Application of Equal Local Levels to Improve Q-Q Plot Testing Bands with R Package qqconf
Quantile-quantile (Q-Q) plots are often difficult to interpret because it is unclear how large the deviation from the theoretical distribution must be to indicate a lack of fit. Most Q-Q plots could benefit from the addition of meaningful global testing bands, but the use of such bands unfortunately...
| Main Authors: | , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Foundation for Open Access Statistics
2023-04-01
|
| Series: | Journal of Statistical Software |
| Online Access: | https://www.jstatsoft.org/index.php/jss/article/view/4843 |
| _version_ | 1797813921821753344 |
|---|---|
| author | Eric Weine Mary Sara McPeek Mark Abney |
| author_facet | Eric Weine Mary Sara McPeek Mark Abney |
| author_sort | Eric Weine |
| collection | DOAJ |
| description | Quantile-quantile (Q-Q) plots are often difficult to interpret because it is unclear how large the deviation from the theoretical distribution must be to indicate a lack of fit. Most Q-Q plots could benefit from the addition of meaningful global testing bands, but the use of such bands unfortunately remains rare because of the drawbacks of current approaches and packages. These drawbacks include incorrect global type-I error rate, lack of power to detect deviations in the tails of the distribution, relatively slow computation for large data sets, and limited applicability. To solve these problems, we apply the equal local levels global testing method, which we have implemented in the R Package qqconf, a versatile tool to create Q-Q plots and probability-probability (P-P) plots in a wide variety of settings, with simultaneous testing bands rapidly created using recently-developed algorithms. qqconf can easily be used to add global testing bands to Q-Q plots made by other packages. In addition to being quick to compute, these bands have a variety of desirable properties, including accurate global levels, equal sensitivity to deviations in all parts of the null distribution (including the tails), and applicability to a range of null distributions. We illustrate the use of qqconf in several applications: assessing normality of residuals from regression, assessing accuracy of p values, and use of Q-Q plots in genome-wide association studies. |
| first_indexed | 2024-03-13T07:59:50Z |
| format | Article |
| id | doaj.art-23533b4fa40a42a39a7686eeccd6e783 |
| institution | Directory Open Access Journal |
| issn | 1548-7660 |
| language | English |
| last_indexed | 2024-03-13T07:59:50Z |
| publishDate | 2023-04-01 |
| publisher | Foundation for Open Access Statistics |
| record_format | Article |
| series | Journal of Statistical Software |
| spelling | doaj.art-23533b4fa40a42a39a7686eeccd6e7832023-06-01T18:48:03ZengFoundation for Open Access StatisticsJournal of Statistical Software1548-76602023-04-0110613110.18637/jss.v106.i108480Application of Equal Local Levels to Improve Q-Q Plot Testing Bands with R Package qqconfEric Weine0Mary Sara McPeek1https://orcid.org/0009-0007-7344-834XMark Abney2https://orcid.org/0000-0002-1718-5676University of ChicagoUniversity of ChicagoUniversity of ChicagoQuantile-quantile (Q-Q) plots are often difficult to interpret because it is unclear how large the deviation from the theoretical distribution must be to indicate a lack of fit. Most Q-Q plots could benefit from the addition of meaningful global testing bands, but the use of such bands unfortunately remains rare because of the drawbacks of current approaches and packages. These drawbacks include incorrect global type-I error rate, lack of power to detect deviations in the tails of the distribution, relatively slow computation for large data sets, and limited applicability. To solve these problems, we apply the equal local levels global testing method, which we have implemented in the R Package qqconf, a versatile tool to create Q-Q plots and probability-probability (P-P) plots in a wide variety of settings, with simultaneous testing bands rapidly created using recently-developed algorithms. qqconf can easily be used to add global testing bands to Q-Q plots made by other packages. In addition to being quick to compute, these bands have a variety of desirable properties, including accurate global levels, equal sensitivity to deviations in all parts of the null distribution (including the tails), and applicability to a range of null distributions. We illustrate the use of qqconf in several applications: assessing normality of residuals from regression, assessing accuracy of p values, and use of Q-Q plots in genome-wide association studies.https://www.jstatsoft.org/index.php/jss/article/view/4843 |
| spellingShingle | Eric Weine Mary Sara McPeek Mark Abney Application of Equal Local Levels to Improve Q-Q Plot Testing Bands with R Package qqconf Journal of Statistical Software |
| title | Application of Equal Local Levels to Improve Q-Q Plot Testing Bands with R Package qqconf |
| title_full | Application of Equal Local Levels to Improve Q-Q Plot Testing Bands with R Package qqconf |
| title_fullStr | Application of Equal Local Levels to Improve Q-Q Plot Testing Bands with R Package qqconf |
| title_full_unstemmed | Application of Equal Local Levels to Improve Q-Q Plot Testing Bands with R Package qqconf |
| title_short | Application of Equal Local Levels to Improve Q-Q Plot Testing Bands with R Package qqconf |
| title_sort | application of equal local levels to improve q q plot testing bands with r package qqconf |
| url | https://www.jstatsoft.org/index.php/jss/article/view/4843 |
| work_keys_str_mv | AT ericweine applicationofequallocallevelstoimproveqqplottestingbandswithrpackageqqconf AT marysaramcpeek applicationofequallocallevelstoimproveqqplottestingbandswithrpackageqqconf AT markabney applicationofequallocallevelstoimproveqqplottestingbandswithrpackageqqconf |