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probability of a score
Message posted by Bill on September 9, 2000 at 12:00 AM (ET)
I am dealing with a test that measures knowledge in a science field. The test has a known mean and standard deviation. Each examinee receives a score rounded to the nearest value of 10, e.g., 230, 240, 250. I have need to determine the probability of an examinee receiving a specific score, e.g., 260. I am tempted to determine the probability of drawing a score from the population between 255 and 265. However, the underlying attribute being measured is a continuos variable, and I understand that the probability of an exact score for a continuous variable is zero. If I calculate P(255 < x < 265) will only the purest be offended or will I condemned by all.
READERS RESPOND:
(In chronological order. Most recent at the bottom.)
Re: probability of a score
Message posted by JG on September 10, 2000 at 12:00 AM (ET)
If you know the distribution and the exact method of rounding then you are doing the right thing. What you actually calculate is
P(255
Re: probability of a score
Message posted by JG on September 10, 2000 at 12:00 AM (ET)
What you actually calcutate is P(255P(255
Re: probability of a score
Message posted by JG on September 10, 2000 at 12:00 AM (ET)
P(255P(255
Re: probability of a score
Message posted by JG on September 10, 2000 at 12:00 AM (ET)
What I type gets garbled when posted. Is it my phone line or what ?
Re: probability of a score
Message posted by Phil on September 10, 2000 at 12:00 AM (ET)
If you think of the score as a discrete random variable, then the score may really be binomial, not normal (in the pure sense). Then, what you are proposing is simply a technique recognized as the "Normal Approximation to the Binomial" and using 245
Re: probability of a score
Message posted by Phil on September 10, 2000 at 12:00 AM (ET)
OK. So we shouldn't use the LT and GT symbols with HTML stuff.Cont'd: what you are doing is sometimes known as "continuity correction". Based on what you have said, it sounds reasonable to me.
Re: probability of a score
Message posted by JG on September 10, 2000 at 12:00 AM (ET)
The continuety correction idea says that you should go from 254.5 to 265.5 since 254.5 to 255.5 continuous is equivalent to 255 discrete.
Re: probability of a score
Message posted by Phil on September 11, 2000 at 12:00 AM (ET)
In this case, with the round-off situation, I would use from 245 to 255 to estimate the probabilty of 250. It is sort of a pseudo-continuity correction...my two cents anyway.
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