A robust Spearman correlation coefficient permutation test
In this work, we show that Spearman's correlation coefficient test about H 0 : ρ s = 0 found in most statistical software is theoretically incorrect and performs poorly when bivariate normality assumptions are not met or the sample size is small. There is common misconception that the tests abo...
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| Vydáno v: | Communications in statistics. Theory and methods Ročník 53; číslo 6; s. 2141 - 2153 |
|---|---|
| Hlavní autoři: | , |
| Médium: | Journal Article |
| Jazyk: | angličtina |
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United States
Taylor & Francis
18.03.2024
Taylor & Francis Ltd |
| Témata: | |
| ISSN: | 0361-0926, 1532-415X |
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| Abstract | In this work, we show that Spearman's correlation coefficient test about
H
0
:
ρ
s
=
0
found in most statistical software is theoretically incorrect and performs poorly when bivariate normality assumptions are not met or the sample size is small. There is common misconception that the tests about
ρ
s
=
0
are robust to deviations from bivariate normality. However, we found under certain scenarios violation of the bivariate normality assumption has severe effects on type I error control for the common tests. To address this issue, we developed a robust permutation test for testing the hypothesis
H
0
:
ρ
s
=
0
based on an appropriately studentized statistic. We will show that the test is asymptotically valid in general settings. This was demonstrated by a comprehensive set of simulation studies, where the proposed test exhibits robust type I error control, even when the sample size is small. We also demonstrated the application of this test in two real world examples. |
|---|---|
| AbstractList | In this work, we show that Spearman’s correlation coefficient test about H0:ρs=0 found in most statistical software is theoretically incorrect and performs poorly when bivariate normality assumptions are not met or the sample size is small. There is common misconception that the tests about ρs=0 are robust to deviations from bivariate normality. However, we found under certain scenarios violation of the bivariate normality assumption has severe effects on type I error control for the common tests. To address this issue, we developed a robust permutation test for testing the hypothesis H0:ρs=0 based on an appropriately studentized statistic. We will show that the test is asymptotically valid in general settings. This was demonstrated by a comprehensive set of simulation studies, where the proposed test exhibits robust type I error control, even when the sample size is small. We also demonstrated the application of this test in two real world examples. In this work, we show that Spearman's correlation coefficient test about found in most statistical software is theoretically incorrect and performs poorly when bivariate normality assumptions are not met or the sample size is small. There is common misconception that the tests about are robust to deviations from bivariate normality. However, we found under certain scenarios violation of the bivariate normality assumption has severe effects on type I error control for the common tests. To address this issue, we developed a robust permutation test for testing the hypothesis based on an appropriately studentized statistic. We will show that the test is asymptotically valid in general settings. This was demonstrated by a comprehensive set of simulation studies, where the proposed test exhibits robust type I error control, even when the sample size is small. We also demonstrated the application of this test in two real world examples. In this work, we show that Spearman's correlation coefficient test about H 0 : ρ s = 0 found in most statistical software is theoretically incorrect and performs poorly when bivariate normality assumptions are not met or the sample size is small. There is common misconception that the tests about ρ s = 0 are robust to deviations from bivariate normality. However, we found under certain scenarios violation of the bivariate normality assumption has severe effects on type I error control for the common tests. To address this issue, we developed a robust permutation test for testing the hypothesis H 0 : ρ s = 0 based on an appropriately studentized statistic. We will show that the test is asymptotically valid in general settings. This was demonstrated by a comprehensive set of simulation studies, where the proposed test exhibits robust type I error control, even when the sample size is small. We also demonstrated the application of this test in two real world examples. In this work, we show that Spearman's correlation coefficient test about H0:ρs=0 found in most statistical software is theoretically incorrect and performs poorly when bivariate normality assumptions are not met or the sample size is small. There is common misconception that the tests about ρs=0 are robust to deviations from bivariate normality. However, we found under certain scenarios violation of the bivariate normality assumption has severe effects on type I error control for the common tests. To address this issue, we developed a robust permutation test for testing the hypothesis H0:ρs=0 based on an appropriately studentized