Confidence Intervals for a Discrete Population Median
In this article, we consider the problem of constructing confidence intervals for a population median when the underlying population is discrete. We describe seven methods of assigning confidence levels to order statistic based confidence intervals, all of which are easy to implement. A simulation s...
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| Veröffentlicht in: | The American statistician 2008-02, Vol.62 (1), p.32-39 |
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| container_end_page | 39 |
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| container_title | The American statistician |
| container_volume | 62 |
| creator | Larocque, Denis Randles, Ronald H |
| description | In this article, we consider the problem of constructing confidence intervals for a population median when the underlying population is discrete. We describe seven methods of assigning confidence levels to order statistic based confidence intervals, all of which are easy to implement. A simulation study shows that, with discrete populations, it is possible to obtain consistently more accurate confidence levels and shorter intervals compared to the ones reported by the classical method which is implemented in commercial software. More precisely, the best results are obtained by inverting a two-tailed sign test that properly takes into account tied observations. Some real data examples illustrate the use of these confidence intervals. |
| doi_str_mv | 10.1198/000313008X269738 |
| format | Article |
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Some real data examples illustrate the use of these confidence intervals.</description><subject>Binomials</subject><subject>Combinatorics</subject><subject>Confidence interval</subject><subject>Confidence intervals</subject><subject>Confidence level</subject><subject>Discrete distribution</subject><subject>Disk stars</subject><subject>Exact sciences and technology</subject><subject>General topics</subject><subject>Integers</subject><subject>Mathematics</subject><subject>Maximum likelihood</subject><subject>Maximum likelihood estimation</subject><subject>Maximum likelihood method</subject><subject>Median</subject><subject>Multinomial distribution</subject><subject>Nonparametric inference</subject><subject>P values</subject><subject>Parametric inference</subject><subject>Population estimates</subject><subject>Probabilities</subject><subject>Probability and statistics</subject><subject>Sample size</subject><subject>Sciences and techniques of general use</subject><subject>Sign test</subject><subject>Statistical median</subject><subject>Statistics</subject><subject>Tied observations</subject><issn>0003-1305</issn><issn>1537-2731</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2008</creationdate><recordtype>article</recordtype><recordid>eNp1kEtLAzEUhYMoWKt7N8IguBzNOxlcSeujUNGFgrshk0lgyjSpSar035syVUFwdbmc755zOQCcIniJUCWvIIQEEQjlG-aVIHIPjBAjosSCoH0w2spl1tkhOIpxkVcoOB4BNvHOdq1x2hQzl0z4UH0srA-FKqZd1MEkUzz71bpXqfOueDRtp9wxOLCZMye7OQavd7cvk4dy_nQ_m9zMS00ETaVqJEINJ9JQKokgmkNsG1MR0_CWVdpKyQVl0iLGLYKyMhxXSlHGW0uRaskYnA--q-Df1yameuHXweXIGmNJSYUZzhAcIB18jMHYehW6pQqbGsF62039t5t8crHzVVGr3gbldBd_7jCENFvzzJ0N3CImH351wXM230ZfD3rncmVL9elD39ZJbXofvk3Jv198AZyMfdw</recordid><startdate>20080201</startdate><enddate>20080201</enddate><creator>Larocque, Denis</creator><creator>Randles, Ronald H</creator><general>Taylor & Francis</general><general>American Statistical Association</general><scope>IQODW</scope><scope>AAYXX</scope><scope>CITATION</scope></search><sort><creationdate>20080201</creationdate><title>Confidence Intervals for a Discrete Population Median</title><author>Larocque, Denis ; Randles, Ronald H</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c374t-ab811b638e448373c602fbe93eb6d59cf8867458f156f1089e629aa456df41ad3</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2008</creationdate><topic>Binomials</topic><topic>Combinatorics</topic><topic>Confidence interval</topic><topic>Confidence intervals</topic><topic>Confidence level</topic><topic>Discrete distribution</topic><topic>Disk stars</topic><topic>Exact sciences and technology</topic><topic>General topics</topic><topic>Integers</topic><topic>Mathematics</topic><topic>Maximum likelihood</topic><topic>Maximum likelihood estimation</topic><topic>Maximum likelihood method</topic><topic>Median</topic><topic>Multinomial distribution</topic><topic>Nonparametric inference</topic><topic>P values</topic><topic>Parametric inference</topic><topic>Population estimates</topic><topic>Probabilities</topic><topic>Probability and statistics</topic><topic>Sample size</topic><topic>Sciences and techniques of general use</topic><topic>Sign test</topic><topic>Statistical median</topic><topic>Statistics</topic><topic>Tied observations</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Larocque, Denis</creatorcontrib><creatorcontrib>Randles, Ronald H</creatorcontrib><collection>Pascal-Francis</collection><collection>CrossRef</collection><jtitle>The American statistician</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Larocque, Denis</au><au>Randles, Ronald H</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Confidence Intervals for a Discrete Population Median</atitle><jtitle>The American statistician</jtitle><date>2008-02-01</date><risdate>2008</risdate><volume>62</volume><issue>1</issue><spage>32</spage><epage>39</epage><pages>32-39</pages><issn>0003-1305</issn><eissn>1537-2731</eissn><coden>ASTAAJ</coden><abstract>In this article, we consider the problem of constructing confidence intervals for a population median when the underlying population is discrete. 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| source | JSTOR Mathematics & Statistics; Jstor Complete Legacy |
| subjects | Binomials Combinatorics Confidence interval Confidence intervals Confidence level Discrete distribution Disk stars Exact sciences and technology General topics Integers Mathematics Maximum likelihood Maximum likelihood estimation Maximum likelihood method Median Multinomial distribution Nonparametric inference P values Parametric inference Population estimates Probabilities Probability and statistics Sample size Sciences and techniques of general use Sign test Statistical median Statistics Tied observations |
| title | Confidence Intervals for a Discrete Population Median |
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