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Science Forum Index » Statistics - Math Forum » How to simulate Cauchy samples...
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| Luis A. Afonso... |
 Posted: Fri May 16, 2008 8:35 am |
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Finally?
Referring my____May 8 , 2008 , 2:28 AM
Let be:
___________A <> B
____A = Quantiles of the sample medians (Critical Values),
____B = Usual Statistical Tables (Cumulative Standard Normal, Chi-squared, and so on).
I hope that this * equivalence * should be, finally, at the I.Q. level the IMBECILE DUO grows to.
It was * extraordinary * that the latter Tables values did vary from sample to sample !!!!!!!!! as they persist absurdly to think
_Luis Amaral Afonso (The Moderator Destriyer) |
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| John Smith... |
| Posted: Fri May 16, 2008 9:07 am |
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Adumbecile,
So you are calling them critical values?
Why, then, did you originally call them confidence intervals?
Were you making a mistake then, or are you making a mistake now?
John * Smith |
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| Luis A. Afonso... |
| Posted: Fri May 16, 2008 10:31 am |
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*** Adumbecile, So you are calling them critical values? Why, then, did you originally call them confidence intervals? Were you making a mistake then, or are you making a mistake now? John * Smith ***
My response
FINALLY (the IMBECILE DUO Jack Tomsky / John Smith) taking conscience through my latter post that he (they) was completely out of the real problem concerning the Lilliefors´s method to Test Hypotheses he (they) try a desperate trick in revealing what in his (their) opinion my list of values are.
EVEN A CHILD WOULD NOT BE FOOLED,
As it can be deduced through a lot of my posts, the list of values are
__________________ * Fractiles *
__what can be used as_ * Critical Values *
____a pair defining a _ * Confidence Interval *
___ allowing us to see if the real sample test value is in rejection region or not, and finally to DECIDE
___________________* Reject H0: ZERO median *, case in which the sample is not a Cauchy´s one, or, ___________________alternatively,_______________ not to have sufficient evidence TO REJECT H0 and the Distribution could be a Cauchy’s one (or EVEN not depending of the POWER relative to the true Distribution Law).
Luis Amaral Afonso (The Moderator Destroyer) |
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| John Smith... |
| Posted: Fri May 16, 2008 12:14 pm |
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Adumbo,
If they are confidence intervals, why don't they make use of sample information?????
Hemphill's correct simulation results make use of the sample information to produce confidence intervals.
Your confidence intervals do not make use of the sample information.
ADUMBO "CONFIDENCE INTERVAL" for n=5: +/-2.012
HEMPHILL CONFIDENCE INTERVAL for n=5: xs +/- 2.01502522
Explain why your "confidence interval" is correct and Hemphill's confidence interval is not.
YOU CAN'T DO IT !!!!!
BWAHAHAHAHAHA
John ! Smith
Quote: As it can be deduced through a lot of my posts, the
list of values are
__________________ * Fractiles *
__what can be used as_ * Critical Values *
____a pair defining a _ * Confidence Interval *
___ allowing us to see if the real sample test value
is in rejection region or not, and finally to DECIDE |
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| Luis A. Afonso... |
| Posted: Sat May 17, 2008 10:11 am |
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Prob. (-2.014 < sample median < 2.014)
= 3.8E6 / 4E6 = 0.95__Approximatelly, _____
For samples, size =5, drawn from a Cauchy Distribution.
Luis Amaral Afonso (The Moderator Destroyer) |
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| John Smith... |
| Posted: Sat May 17, 2008 8:40 pm |
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Adumbo,
Now you are implying that your quantities are confidence intervals. Yet in your post of May 10, 2:08 am (part reproduced below) you called them "critical values".
Why did you call them critical values????
Clearly you do not know the difference between critical values and confidence intervals.
John
__n__________5%__________1%signf
__5________+/-2.014_____+/-3.752___
__7__________ 1.533_______ 2.584___
__9__________ 1.272_______ 2.022___
_11__________ 1.108_______ 1.700___
_13__________ 0.990_______ 1.482___
_15__________ 0.905_______ 1.330___
_17__________ 0.838_______ 1.214___
_19__________ 0.782_______ 1.122___
_21__________ 0.738_______ 1.049___
_23__________ 0.698_______ 0.986___
_25__________ 0.666_______ 0.936___
(Seemly, these sample sizes the Critical Values show pronounced asymptotical tendency).