statistic. We will show that the test is asymptotically valid in general settings. This was demonstrated by a comprehensive set of simulation studies, where the proposed test exhibits robust type I error control, even when the sample size is small. We also demonstrated the application of this test in two real world examples.In this work, we show that Spearman's correlation coefficient test about H0:ρs=0 found in most statistical software is theoretically incorrect and performs poorly when bivariate normality assumptions are not met or the sample size is small. There is common misconception that the tests about ρs=0 are robust to deviations from bivariate normality. However, we found under certain scenarios violation of the bivariate normality assumption has severe effects on type I error control for the common tests. To address this issue, we developed a robust permutation test for testing the hypothesis H0:ρs=0 based on an appropriately studentized statistic. We will show that the test is asymptotically valid in general settings. This was demonstrated by a comprehensive set of simulation studies, where the proposed test exhibits robust type I error control, even when the sample size is small. We also demonstrated the application of this test in two real world examples. |
| Author | Yu, Han Hutson, Alan D. |
| Author_xml | – sequence: 1 givenname: Han surname: Yu fullname: Yu, Han organization: Department of Biostatistics and Bioinformatics, Roswell Park Comprehensive Cancer Center – sequence: 2 givenname: Alan D. surname: Hutson fullname: Hutson, Alan D. organization: Department of Biostatistics and Bioinformatics, Roswell Park Comprehensive Cancer Center |
| BackLink | https://www.ncbi.nlm.nih.gov/pubmed/38646087$$D View this record in MEDLINE/PubMed |
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| Cites_doi | 10.3892/ijmm.2016.2620 10.1080/03610926.2013.802808 10.1007/s11222-008-9085-8 10.1007/s11222-009-9145-8 10.1080/10485250902807407 10.1002/pst.2101 10.1371/journal.pone.0216287 10.1007/s11222-011-9261-0 10.1186/1471-2105-12-323 10.1093/biomet/35.1-2.203 10.1080/03610918.2012.625338 10.1037/11491-005 10.1037/0033-2909.95.3.576 10.1080/10485250802195440 10.1177/0962280220909959 10.1080/10691898.2001.11910537 10.1093/biomet/44.3-4.470 10.1098/rsta.1896.0007 10.1016/j.jmva.2014.07.009 10.1080/00949655.2013.766189 10.1056/NEJMoa1503747 10.1080/03610926.2013.810270 10.1080/01621459.2016.1202117 |
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| References_xml | – ident: e_1_3_2_13_1 doi: 10.3892/ijmm.2016.2620 – volume: 70 start-page: 481 issue: 4 year: 2010 ident: e_1_3_2_21_1 article-title: The permutation testing approach: A review publication-title: Statistica – ident: e_1_3_2_9_1 doi: 10.1080/03610926.2013.802808 – ident: e_1_3_2_3_1 doi: 10.1007/s11222-008-9085-8 – ident: e_1_3_2_4_1 doi: 10.1007/s11222-009-9145-8 – ident: e_1_3_2_20_1 doi: 10.1080/10485250902807407 – ident: e_1_3_2_12_1 doi: 10.1002/pst.2101 – ident: e_1_3_2_11_1 doi: 10.1371/journal.pone.0216287 – ident: e_1_3_2_22_1 doi: 10.1007/s11222-011-9261-0 – ident: e_1_3_2_15_1 doi: 10.1186/1471-2105-12-323 – ident: e_1_3_2_17_1 doi: 10.1093/biomet/35.1-2.203 – ident: e_1_3_2_23_1 doi: 10.1080/03610918.2012.625338 – ident: e_1_3_2_28_1 doi: 10.1037/11491-005 – ident: e_1_3_2_24_1 – ident: e_1_3_2_6_1 doi: 10.1037/0033-2909.95.3.576 – ident: e_1_3_2_10_1 doi: 10.1080/10485250802195440 – start-page: 240 volume-title: The advanced theory of statistics year: 1979 ident: e_1_3_2_14_1 – ident: e_1_3_2_18_1 doi: 10.1177/0962280220909959 – ident: e_1_3_2_29_1 doi: 10.1080/10691898.2001.11910537 – volume-title: Statistical tables: For biological, agricultural and medical research year: 1938 ident: e_1_3_2_8_1 – ident: e_1_3_2_7_1 doi: 10.1093/biomet/44.3-4.470 – ident: e_1_3_2_19_1 doi: 10.1098/rsta.1896.0007 – ident: e_1_3_2_2_1 doi: 10.1016/j.jmva.2014.07.009 – ident: e_1_3_2_16_1 doi: 10.1080/00949655.2013.766189 – ident: e_1_3_2_30_1 doi: 10.1056/NEJMoa1503747 – volume-title: Base SAS 9.4 procedures guide year: 2015 ident: e_1_3_2_27_1 – ident: e_1_3_2_25_1 doi: 10.1080/03610926.2013.810270 – ident: e_1_3_2_5_1 doi: 10.1080/01621459.2016.1202117 – volume-title: Permutation tests for complex data: Theory, applications and software year: 2010 ident: e_1_3_2_26_1 |
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| Snippet | In this work, we show that Spearman's correlation coefficient test about
H
0
:
ρ
s
=
0
found in most statistical software is theoretically incorrect and... In this work, we show that Spearman's correlation coefficient test about found in most statistical software is theoretically incorrect and performs poorly when... In this work, we show that Spearman’s correlation coefficient test about H0:ρs=0 found in most statistical software is theoretically incorrect and performs... In this work, we show that Spearman's correlation coefficient test about H0:ρs=0 found in most statistical software is theoretically incorrect and performs... |
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| SubjectTerms | Bivariate analysis Correlation coefficients non-normality Normality Permutations Rank correlation Robust control small sample Statistical analysis studentized |
| Title | A robust Spearman correlation coefficient permutation test |
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