statds package

Submodules

statds.homoscedasticity module

statds.homoscedasticity.bartlett_test(dataset: DataFrame, alpha: float = 0.05)

Perform Bartlett’s test for homogeneity of variances. This test checks the null hypothesis that all input samples (represented as columns in the dataset) come from populations with equal variances. It is commonly used before conducting ANOVA, as equal variances are an assumption of ANOVA.

Parameters

datasetpandas DataFrame

A DataFrame where each column represents a different group/sample. The first column is ignored.

alphafloat, optional

The significance level for the test, default is 0.05.

Returns

statistical_bartlettfloat

Bartlett’s test statistic. A higher value indicates a greater likelihood of differing variances.

p_valuefloat

The p-value for the hypothesis test. A small p-value (typically ≤ 0.05) rejects the null hypothesis, suggesting that the variances across groups are not equal.

cv_valuefloat

Critical value for the test at the specified alpha level.

hypothesisstr

A string stating the conclusion of the test based on the test statistic and alpha. It indicates whether the null hypothesis of equal variances can be rejected or not.

Notes

Bartlett’s test is sensitive to departures from normality. Therefore, if the data are not normally distributed, Levene’s test is a more appropriate choice. The test statistic is compared against a chi-squared distribution to obtain the p-value. The formula for the test statistic takes into account the number of groups and the total number of samples.

statds.homoscedasticity.levene_test(dataset: DataFrame, alpha: float = 0.05, center: str = 'mean')

Perform the Levene test for equality of variances. This test is used to assess whether the variances of two or more groups are equal. It is an essential test before conducting ANOVA, as ANOVA assumes homogeneity of variances.

Parameters

datasetpandas DataFrame

A DataFrame where each column represents a different group/sample. The first column is ignored.

alphafloat, optional

The significance level for the test, default is 0.05.

center{‘mean’, ‘median’, ‘trimmed’}, optional

The method for calculating the center of each group. Default is ‘mean’.

Returns

statistic_levenefloat

The Levene test statistic. A higher value indicates a greater likelihood of differing variances.

p_valuefloat

The p-value for the hypothesis test. A small p-value (typically ≤ 0.05) rejects the null hypothesis, suggesting that the variances across groups are not equal.

rejected_valuefloat

The critical value for the test at the specified alpha level.

hypothesisstr

A string stating the conclusion of the test based on the test statistic and alpha. It indicates whether the null hypothesis of equal variances can be rejected or not.

Notes

The Levene test is robust to non-normal distributions, making it preferable to Bartlett’s test when data are not normally distributed. The choice of ‘center’ parameter (mean, median, trimmed) can affect the test’s sensitivity to departures from normality. The test statistic is computed based on the absolute deviations from the group centers and then compared against an F-distribution to obtain the p-value.

statds.no_parametrics module

exception statds.no_parametrics.LibraryError(message)

Bases: Exception

statds.no_parametrics.binomial(dataset: DataFrame, alpha: float = 0.05, verbose: bool = False)

Perform the Binomial Sign Test. This non-parametric test is used to determine if there is a significant difference between the medians of two dependent samples. It serves as an alternative to the paired t-test and Wilcoxon signed-rank test, particularly useful when the data does not meet the assumptions of these tests or when the data is on an ordinal scale.

Parameters

datasetpandas.DataFrame

A DataFrame with exactly two columns, each representing a different condition or time point for the same subjects.

alphafloat, optional

The significance level for the test. Default is 0.05.

verbosebool, optional

If True, prints the detailed results table.

Returns

statistical_binomialfloat

The Binomial test statistic, which is the largest of the counts of positive or negative differences.

p_valuefloat

The p-value for the hypothesis test, calculated from the binomial distribution.

cv_valuefloat or None

The critical value for the test at the specified alpha level (not calculated in this function, hence None).

hypothesisstr

A string stating the conclusion of the test based on the test statistic and p-value in comparison to alpha.

Note

The Binomial Sign Test counts the number of positive and negative differences between paired observations and then tests if the observed proportion of positive (or negative) differences is significantly different from 0.5 (no difference). The test assumes that the distribution of differences is symmetric around the median and ignores pairs with no difference.

statds.no_parametrics.bonferroni(ranks: dict, num_cases: int, alpha: float = 0.05, control: str | None = None, type_rank: str = 'Friedman', verbose: bool = False)

This function performs the Bonferroni correction for multiple comparisons of algorithms or treatments. The Bonferroni correction is a method to adjust significance levels when multiple statistical tests are conducted simultaneously.

