in my book (it's an openbook quiz) and I can't find a corrected vs. uncorrected equation, and C) the only equation I can find is for estimated reliability and it requires you to know the obtained reliability, which is what I'm looking for in the first place! ARRRRGGGGHH!!! What am I supposed to do, huh? I can answer part A. (Yes, as the scores are greater than one standard deviation apart). But I think I've done really badly on the rest of the quiz, so I'm rather loath to leave part B blank, although if he said if our exam average is higher than our quiz average at the end of the semester, the quizzes won't count at all... I can't even attempt the equations, because they're the only ones I have, and yet I'm missing more than one variable, mainly because the SAT tests are NOT splithalf tests! So how can you do a splithalf test on them?!?!? This sucks. 
you're comparing apples and oranges. a point verbal is not equivlent to a point mathmatical. 

while we're talking about tests, has anyone here taken the gre's? if so, what was it like? 
Rhi, it's probably too late, but for the second question fill in why you feel you can't answer, maybe that's the correct one. unless you missed that day. Anyway, I took the ACTs. 
Agatha, it's a class in psychometrics (basically, the mechanics of IQ and personality tests...lots of statistical math). I have to take the GRE's in November...actually, I have to sign up for them this week as the deadline's 10/1. One more thing I have to do. (Oh, yeah, I'm not looking forward to them at all). I took a class in logic my freshman year. Failed it, too...the only class I've ever failed. The first few weeks it was all verbal syllogisms ("Mary is smarter than Bob. John is smarter than Mary" etc). THEN, as soon as it became too late to drop the class, it suddenly became all geometric logic from that point on ("Given point y is between point x and z, prove points x y and z form a line" or something like that...). It was a lot more involved than that, but if I could remember it now, I would have understood it then. (How's that for logic? :) ) 
You build a square house. All the outside walls face south. A bear knocks on the door. What color is the bear? Why? 

they do not acknowledge our human custom of "knocking" therfore his color is irrelavent. 



But maybe he has a brown friend with him... 



what if there was a traveling circus? 





First, picture in your mind the world's largest and fiercest landdwelling predator, the polar bear. Now, put him on a Harley on the streets of Anchorage, where there happens to be a ratio of one tavern for just about every 1.8 human beings. Just be happy that circus bears don't drive semi's, or he'd be making a road trip back up to the love shack to bring his buddies down for a poker run. 

You were right, Nate, about, um, what you said...the answer was no. But not for that reason. It was for some weird reason, like the standard error of measurement for both tests include different errors, so the true scores aren't necessarily the ones up there...or something...I wasn't paying attention. Unfortunately, we all have to redo that question for Friday. So I'd better figure out that formula real fast. 
math knowledge and verbal knowledge doesn't quantitate the same. a point of SAT math knowledge does not refer to a percentage of the total math knowledge that is the same as a point of SAT verbal knowledge as a percentage of total verbal knowledge. philosophically, the set of math knowledge is greater than the set of verbal knowledge. the subset of math knowledge that the SAT tests is a considerably smaller percentage of the total set of math knowledge that the subset of verbal knowledge is of the total set of verbal knowledge. in addition, if you take the whole of test results you can determine a percentile that each test score will fall into. equal scores in each of math and verbal will not fall into equal percentiles. i blame god. 



To do part A) What you're looking for is the sampling distribution of the differences, also known as the standard error of the differences. What you have are two observed scores for Tom. You want to know if the difference between the scores would stay the same/change if Tom took the two tests a million times. So here's what you do: To find the standard error of the differences, you take the square root of (the variance of the errors for test 1 + the variance of errors for test 2). In this case, that would be the square root of 300 (30 squared) + 1600 (40 squared), which would give you the square root of 2500, or 50. Because 50 is half of 100 (the standard deviation of the means of the tests), you know that the results are not significant at the .05 level. (Look at a chart of t scores for an accurate significance value.) Part B) Okay, in the real world, you ONLY know the reliability for splithalf tests. In this question you ONLY know the reliability for the whole test, so things are a little backwards. The uncorrected reliability formula gets you the splithalf reliability, the corrected formula gets you wholetest reliability. We in this case have to work backwards. So, to get corrected/whole test reliability...use the formula that gets you the standard error of measurement. That formula states that the SEM is equal to the standard deviation times the square root of 1 minus the reliability coefficient. In this case, we have the SEM and the SD, so it's just a matter of solving for r. So: SEM = SD (square root of 1r) 40 = 100 (sq.rt. of 1r) .4 = sq.rt. of 1r .16 = 1r .84 = r .84 = r Now, knowing that, we can do the uncorrected reliability coefficient: R = {length of test adjustment [called n] times correlation of splithalf test differences [called r])/1+(n1)(r)} So, in this case: R= (.5)(.84) / 1+(.51)(.84) It's .5 in the numerator because we're taking the split HALF of the whole test. This gives us an R of .72. It makes sense that the reliability of the splithalf test should be less than the reliability of the whole test, because as you increase the length of the test, you get more of a chance for the errors to average themselves out. Dig? 

know? you love us or you hate us. ive seen a snail crawl along the straight edge of a srarp razor. ive seen a snail slither along the straight sharp edge of a razor blade....and live. these are my dreams these are my nightmares 
