<!-- README.md is generated from README.Rmd. Please edit that file -->
# wmwm
<!-- badges: start -->
<!-- badges: end -->
This package performs the two-sample hypothesis test method proposed in
(Zeng et al., 2024) for univariate data when data are not fully observed.
This method is a theoretical extension of Wilcoxon-Mann-Whitney test in
the presence of missing data, which controls the Type I error regardless
of values of missing data.
Bounds of the Wilcoxon-Mann-Whitne test statistic and its p-value will be
computed in the presence of missing data. The p-value of the test method
proposed in (Zeng et al., 2024) is then returned as the maximum possible
p-value of the Wilcoxon-Mann-Whitney test.
## Installation
``` sh
pip install wmwm
```
## Example
This is a basic example which shows you how to perform the test with
missing data:
``` python
import numpy as np
from wmwm import wmwm_test
#### Assume all samples are distinct.
X = np.array([6.2, 3.5, np.nan, 7.6, 9.2])
Y = np.array([0.2, 1.3, -0.5, -1.7])
## By default, when the sample sizes of both X and Y are smaller than 50,
## exact distribution will be used.
wmwm_test(X, Y, ties = False, alternative = 'two.sided')
## using normality approximation with continuity correction:
wmwm_test(X, Y, ties = False, alternative = 'two.sided', exact = False, correct = True)
#### Assume samples can be tied.
X = np.array([6, 9, np.nan, 7, 9])
Y = np.array([0, 1, 0, -1])
## When the samples can be tied, normality approximation will be used.
## By default, lower_boundary = -Inf, upper_boundary = Inf.
wmwm_test(X, Y, ties = True, alternative = 'two.sided')
## specifying lower_boundary and upper_boundary:
wmwm_test(X, Y, ties = True, alternative = 'two.sided', lower_boundary = -1, upper_boundary = 9)
```
## References
Zeng Y, Adams NM, Bodenham DA. On two-sample testing for data with
arbitrarily missing values. arXiv preprint arXiv:2403.15327. 2024 Mar
22.
Mann, Henry B., and Donald R. Whitney. “On a test of whether one of two
random variables is stochastically larger than the other.” The annals of
mathematical statistics (1947): 50-60.
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"description": "\n<!-- README.md is generated from README.Rmd. Please edit that file -->\n\n# wmwm\n\n<!-- badges: start -->\n<!-- badges: end -->\n\nThis package performs the two-sample hypothesis test method proposed in \n(Zeng et al., 2024) for univariate data when data are not fully observed. \nThis method is a theoretical extension of Wilcoxon-Mann-Whitney test in \nthe presence of missing data, which controls the Type I error regardless \nof values of missing data.\n\nBounds of the Wilcoxon-Mann-Whitne test statistic and its p-value will be \ncomputed in the presence of missing data. The p-value of the test method \nproposed in (Zeng et al., 2024) is then returned as the maximum possible \np-value of the Wilcoxon-Mann-Whitney test.\n\n## Installation\n\n``` sh\npip install wmwm\n```\n\n## Example\n\nThis is a basic example which shows you how to perform the test with\nmissing data:\n\n``` python\nimport numpy as np\nfrom wmwm import wmwm_test\n\n#### Assume all samples are distinct.\nX = np.array([6.2, 3.5, np.nan, 7.6, 9.2])\nY = np.array([0.2, 1.3, -0.5, -1.7])\n## By default, when the sample sizes of both X and Y are smaller than 50,\n## exact distribution will be used.\nwmwm_test(X, Y, ties = False, alternative = 'two.sided')\n\n\n## using normality approximation with continuity correction:\nwmwm_test(X, Y, ties = False, alternative = 'two.sided', exact = False, correct = True)\n\n\n#### Assume samples can be tied.\nX = np.array([6, 9, np.nan, 7, 9])\nY = np.array([0, 1, 0, -1])\n## When the samples can be tied, normality approximation will be used.\n## By default, lower_boundary = -Inf, upper_boundary = Inf.\nwmwm_test(X, Y, ties = True, alternative = 'two.sided')\n\n\n## specifying lower_boundary and upper_boundary:\nwmwm_test(X, Y, ties = True, alternative = 'two.sided', lower_boundary = -1, upper_boundary = 9)\n\n\n```\n\n## References\n\nZeng Y, Adams NM, Bodenham DA. On two-sample testing for data with\narbitrarily missing values. arXiv preprint arXiv:2403.15327. 2024 Mar\n22.\n\nMann, Henry B., and Donald R. Whitney. \u201cOn a test of whether one of two\nrandom variables is stochastically larger than the other.\u201d The annals of\nmathematical statistics (1947): 50-60.\n",
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