Parameters

ranksdict

A dictionary where keys are the names of the algorithms and values are their respective ranks. The ranks must be obtained based on multiple non-parametric tests.

num_casesint

An integer representing the number of cases, datasets, or instances over which the rankings were calculated.

alphafloat, optional

A float representing the significance level used in the test. It defaults to 0.05, which is a common choice in statistical testing.

controlstr, optional

An optional string specifying a control algorithm against which others will be compared. If None, all algorithms are compared against each other.

type_rankstr, optional

A string indicating the type of ranking used (e.g., “Friedman”). Defaults to “Friedman”.

verbosebool, optional

A boolean indicating whether to print additional information (like the critical distance). Defaults to False.

Returns

comparison_resultspandas.DataFrame

A DataFrame with the results of the comparisons, including adjusted z-values and adjusted p-values.

comparison_figurematplotlib.figure.Figure

A figure graphically displaying the results of the tests, typically a bar chart or scatter plot.

Note

This function is useful in statistical analysis where multiple algorithms or treatments are compared and there is a need to control the Type I error (false positive) that increases with the number of comparisons.

statds.no_parametrics.contrast_estimation_based_on_medians(dataset: DataFrame, minimize: bool = False, verbose: bool = False)

statds.no_parametrics.create_dataframe_results(comparisons: list, z_statistics: list, p_values: list, alphas: list, adj_p_values: list, adj_alphas: list)

statds.no_parametrics.finner(ranks: dict, num_cases: int, alpha: float = 0.05, control: str | None = None, type_rank: str = 'Friedman', verbose: bool = False)

This function implements the Finner correction, a statistical method for controlling the family-wise error rate in multiple comparisons. The Finner correction is an alternative to other methods like Bonferroni or Holm, and it is generally more powerful than the Bonferroni correction.

Parameters

ranksdict

A dictionary where keys are the names of the algorithms and values are their respective ranks. The ranks must be obtained based on multiple non-parametric tests.

num_casesint

An integer representing the number of cases, datasets, or instances over which the rankings were calculated.

alphafloat, optional

A float representing the significance level used in the test. It defaults to 0.05, which is a common choice in statistical testing.

controlstr, optional

An optional string specifying a control algorithm against which others will be compared. If None, all algorithms are compared against each other.

type_rankstr, optional

A string indicating the type of ranking used (e.g., “Friedman”). Defaults to “Friedman”.

verbosebool, optional

A boolean indicating whether to print additional information (like the critical distance). Defaults to False.

Returns

comparison_resultspandas.DataFrame

A DataFrame with the results of the comparisons, including adjusted z-values and adjusted p-values.

comparison_figurematplotlib.figure.Figure

A figure graphically displaying the results of the tests, typically a bar chart or scatter plot.

Note

The Finner method is particularly useful in scenarios involving multiple comparisons, where it provides a balance between statistical power and control over Type I errors. This makes it a valuable tool in comparative studies of algorithms or treatments across various datasets.

statds.no_parametrics.friedman(dataset: DataFrame, alpha: float = 0.05, minimize: bool = False, verbose: bool = False, apply_correction: bool = False) → object

Perform the Friedman test, a non-parametric statistical test similar to the parametric ANOVA, but for repeated measures. The Friedman test is used to detect differences in treatments across multiple test attempts. It ranks the treatments for each block (or subject), then considers these ranks.

Parameters

datasetpandas.DataFrame

A DataFrame with the first column as the block or subject identifier and the remaining columns as different treatments or conditions.

alphafloat, optional

The significance level for the test, default is 0.05.

minimizebool, optional

Determines whether the metric of interest should be minimized or maximized. If True, the metric is to be minimized; if False, it is to be maximized. This parameter is crucial for tailoring the function’s behavior to the specific nature of the data or the goal of the analysis.

verbosebool, optional

If True, prints the detailed results table including ranks.

apply_correctionbool, optional

If True, apply Tie correction for the Friedman two-way analysis of variance by rank

Returns

rankings_with_labeldict

A dictionary with the average ranks of each treatment or condition.

statistic_friedmanfloat

The Friedman test statistic, which is chi-squared distributed under the null hypothesis.

p_valuefloat

The p-value for the hypothesis test.

cv_alpha_selectedfloat or None

The critical value for the test at the specified alpha level.

hypothesisstr

A string stating the conclusion of the test based on the test statistic, critical value, and alpha.