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| Luis A. Afonso... |
| Posted: Sun May 18, 2008 5:33 am |
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TWO ENLIGTHEN EXPERIENCES
____n=5
_Cauchy medians____________ N(0,1): 31, means
___________A________________B_________
_a1) simulate the sample b1) idem
_a2) find its median b2) the mean
_a3) Test Statistics b3) T (*)
_a4) code/memorize b4) idem
_a5) find the 2.5 percentile b5) idem
_a6) the 97.5 percentile b6) idem
_a7) central 95% C.I b7) idem
___[-2.014, 2.014]___________
_______________________0.025 quantile -2.042
_______________________0.975 quantile 2.045
(400´000 samples).
Do YOU SEE IMBECILES Jack Tomsky / John Smith the difference on considering the sample median representing the Population median and to know a priori what is exactly the Test Statistics Distribution, (TED) case in which is possible the comparison between the simulated TED and the exact one: T(0.975, 30 df) = 2.042 ? DO YOU SEE STUPID GUYS?
(*) T = (Xbar - 0) / [ Sx / Sqrt(n) ];
___________Sx = Sqrt [ssd/ (n-1)]
This proves only ding-dong schools educated on Statistics HAVE RELUCTANCE TO ADMIT ( the Jack Tomsky / John Smith´ case).THAT MONTE CARLO SIMULATIONS ARE ABLE TO BE USED ON STATISTICAL HYPOTHESES TESTS DECISIONS: fail to reject H0, reject it.
AND THAT after HUBERT LILLIEFORS paper is being used intensively the last 40 years.
Luis Amaral Asonso (The Moderator Destroyer) |
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| Luis A. Afonso... |
| Posted: Sun May 18, 2008 8:47 am |
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John Smith, if * the good doctor Jack Smith * as you lovely call him was your teacher of Statistics (in special on Test Hypotheses) he worth to be charged with the accusation (at Court) to has created a relatively coarse ROBOT that IS NOT ABLE TO THINK: * it * has ONLY AUTOMATIC REACTIONS has
_____Confidence Interval, ---> EXCLUSIVE OF A REAL SAMPLE --- > DATA NEEDING
_____Critical Value --- > MUST BE MULTIPLED BY THE OBSERVED TEST STATISTICS VALUE IN ORDER THAT ONE OBTAIN A CUT-OFF NUMBER.
*********************
Robots cannot understand that IN SIMULATION TRENDS the confidence interval * could * be limited by the critical values because the method DOES NOT NEED (at all) to know what the analytical test statistics is.
THIS IS TRUE; IN PARTICULAR, IN THE SELF-PROPOSED PTOBLEM: TO FIND CONFIDENCE INTERVALS FOR CAUCHY MEDIANS.
***********************************
FINALLY
___It was shown (analytically) that my C.I. is correct.
Luis Amaral Afonso (The Moderator Destroyer) |
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| John Smith... |
| Posted: Sun May 18, 2008 9:01 am |
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Adumbo,
Then why did you call it a critical value?????
Critical values and confidence intervals are NOT the same thing, though you obviously believe otherwise.
You are too stupid for words.
John ^ Smith
Quote: FINALLY
___It was shown (analytically) that my C.I. is
correct.
Luis Amaral Afonso (The Moderator Destroyer) |
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| Luis A. Afonso... |
| Posted: Sun May 18, 2008 10:13 am |
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QUIZ
How to stop a ROBOT?
RESPONSE
SWITCHING-OFF
******************
Luis Amaral Afonso (The Moderator Destroyer) |
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| John Smith... |
| Posted: Sun May 18, 2008 11:34 am |
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Adumdo calls his quantities both critical values and confidence intervals, when clearly these are not equivalent. Yet when called on this lie, he refuses to explain it or admit that he is wrong.
What a scholar!!!!
John $ Smith |
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| Luis A. Afonso... |
| Posted: Mon May 19, 2008 3:04 am |
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A scholar me (mo…ooi? As PIGGY used to said) NO, OF COURSE, DEFINITIVELY NO!
I do not belong to this ASININE, PARROTIC; QUADRUPODE, BAD SMELLING, ULTRAGEOUS, CANIBALE, ONANISTIC, BYZANTINE and WORTHLESS GANG.
Luis Amaral Afonso [The Moderator Destroyer]
Adumdo calls his quantities both critical values and confidence intervals, when clearly these are not equivalent. Yet when called on this lie, he refuses to explain it or admit that he is wrong. What a scholar!!!! John $ Smith |
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| Luis A. Afonso... |
| Posted: Fri May 23, 2008 5:12 pm |
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*** Exact Statistics
Exact statistics can be useful in situations where the asymptotic assumptions are not met, and so the asymptotic p-values are not close approximations for the true p-values. Standard asymptotic methods involve the assumption that the test statistic follows a particular distribution when the sample size is sufficiently large. When the sample size is not large, asymptotic results may not be valid, with the asymptotic p-values differing perhaps substantially from the exact p-values. Asymptotic results may also be unreliable when the distribution of the data is sparse, skewed, or heavily tied. Refer to Agresti (1996) and Bishop, Fienberg, and Holland (1975). Exact computations are based on the statistical theory of exact conditional inference for contingency tables, reviewed by Agresti (1992).***
Considering the Cauchy medians I was able to evaluate the CONFIDENCE INTERVALS for EXACT p-values (alpha = 0.05) because finding the two extreme points (symmetrical), the CRITICAL VALUES, I obtain the interval [-a , +a] THAT CONTAINS 95% of the TEST STATISTICS which is the sample median.
