At 07:06 PM 11/21/02 +0000, Jerry Dallal wrote:
i disagree i guessConfidence intervals are not betworthy.
look at the following simulation
i generated 10000 samples of n=25 from a nd population where mu = 50 and sigma = 8 ... found the sample means ... went 2 standard errors on either side of the mean ... then, let mtb figure out how many intervals contained 50
MTB > rand 10000 c1-c25;
SUBC> norm 50 8.
MTB > rmean c1-c25 c26
MTB > rstdev c1-c25 c27
MTB > let c28=c27/5
MTB > let c29=c26-(2*c28)
MTB > let c30=c26+(2*c28)
MTB > let c31=(c29 lt 50) and (c30 gt 50)
MTB > sum c31
Sum of C31
Sum of C31 = 9446.0
MTB > let k1=9446/10000
MTB > prin k1
Data Display
K1 0.944600
94.46 % of the intervals contained 50
are you suggesting that if i put all intervals into a hat ... and we made a bet that mu would be in the interval ... that if it is i win 1 buck ... and if it does not i lose a buck ... that, if i keep drawing at random CIs ... i will lose as much as i win?
i don't think so
Our mystery user is correct, although s/he is not expressing him/herself as clearly as s/he might, which is not to say I'll do any better.A confidence interval is an interval generated by a process that has the property that the resulting interval will contain the parameter(s) of interest in the specified proportion of cases. Let X1, X2 be i.i.d. U(theta-1, theta+1), that is, uniform over (theta-1, theta +1). There is a 25% chance that both X1 and X2 will lie below theta. There is a 25% chance that both X1 and X2 will lie above theta. Therefore, there is a 50% chance that theta will lie between them. Then (Y1=min(x1,x2), Y2=max(x1,x2)) is a 50% confidence interval because it covers theta 50% of the time. However, when Y2-Y1 is greater than 1, it MUST contain theta, even though (Y1,Y2) is a 50% CI! . . ================================================================= Instructions for joining and leaving this list, remarks about the problem of INAPPROPRIATE MESSAGES, and archives are available at: . http://jse.stat.ncsu.edu/ . =================================================================
. . ================================================================= Instructions for joining and leaving this list, remarks about the problem of INAPPROPRIATE MESSAGES, and archives are available at: . http://jse.stat.ncsu.edu/ . =================================================================