Note

The Friedman test is appropriate when data is ordinal and the assumptions of parametric tests (like ANOVA) are not met. It considers the ranks of the treatments within each block, summing these ranks, and then analyzing the sums’ distribution. The test is robust against non-normal distributions and is ideal for small sample sizes.

statds.no_parametrics.friedman_aligned_ranks(dataset: DataFrame, alpha: float = 0.05, minimize: bool = False, verbose: bool = False)

Perform the Friedman Aligned Ranks test, an extension of the Friedman test. This test is used when dealing with multiple treatments or conditions over different subjects or blocks, especially in cases where the assumptions of the classical Friedman test may not hold. The test aligns the data by subtracting the mean across treatments for each subject before ranking.

Parameters

datasetpandas.DataFrame

A DataFrame with the first column as the block or subject identifier and the remaining columns as different treatments or conditions.

alphafloat, optional

The significance level for the test, default is 0.05.

minimizebool, optional

Determines whether the metric of interest should be minimized or maximized. If True, the metric is to be minimized; if False, it is to be maximized. This parameter is crucial for tailoring the function’s behavior to the specific nature of the data or the goal of the analysis.

verbosebool, optional

If True, prints the detailed results table including aligned ranks.

Returns

rankings_with_labeldict

A dictionary with the average ranks of each treatment or condition.

statistic_friedmanfloat

The Friedman Aligned Ranks test statistic.

p_valuefloat

The p-value for the hypothesis test.

cv_alpha_selectedfloat or None

The critical value for the test at the specified alpha level.

hypothesisstr

A string stating the conclusion of the test based on the test statistic, critical value, and alpha.

Note

The Friedman Aligned Ranks test modifies the standard Friedman test by aligning the data for each subject before ranking. This alignment is achieved by subtracting the average rank across treatments for each subject, making the test more robust to certain types of data irregularities, like outliers. It is appropriate for ordinal data and assumes that the groups are independent and identically distributed within each block.

statds.no_parametrics.generate_graph_p_values(data: DataFrame, name_control, all_vs_all)

statds.no_parametrics.hochberg(ranks: dict, num_cases: int, alpha: float = 0.05, control: str | None = None, type_rank: str = 'Friedman', verbose: bool = False)

This function implements the Hochberg step-up procedure for multiple comparisons correction. It is an alternative to the Bonferroni method and is generally more powerful, especially when there are a large number of comparisons. The Hochberg procedure controls the family-wise error rate more effectively than some other methods.

Parameters

ranksdict

A dictionary where keys are the names of the algorithms and values are their respective ranks. The ranks must be obtained based on multiple non-parametric tests.

num_casesint

An integer representing the number of cases, datasets, or instances over which the rankings were calculated.

alphafloat, optional

A float representing the significance level used in the test. It defaults to 0.05, which is a common choice in statistical testing.

controlstr, optional

An optional string specifying a control algorithm against which others will be compared. If None, all algorithms are compared against each other.

type_rankstr, optional

A string indicating the type of ranking used (e.g., “Friedman”). Defaults to “Friedman”.

verbosebool, optional

A boolean indicating whether to print additional information (like the critical distance). Defaults to False.

Returns

comparison_resultspandas.DataFrame

A DataFrame with the results of the comparisons, including adjusted z-values and adjusted p-values.

comparison_figureobject

A figure graphically displaying the results of the tests, typically a bar chart or scatter plot.

Note

The Hochberg procedure is particularly valuable when conducting multiple comparisons in statistical analysis, as it provides a more refined approach to controlling the Type I error rate compared to more conservative methods.

statds.no_parametrics.holland(ranks: dict, num_cases: int, alpha: float = 0.05, control: str | None = None, type_rank: str = 'Friedman', verbose: bool = False)

This function applies the Holland step-down procedure for controlling the family-wise error rate in multiple comparisons. It’s an improvement over the simple Bonferroni method and is particularly useful when dealing with a large number of comparisons, and it is generally more powerful than the Bonferroni correction.

