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Math Help - 95% confidence limit on proportion... which distribution tables does H95CL code use?

  1. #1
    Newbie
    Joined
    Jun 2011
    Posts
    4

    95% confidence limit on proportion... which distribution tables does H95CL code use?

    On many Java statistical opensource codes there is a function called H95CL, with this header description:

    /**
    *
    * **MEMBER** H95CL
    *
    * H95CL RETURNS THE 95% CONFIDENCE LIMITS ON THE PROPORTION
    *
    * R1/R2
    *
    * WHERE R1 IS THE NUMBER OF SUCCESSES
    * R2 IS THE NUMBER OF TRIALS
    * IER IS 1 FOR THE UPPER LIMIT
    * 2 FOR THE LOWER LIMIT
    * H95CL RETURNS THE ERROR VALUE CORRESPONDING TO THIS LIMIT.
    *
    * THE METHOD USES THE TABLES TAKEN FROM
    *
    * HANDBOOK OF STATISTICAL TABLES
    * OWEN (QA297 Q9)
    *
    * AUTHOR: A. BOYARSKI, SLAC 1980.
    * @author Tony Johnson - Converted to Java
    */


    And these tables code:

    static final double[][]
    TAB1 = { { .0000,1.0000},{ .0000,.9750 },{ .0126,.9874 },
    { .0000,.8419 },{ .0084,.9057 },{ .0676,.9324 },
    { .0000,.7076 },{ .0063,.8059 },{ .0527,.8534 },
    { .1181,.8819 },{ .0000,.6024 },{ .0051,.7164 },
    { .0433,.7772 },{ .0990,.8159 },{ .1570,.8430 },
    { .0000,.5218 },{ .0042,.6412 },{ .0367,.7096 },
    { .0852,.7551 },{ .1370,.7880 },{ .1871,.8129 },
    { .0000,.4593 },{ .0036,.5787 },{ .0319,.6509 },
    { .0749,.7007 },{ .1216,.7376 },{ .1675,.7662 },
    { .2110,.7890 },{ .0000,.4096 },{ .0032,.5265 },
    { .0281,.6001 },{ .0667,.6525 },{ .1093,.6921 },
    { .1517,.7233 },{ .1923,.7486 },{ .2304,.7696 },
    { .0000,.3694 },{ .0028,.4825 },{ .0252,.5561 },
    { .0602,.6097 },{ .0993,.6511 },{ .1386,.6842 },
    { .1766,.7114 },{ .2127,.7341 },{ .2466,.7534 },
    { .0000,.3363 },{ .0025,.4450 },{ .0228,.5178 },
    { .0549,.5719 },{ .0909,.6143 },{ .1276,.6486 },
    { .1634,.6771 },{ .1975,.7012 },{ .2298,.7218 },
    { .2602,.7398 }};

    static final double[][][]
    TAB2 = { { { .0000,.3085 } , { .0023,.4128} , { .0209,.4841},
    { .0504,.5381 } , { .0839,.5810} , { .1182,.6162},
    { .1520,.6456 } , { .1844,.6707} , { .2153,.6924},
    { .2445,.7114 } } ,
    { { .0000,.2849 } , { .0021,.3848} , { .0192,.4545},
    { .0466,.5080 } , { .0779,.5510} , { .1102,.5866},
    { .1421,.6167 } , { .1730,.6425} , { .2025,.6649},
    { .2306,.6847 } } ,
    { { .0000,.2646 } , { .0019,.3603} , { .0178,.4281},
    { .0433,.4809 } , { .0727,.5238} , { .1031,.5596},
    { .1334,.5900 } , { .1629,.6164} , { .1912,.6394},
    { .2182,.6598 } } ,
    { { .0000,.2180 } , { .0016,.3023} , { .0146,.3644},
    { .0358,.4142 } , { .0605,.4557} , { .0866,.4910},
    { .1128,.5217 } , { .1387,.5487} , { .1638,.5726},
    { .1880,.5941 } } ,
    { { .0000,.1684 } , { .0012,.2382} , { .0112,.2916},
    { .0278,.3359 } , { .0474,.3738} , { .0683,.4070},
    { .0897,.4364 } , { .1112,.4628} , { .1322,.4865},
    { .1529,.5083 } } ,
    { { .0000,.1372 } , { .0010,.1964} , { .0091,.2429},
    { .0227,.2823 } , { .0389,.3167} , { .0564,.3473},
    { .0745,.3747 } , { .0928,.3997} , { .1109,.4225},
    { .1288,.4437 } } ,
    { { .0000,.0711 } , { .0005,.1045} , { .0047,.1321},
    { .0118,.1567 } , { .0206,.1790} , { .0302,.1996},
    { .0403,.2187 } , { .0508,.2367} , { .0615,.2537},
    { .0722,.2699 } } ,
    { { .0000,.0362 } , { .0003,.0539} , { .0024,.0691},
    { .0060,.0828 } , { .0106,.0956} , { .0156,.1077},
    { .0211,.1191 } , { .0267,.1301} , { .0325,.1407},
    { .0385,.1510 } } ,
    { { .0000,.0074 } , { .0001,.0111} , { .0005,.0143},
    { .0012,.0173 } , { .0022,.0202} , { .0032,.0230},
    { .0044,.0256 } , { .0056,.0282} , { .0068,.0308},
    { .0081,.0333 } } };

    I don't have the "HANDBOOK OF STATISTICAL TABLES" book and from other books I couldn't figure it out which distribution the tables are about. Is it normal distribution or binomial distribution?
    What I don't get is why the second table is a 3-dimensional array.
    Could anyone please provide an explanation?
    Thanks.
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  2. #2
    Super Member
    Joined
    Jul 2009
    Posts
    593
    Thanks
    4

    Re: 95% confidence limit on proportion... which distribution tables does H95CL code u

    I can't imagine this is any different than any other software (such as that found in a calculator) where you would need to specify if you standard deviation is a population or sample value (which would use a normal or t distribution) to produce the estimate.
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