Implementation of Fishers permutation test

## Project description

## What is it

Implementation of Fisher’s permutation test.

The test is described in following publications:

- Fisher, R. A. (1935). The design of experiments. 1935. Oliver and Boyd, Edinburgh.
- Ernst, M. D. (2004). Permutation methods: a basis for exact inference. Statistical Science, 19(4), 676-685

## How to install it

Install with pip:

$ pip install permutation_test

## Command Line Script Usage

Example:

permtest [path/to/data.csv] [groups_colname] [reference_group_name] -t [test_group_name]

Use help to get info about parameters:

$ permtest -h usage: permtest [-h] [-t TESTGROUP] input_filepath treatment_column_name referencegroup positional arguments: input_filepath e.g. path/to/my/data.csv, path to csv file with data treatment_column_name name of column in the csv table that specifies the group referencegroup name of the reference group as named in the csv table optional arguments: -h, --help show this help message and exit -t TESTGROUP, --testgroup TESTGROUP name of the test group as named in th csv table. If not defined, test group is determined automatically. -a ALPHA, --alpha ALPHA significance level alpha (between 0 and 1) If not defined, alpha is set to 0.05. -m MULTI_COMP_CORR, --multi_comp_corr MULTI_COMP_CORR perform multiple comparison correction with benjamini hochberg procedure yes/no, If not defined, correction is performed.

## Specifications of data structure in csv file

- The csv should contain comma separated values. One ore more columns should contain measurement data.
- All columns need to have a name, specified in the first row.
- One column contains names for the groups

Example *my_data.csv*:

experiment_1 | experiment_2 | experiment_3 | group_names |
---|---|---|---|

1.4 | 3 | 2.5 | condition_2 |

2 | 5 | 2 | condition_1 |

5.6 | 3 | 17 | condition_2 |

9 | 6.5 | 2 | condition_1 |

17 | 5 | 13.0 | condition_1 |

17 | 2 | 13.0 | condition_3 |

12 | 8 | 18.7 | condition_3 |

To perform tests for all experiments, where *condition_1* is the reference and *condition_2* is
the test data, run follwoing command:

$ permtest my_data.csv group_names condition_1 -t condition_2

Often, it is convenient to save the output in a textfile:

$ permtest my_data.csv group_names condition_1 -t condition_2 > my_test_result.txt

## Python Library Use Example

>>> import permutation_test as p >>> data = [1,2,2,3,3,3,4,4,5] >>> ref_data = [3,4,4,5,5,5,6,6,7] >>> p_value = p.permutation_test(data, ref_data) taking random subsample of size 20000 from 48620 possible permutations nr of mean diffs: 20000 Distribution of mean differences │ * ┼+1.73038 │ * │ * │ * │ * │ * │ │ * │ * │ │ * │ * │ * │ * │ * │ * * * ┼+0.037 * * ───┼*****─***─**─***─**─**─***─**─**─**┼**─***─**─***─**─**─***─**─***─*****┼─── -2.38713 │ +2.39919 mean difference of tested dataset: -2.0 p_value: 0.00345 p_lower_than (probability that mean of test data is not lower than mean of ref data): 0.00345 p_value_greater_than (probability that mean of test data is not greater than mean of ref data): 0.9998 0.0034500000000000121

The asccii art plot shows the ditribution of mean differences for the permutations. The ascii art plot is done with [AP](https://github.com/mfouesneau/asciiplot), a plotting package by Morgan Fouesneau.

If the number of possible combinations is grater than n_combinations_max, a random subsample of size n_combinations_max is taken for histogram calculation.

If detailed is False, only (two-sided) p_value is returned, i.e. the probability that data is not different from ref_data

If detailed is True, one-sided p values and histogram data of mean differences is returned in a dict:

hist_data: distribution of mean differences for all permutations p_value: two sided p_value (the probability that data is not different from ref_data ) p_value_lower_than: the probability that mean of data is not lower than mean of ref_data p_value_greater_than: the probability that mean of data is not grater than mean of ref_data

Christoph Möhl, Image and Data Analysis Facililty/Core Faciliies, Deutsches Zentrum für Neurodegenerative Erkrankungen e. V. (DZNE) in der Helmholtz-Gemeinschaft German Center for Neurodegenerative Diseases (DZNE) within the Helmholtz Association

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