Parameters

ranksdict

A dictionary where keys are the names of the algorithms and values are their respective ranks. The ranks must be obtained based on multiple non-parametric tests.

num_casesint

An integer representing the number of cases, datasets, or instances over which the rankings were calculated.

alphafloat, optional

A float representing the significance level used in the test. It defaults to 0.05, which is a common choice in statistical testing.

controlstr, optional

An optional string specifying a control algorithm against which others will be compared. If None, all algorithms are compared against each other.

type_rankstr, optional

A string indicating the type of ranking used (e.g., “Friedman”). Defaults to “Friedman”.

verbosebool, optional

A boolean indicating whether to print additional information (like the critical distance). Defaults to False.

Returns

comparison_resultspandas.DataFrame

A DataFrame with the results of the comparisons, including adjusted z-values and adjusted p-values.

comparison_figurematplotlib.figure.Figure

A figure graphically displaying the results of the tests, typically a bar chart or scatter plot.

Note

The Holland method adjusts the alpha values for each comparison based on their rank in p-value, offering a more nuanced control over Type I errors compared to the Bonferroni method. It’s particularly effective in scenarios with multiple algorithm comparisons, ensuring a more accurate interpretation of statistical results.

statds.no_parametrics.holm(ranks: dict, num_cases: int, alpha: float = 0.05, control: str | None = None, type_rank: str = 'Friedman', verbose: bool = False)

This function implements the Holm-Bonferroni method, an adjustment for multiple comparisons. It is used to control the family-wise error rate when comparing multiple algorithms or treatments. This method is more powerful than the simple Bonferroni correction, especially when the number of comparisons is large.

Parameters

ranksdict

A dictionary where keys are the names of the algorithms and values are their respective ranks. The ranks must be obtained based on multiple non-parametric tests.

num_casesint

An integer representing the number of cases, datasets, or instances over which the rankings were calculated.

alphafloat, optional

A float representing the significance level used in the test. It defaults to 0.05, which is a common choice in statistical testing.

controlstr, optional

An optional string specifying a control algorithm against which others will be compared. If None, all algorithms are compared against each other.

type_rankstr, optional

A string indicating the type of ranking used (e.g., “Friedman”). Defaults to “Friedman”.

verbosebool, optional

A boolean indicating whether to print additional information (like the critical distance). Defaults to False.

Returns

comparison_resultspandas.DataFrame

A DataFrame with the results of the comparisons, including adjusted z-values and adjusted p-values.

comparison_figurematplotlib.figure.Figure

A figure graphically displaying the results of the tests, typically a bar chart or scatter plot.

Note

The Holm-Bonferroni method adjusts the significance levels of each comparison based on the order of their p-values, providing a less conservative approach than the original Bonferroni correction. It’s particularly useful in scenarios with multiple comparisons to control the overall type I error rate.

statds.no_parametrics.hommel(ranks: dict, num_cases: int, alpha: float = 0.05, control: str | None = None, type_rank: str = 'Friedman', verbose: bool = False)

This function implements the Hommel correction, a statistical method for adjusting p-values when performing multiple comparisons. The Hommel correction is a more powerful alternative to the Bonferroni correction, particularly when the number of comparisons is large.

Parameters

ranksdict

A dictionary where keys are the names of the algorithms and values are their respective ranks. The ranks must be obtained based on multiple non-parametric tests.

num_casesint

An integer representing the number of cases, datasets, or instances over which the rankings were calculated.

alphafloat, optional

A float representing the significance level used in the test. It defaults to 0.05, which is a common choice in statistical testing.

controlstr, optional

An optional string specifying a control algorithm against which others will be compared. If None, all algorithms are compared against each other.

type_rankstr, optional

A string indicating the type of ranking used (e.g., “Friedman”). Defaults to “Friedman”.

verbosebool, optional

A boolean indicating whether to print additional information (like the critical distance). Defaults to False.

Returns

comparison_resultspandas.DataFrame

A DataFrame with the results of the comparisons, including adjusted z-values and adjusted p-values.

comparison_figurematplotlib.figure.Figure

A figure graphically displaying the results of the tests, typically a bar chart or scatter plot.