THIS IS COMPLETELY UNDERSTOOD and ACCEPTED in Statistical Theory TERMS and is an overall practice since 4 decades.
Luis Amaral Afonso [The Moderator Destroyer] |
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| Luis A. Afonso... |
| Posted: Fri May 23, 2008 5:56 pm |
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The HYSTERICAL claim from the IMBECILE DUO that´s is impossible two different Parameters estimation to have two equal HYPOTHESE TEST DECISIONS is absolutely WRONG.
I assure all the Readers that given the 5 sized samples A and B from Cauchy Distribution:
__A_______-0.16__0.57__1.03__2.21__7.57_
__B_______-0.34_ -0.09__1.42__2.41__6.79_
that the MEDIANS 1.03 and 1.42 are included at the 3´800´000 out 4 million samples I simulate. The Confidence Interval is [-2.014 , +2.014].consequently are outside the REJECTION REGION. The only DECISION is fail to REJECT H0.
More : go to WEB, lebel
_____Critical Values and Monte Carlo_______
and the Readers will find a lot of examples how this technique is used to find exact critical values at the most different scientific-technical branches. Though are not persuaded DO REPEAT MY EVALUATIONS using the software you can accede or made a program, the language you think more adequate.
The fact THAT SO MUCH scandalize the IMBECILE DUO has a simple explanation the sample medians 1.03, divides the real line in to portions: at left containing less than 0.025 + 0.95 of all sample medians , and at right more than 0.025. In terms of Hypotheses Test we FAIL TO REJECT H0: which’s data originated from a Cauchy Distribution. (The same way for the sample which median is 1.49). THIS IS THE LILIEFORS RATIONALE that is followed by Statisticians all around the world as one can see below.
See *** p-values Monte Carlo ***
www.tau.ac.il/cc/pages/docs/sas8/stat/chap28/sect28.htm
*** Exact Statistics
Exact statistics can be useful in situations where the asymptotic assumptions are not met, and so the asymptotic p-values are not close approximations for the true p-values. Standard asymptotic methods involve the assumption that the test statistic follows a particular distribution when the sample size is sufficiently large. When the sample size is not large, asymptotic results may not be valid, with the asymptotic p-values differing perhaps substantially from the exact p-values. Asymptotic results may also be unreliable when the distribution of the data is sparse, skewed, or heavily tied. Refer to Agresti (1996) and Bishop, Fienberg, and Holland (1975). Exact computations are based on the statistical theory of exact conditional inference for contingency tables, reviewed by Agresti (1992).***
Considering the Cauchy medians I was able to evaluate the CONFIDENCE INTERVALS for EXACT p-values (alpha = 0.05) because finding the two extreme points (symmetrical), the CRITICAL VALUES, I obtain the interval [-a , +a] THAT CONTAINS 95% of the TEST STATISTICS which is the sample median.
THIS IS COMPLETELY UNDERSTOOD and ACCEPTED in Statistical Theory TERMS and is an overall practice since 4 decades.
Luis Amaral Afonso [The Moderator Destroyer] |
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| Jack Tomsky... |
| Posted: Fri May 23, 2008 7:54 pm |
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Quote: RESULTS:
Limits of the 95% C.I. of Cauchy MEDIANS (as it was
shown on Apr. 24, 2008 11:30 AM)
___n=5_______+/-2.012
_____7_________ 1.535
_____9_________ 1.274
____11_________ 1.110
____13_________ 0.989
____15_________ 0.905
____17_________ 0.838
(400´000 samples)
The 95% Afonso confidence intervals are based on him assuming that the population median is zero. Therefore, the confidence interval for the population median is [0, 0] = {0} for all confidence levels and sample sizes.
The results Afonso presents have the property that for certain median values known to be untrue, the probability of coverage is 100% rather than 0%. For example, for n = 5, all nonzero medians between -2.012 and +2.012 have 100% coverage. That is, they are contained in the Afonso confidence intervals for every sample.
Because of these poor properties, I recommend that the Afonso confidence intervals never be used.
Jack (moderator) |
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