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ramblings of an unknown psychiatrist

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Being caught on one side of the ‘cut-off’

Posted by Dheeraj Kattula on May 26, 2009

Have you wondered how marks of an exam are distributed? Normal Curve? Skewed to right? or left? Ok. All answers are accepted. But wait…

Who are the ones who fail? The ones below a “cut off” point.

If the examiner feels only 50 % of the people should pass, the median would be the ‘cut off’ point. At different cut off points the percentage of people who pass and fail differs.

In Life, aren’t cut off points arbitrary? How is the person just above the cut-off better than the one just below it? Let us leave this for the moment and consider a cut-off point such that 40 students of a class of 100 students failed an exam as they got less than 30 marks.

Good news is that the school has ‘supplementary exams’. The exam can be taken again in 2 weeks time and people are given a chance to move on or they would have to repeat the course.

Hey!!! A naughty fellow is taking them for a 10 day trek into the woods. What do you think would happen, if this bunch of 40 students NEVER touched the book in 2 weeks and re-appear for the exam? Would all of them fail again? Remember, they were ‘failures’ in the first place and they wasted the time they got by enjoying themselves. They all ought to fail. Right?

Nope!!! Many of them passed. 35 of them! Only 5 failed again. How is that????

Let us confess that our performance is not stable at all times. We have our peaks and dips. In any exam the bright ones, whose dip would always be higher than the cut-off would always clear. Many average ones, when caught in the peak manage to clear the cut-off and when caught in the dip fail to do so.

Few of the ones who fail to do so, if given another chance through a supplementary exam would clear the cut-off. This happens by pure chance. It need not be due to preparation. If all 100 had re-written the exam may be a different set of 40 would have failed. The ones, who fail repeatedly, show that their preparation was inadequate that even in their peak moments they are not clearing the cut off.

Now if you have failed in your life. Don’t worry. Chance had caught you on the wrong side. There are many on the other side, who aren’t significantly different from you. They are there by chance alone. You will get to that side in a short-time with more trials. Don’t worry. Be patient.

If you have failed repeatedly, friend…you have to work harder. Your peak should go higher.

If you have passed this time and you think you are lucky, thank God. He is the one who made uncertainty a certainty. He favored you blindly as you played dice this time.

If you always pass, thank God again. You are too favored, my friend. You are on the extreme of normal curve of capability. You are here not by chance; you were designed to be here. Also be careful. Life is like a tennis match with many sets and many games. As you play more games, you will encounter dips…you might get caught below the cut off at one point. There is never a case when you need not be thankful and never a case when you need to give up.

7 Responses to “Being caught on one side of the ‘cut-off’”

  1. RPR said

    Can’t comment on the morality of the study, so let me stick to the mathematics:
    In a purely random sample, findings would be as you described.
    However, in examinations, there are several confounding factors that come into play.
    A person who generally scores 50-60% isn’t going to score 95% all of a sudden “just due to chance”.
    Similarly, a person who scores 95% all the time isn’t going to suddenly fail one time “just as a chance findings”.
    Chance findings are chance findings because they are due to chance, and chance alone.The minute any of your “sample” can influence the results, your assumptions are screwed.(In general, that is.)
    Which is why trials of, say, dieting to reduce drug-induced weight gain don’t capture a good picture.There will always be a subset who follow instructions strictly and do well.Another subset who do not and will be “non-responders”.And the “normal” sample who partially follow treatment.
    Average all the three and you may get a “mean” response…… but it tells you little about the different subgroups.

    The point about an arbitrary cut-off is good.Sometimes the cut-off is too high.For example, nowadays thousands of people score 95% in exams because of scoring inflation. 50 years ago, you could get a university rank by scoring 58%.

    Keep up the posts.

    • Dheeraj Kattula said

      Thanks for your comment.
      I agree with you.A controlled study will not be allowed by any ethical committee if its outcomes could harm a student, especially when an intervention could adversely affect an outcome logically.
      I agree that any student is not going to vary between 0 and 100 based on chance.My assumption was that he/she would vary normally around his/her own mean performance in tests of similar kind. So each student has a mean, a crest (peak) and trough (dip).
      The exam is a point estimate capturing a student randomly on his own graph.
      Your example of study not capturing the sub-group differences despite capturing a mean difference reinforces my point on an exam score (as mean in the example cited) cannot label students into subgroups like bright or dumb. It is simply not geared to.
      Thanks for making me think deeper on this.

  2. RS said

    As you say, your conclusions are valid for those who are in & around mean…by the way there are others who are on the extremes…or outliers…they will be unaffected whatever the situation maybe…
    the point in experimental studies is essentially to see the mean difference… no one cares about the extreme values..
    just call them outliers…& take them out of the analysis…
    but, sometimes the outliers also give vital clues
    sometimes more than those in the mean..
    prob. is that we do not pursue them as we do not have statistics robust enough…
    also, in most interventions we are bothered more about the “mean” as that is where most of the people are expected to lie…

    does it make any sense?????

    • Dheeraj Kattula said

      Thanks for your comment.
      Looks like you are an outlier, with a deep understanding of methodology 🙂
      You are right that scientists look at significant differences in means as most people lie here and also that outliers give vital clues.
      The insight that we must study the outliers of either group,what makes them be/get there is interesting.
      Anyway the post was more about being humble in success and hopeful in failure than the mathematics behind getting there 🙂

  3. […] Being caught on one side of the ‘cut-off’ […]

  4. peterrocks said

    Dheeraj,I am taking this for our college magazine and i know it will be a dubbing movie with production name changed,but director and hero are all same i am not making any changes full credit to you.

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