Note

The Hommel correction is particularly useful in scenarios with multiple comparisons, as it provides a balance between controlling the family-wise error rate and maintaining statistical power. This makes it an effective tool in the comparative analysis of algorithms or treatments across various datasets.

statds.no_parametrics.iman_davenport(dataset: DataFrame, alpha: float = 0.05, minimize: bool = False, verbose: bool = False)

Perform the Iman-Davenport test, a non-parametric statistical test that is a modification of the Friedman test. This test is used when comparing more than two treatments or conditions across multiple blocks or subjects. Unlike the Friedman test, the Iman-Davenport test converts the Friedman statistic into an F-distribution providing a better approximation in certain cases, especially when dealing with small sample sizes.

Parameters

datasetpandas.DataFrame

A DataFrame with the first column as the block or subject identifier and the remaining columns as different treatments or conditions.

alphafloat, optional

The significance level for the test, default is 0.05.

minimizebool, optional

Determines whether the metric of interest should be minimized or maximized. If True, the metric is to be minimized; if False, it is to be maximized. This parameter is crucial for tailoring the function’s behavior to the specific nature of the data or the goal of the analysis.

verbosebool, optional

If True, prints the detailed results table including ranks.

Returns

rankings_with_labeldict

A dictionary with the average ranks of each treatment or condition.

statistic_iman_davenportfloat

The Iman-Davenport test statistic, which follows an F-distribution under the null hypothesis.

reject_valuetuple

A tuple containing the critical value for the test and the p-value (if applicable).

hypothesisstr

A string stating the conclusion of the test based on the test statistic, critical value, and alpha.

Note

The Iman-Davenport test is particularly useful in cases where the assumptions of the Friedman test are not fully met or when a more sensitive analysis is required. It is especially effective in small sample sizes and is robust against non-normal distributions, similar to the Friedman test. However, it provides a more accurate approximation to the F-distribution, making it preferable in certain statistical analyses.

statds.no_parametrics.kruskal_wallis(dataset: DataFrame, alpha: float = 0.05, minimize: bool = False, verbose: bool = False)

Perform the Kruskal-Wallis H-test for independent samples to determine whether the population medians on a dependent variable are the same across all groups or not. This non-parametric method does not assume a normal distribution of the residuals, making it a robust alternative to the one-way ANOVA.

The function includes an option to adjust for ties and provides detailed output, including the test statistic, p-value, and a critical value based on the significance level (alpha). It can also print the dataset if verbose mode is enabled.

Parameters

datasetpd.DataFrame

A pandas DataFrame containing the dataset to be tested. The first column should be the grouping variable, and the remaining columns should contain the data for each group.

alphafloat, optional

Significance level used to determine the critical value for the test. Default is 0.05.

minimizebool, optional

Determines whether the metric of interest should be minimized or maximized. If True, the metric is to be minimized; if False, it is to be maximized. This parameter is crucial for tailoring the function’s behavior to the specific nature of the data or the goal of the analysis.

verbosebool, optional

If True, prints the dataset after melting and ranking. Useful for debugging or detailed analysis. Default is False.

Returns

statistic_kruskalfloat

The Kruskal-Wallis H statistic, adjusted for ties.

p_valuefloat

The p-value for the test statistic.

critical_valuefloat

The critical chi-square value from the chi-square distribution table based on the alpha level.

hypothesisstr

A string stating the result of the hypothesis test based on the p-value and alpha.

Notes

• The test is applied to data that is at least ordinal (rankable).

• This implementation automatically adjusts for ties in the data.

• The function converts the input data into long format, ranking the data, and then computes the test statistic.

statds.no_parametrics.li(ranks: dict, num_cases: int, alpha: float = 0.05, control: str | None = None, type_rank: str = 'Friedman', verbose: bool = False)

This function implements the Li method for adjusting p-values in multiple comparisons. The Li method is particularly useful when there is a control algorithm to compare against other algorithms. It adjusts p-values based on the performance of the control algorithm relative to others.

Parameters

ranksdict

A dictionary where keys are the names of the algorithms and values are their respective ranks. The ranks must be obtained based on multiple non-parametric tests.

num_casesint

An integer representing the number of cases, datasets, or instances over which the rankings were calculated.

alphafloat, optional

A float representing the significance level used in the test. It defaults to 0.05, which is a common choice in statistical testing.

controlstr, optional

An optional string specifying a control algorithm against which others will be compared. If None, all algorithms are compared against each other.

type_rankstr, optional

A string indicating the type of ranking used (e.g., “Friedman”). Defaults to “Friedman”.

verbosebool, optional

A boolean indicating whether to print additional information (like the critical distance). Defaults to False.

Returns

comparison_resultspandas.DataFrame

A DataFrame with the results of the comparisons, including adjusted z-values and adjusted p-values.

comparison_figureobject

A figure graphically displaying the results of the tests, typically a bar chart or scatter plot.

Note

The Li method is effective in scenarios where a specific algorithm (the control) is of particular interest, and the comparisons are made between this control and other algorithms. It provides a nuanced way to adjust for multiple comparisons by considering the performance of the control algorithm.

statds.no_parametrics.mannwhitneyu(dataset: DataFrame, alpha: float = 0.05, verbose: bool = False)

Perform the Mann-Whitney U Test, also known as the Wilcoxon rank-sum test. This non-parametric test is utilized to determine whether there is a significant difference between the distributions of two independent samples. It serves as an alternative to the independent t-test, particularly when the data does not satisfy the assumptions of the t-test.

Parameters

datasetpandas.DataFrame

A DataFrame with exactly two columns, each representing a different independent sample.

alphafloat, optional

The significance level for the test. Default is 0.05.

verbosebool, optional

If True, prints the detailed results table.

Returns

z_valuefloat

The z-value computed from the U statistic.

cv_alpha_selectedfloat or None

The critical value for the test at the specified alpha level (not calculated in this function, hence None).

p_valuefloat

The p-value for the hypothesis test, calculated from the normal approximation of the U distribution.

hypothesisstr

A string stating the conclusion of the test based on the z-value and p-value in comparison to alpha.

Note

The Mann-Whitney U test ranks all observations from both groups together and then compares the sum of ranks in each group. It is suitable for ordinal data and is robust against non-normal distributions. The test assumes that the two groups are independent and that the observations are ordinal or continuous. The normal approximation for the p-value calculation is valid for large sample sizes.

statds.no_parametrics.mcnemar(results_1, results_2, real_results, alpha: float = 0.05, verbose: bool = False)

statds.no_parametrics.multiple_sign_test(dataset: DataFrame, alpha: float = 0.05, minimize: bool = False, verbose: bool = False)

statds.no_parametrics.nemenyi(ranks: dict, num_cases: int, alpha: float = 0.05, verbose: bool = False)

The Nemenyi test is a post-hoc analysis method used in statistics to compare multiple algorithms or treatments. It is often used after a Friedman test has indicated significant differences across algorithms.

Parameters

ranksdict

A dictionary where keys are the names of the algorithms and values are their respective ranks. The ranks must be obtained based on multiple non-parametric tests.

num_casesint

An integer representing the number of cases, datasets, or instances over which the rankings were calculated.

alphafloat, optional

A float representing the significance level used in the test. It defaults to 0.05, which is a common choice in statistical testing.

verbosebool, optional

A boolean indicating whether to print additional information (like the critical distance). Defaults to False.

Returns

rank_valueslist

The list of rank values for each algorithm.

critical_distancefloat

The critical distance for the Nemenyi test, which is a threshold used to determine if differences between algorithm rankings are statistically significant.

figurematplotlib.figure.Figure

A figure representing the ranking of the algorithms and the critical distances visually, often as a CD diagram.

Note

The Nemenyi test is non-parametric and is used when the assumptions of parametric tests (like ANOVA) are not met. It’s particularly useful in scenarios where multiple algorithms are compared across various datasets.

statds.no_parametrics.prepare_comparisons(ranks: dict, num_algorithm: int, num_cases: int, control: str | None = None, type_rank: str = 'Friedman')

statds.no_parametrics.quade(dataset: DataFrame, alpha: float = 0.05, minimize: bool = False, verbose: bool = False)

Perform the Quade test, a non-parametric statistical test used to identify significant differences between three or more matched groups. This test is particularly useful for blocked designs where treatments are applied to matched groups or blocks. The Quade test considers the relative differences between treatments within each block and ranks these differences.

Parameters

datasetpandas.DataFrame

A DataFrame with the first column as the block or subject identifier and the remaining columns as different treatments or conditions.

alphafloat, optional

The significance level for the test, default is 0.05.

minimizebool, optional

Determines whether the metric of interest should be minimized or maximized. If True, the metric is to be minimized; if False, it is to be maximized. This parameter is crucial for tailoring the function’s behavior to the specific nature of the data or the goal of the analysis.

verbosebool, optional

If True, prints the detailed results table including ranks.

Returns

rankings_with_labeldict

A dictionary with the average ranks of each treatment or condition.

statistic_quadefloat

The Quade test statistic.

p_valuefloat

The p-value for the hypothesis test.

cv_alpha_selectedNone

The critical value for the test at the specified alpha level.

hypothesisstr

A string stating the conclusion of the test based on the test statistic, critical value, and alpha.

Note

The Quade test adjusts for differences in treatment effects within each block by incorporating the range of each block into the ranking process. This makes it more sensitive to treatment effects in the presence of block-to-block variability. It’s appropriate for ordinal data and assumes that the treatments are independent and identically distributed within each block.

statds.no_parametrics.rom(ranks: dict, num_cases: int, alpha: float = 0.05, control: str | None = None, type_rank: str = 'Friedman', verbose: bool = False)

This function implements the Rom method, which is a step-down procedure for adjusting p-values in the context of multiple comparisons. The Rom method is an improvement over the Bonferroni correction, providing a more powerful approach, especially when the number of comparisons is large.

Parameters

ranksdict

A dictionary where keys are the names of the algorithms and values are their respective ranks. The ranks must be obtained based on multiple non-parametric tests.

num_casesint

An integer representing the number of cases, datasets, or instances over which the rankings were calculated.

alphafloat, optional

A float representing the significance level used in the test. It defaults to 0.05, which is a common choice in statistical testing.

controlstr, optional

An optional string specifying a control algorithm against which others will be compared. If None, all algorithms are compared against each other.

type_rankstr, optional

A string indicating the type of ranking used (e.g., “Friedman”). Defaults to “Friedman”.

verbosebool, optional

A boolean indicating whether to print additional information (like the critical distance). Defaults to False.

Returns

comparison_resultspandas.DataFrame

A DataFrame with the results of the comparisons, including adjusted z-values and adjusted p-values.

comparison_figureobject

A figure graphically displaying the results of the tests, typically a bar chart or scatter plot.

Note

The Rom method is particularly useful in scenarios involving multiple comparisons, as it offers a more accurate control of the family-wise error rate compared to simpler methods like Bonferroni, especially in cases with a large number of algorithms or treatments being compared.

statds.no_parametrics.shaffer(ranks: dict, num_cases: int, alpha: float = 0.05, type_rank: str = 'Friedman', verbose: bool = False)

This function applies Shaffer’s multiple comparison procedure, which is a more refined method for adjusting p-values in the context of multiple comparisons. Shaffer’s method is an extension of the Bonferroni correction and is generally more powerful, particularly when the number of comparisons is large.

Parameters

ranksdict

A dictionary where keys are the names of the algorithms and values are their respective ranks. The ranks must be obtained based on multiple non-parametric tests.

num_casesint

An integer representing the number of cases, datasets, or instances over which the rankings were calculated.

alphafloat, optional

A float representing the significance level used in the test. It defaults to 0.05, which is a common choice in statistical testing.

type_rankstr, optional

A string indicating the type of ranking used (e.g., “Friedman”). Defaults to “Friedman”.

verbosebool, optional

A boolean indicating whether to print additional information (like the critical distance). Defaults to False.

Returns

comparison_resultspandas.DataFrame

A DataFrame with the results of the comparisons, including adjusted z-values and adjusted p-values.

comparison_figurematplotlib.figure.Figure

A figure graphically displaying the results of the tests, typically a bar chart or scatter plot.

Note

Shaffer’s method is particularly effective in scenarios with multiple comparisons, as it provides a more accurate control of the family-wise error rate compared to simpler methods like Bonferroni, especially when the number of algorithms or treatments being compared is large.

statds.no_parametrics.wilconxon(dataset: DataFrame, alpha: float = 0.05, verbose: bool = False)

Perform the Wilcoxon signed-rank test. This non-parametric test is used to compare two related samples, matched samples, or repeated measurements on a single sample to assess whether their population mean ranks differ. It is an alternative to the paired Student’s t-test when the data is not normally distributed.

Parameters

datasetpandas.DataFrame

A DataFrame with exactly two columns, each representing a different condition or time point for the same subjects.

alphafloat, optional

The significance level for the test. Default is 0.05.

verbosebool, optional

If True, prints the detailed results table.

Returns

w_wilcoxonfloat

The Wilcoxon test statistic, which is the smallest of the sums of the positive and negative ranks.

p_valuefloat or None

The p-value for the hypothesis test (only for large sample sizes, otherwise None).

cv_alpha_selectedfloat or None

The critical value for the test at the specified alpha level (only for small sample sizes, otherwise None).

hypothesisstr

A string stating the conclusion of the test based on the test statistic, critical value, or p-value and alpha.

Note

The Wilcoxon signed-rank test makes fewer assumptions than the t-test and is appropriate when the data are not normally distributed. It ranks the absolute differences between pairs, then compares these ranks. The test is sensitive to ties and has different procedures for small and large sample sizes. For large samples, the test statistic is approximately normally distributed, allowing the use of normal approximation for p-value calculation.

statds.normality module

statds.normality.d_agostino_pearson(data: array, alpha: float = 0.05)

Perform the D’Agostino and Pearson’s omnibus test for normality. This test combines skew and kurtosis to produce an omnibus test of normality, testing the null hypothesis that a sample comes from a normally distributed population.

Parameters

datanumpy.array

Array of sample data. It should be a one-dimensional numpy array.

alphafloat, optional

The significance level for test analysis. Default is 0.05.

Returns

statistic_dpfloat

The D’Agostino and Pearson’s test statistic.

p_valuefloat

The p-value for the hypothesis test. A small p-value (typically ≤ 0.05) rejects the null hypothesis, indicating the data is not normally distributed.

cv_valuefloat

Critical value for the test based on the chi-squared distribution with 2 degrees of freedom.

hypothesisstr

A string stating the conclusion of the test based on the p-value and alpha. It indicates whether the null hypothesis can be rejected or not.

Note

The test calculates skewness and kurtosis of the data, standardizes these values, and then calculates a test statistic that follows a chi-squared distribution with 2 degrees of freedom under the null hypothesis. The p-value is then derived from this chi-squared distribution.

statds.normality.kolmogorov_smirnov(data: array, alpha: float = 0.05)

Perform the Kolmogorov-Smirnov test for goodness of fit. This non-parametric test compares a sample with a reference probability distribution (in this case, the normal distribution), assessing whether the sample data follows the same distribution as the reference distribution.

Parameters

datanumpy.array

Array of sample data. It should be a one-dimensional numpy array.

alphafloat, optional

The significance level for the test. Default is 0.05.

Returns

d_maxfloat

The maximum difference between the Empirical Cumulative Distribution Function (ECDF) of the data and the Cumulative Distribution Function (CDF) of the reference distribution (normal distribution in this case).

p_valuefloat

The p-value for the hypothesis test. A small p-value (typically ≤ 0.05) rejects the null hypothesis, suggesting that the sample data does not follow the reference distribution.

cv_valuefloat

Critical value for the Kolmogorov-Smirnov test. This is currently set to None.

hypothesisstr

A string stating the conclusion of the test based on the p-value and alpha. It indicates whether the null hypothesis can be rejected or not.

Note

The test calculates the maximum difference (d_max) between the ECDF of the sample data and the CDF of the normal distribution. The KS statistic is then derived from this difference and the sample size. The p-value is estimated from the KS statistic. This test is non-parametric and does not assume a normal distribution of the data.

statds.normality.kurtosis(data: array, bias: bool = True)

Calculate the kurtosis of the given data. Kurtosis is a measure of the “tailedness” of the probability distribution of a real-valued random variable. In a general sense, kurtosis quantifies whether the tails of the data distribution are heavier or lighter compared to a normal distribution.

Parameters

datanumpy.array

Array of sample data. It should be a one-dimensional numpy array.

biasbool, optional

A boolean indicating whether to correct for statistical bias. If False, calculations are corrected for bias. Default is True, meaning no bias correction is applied.

Returns

float

The kurtosis of the data, representing the degree of kurtosis in the distribution: A value greater than 3 indicates a distribution with heavier tails and a sharper peak compared to a normal distribution. A value less than 3 indicates a distribution with lighter tails and a flatter peak compared to a normal distribution. A value close to 3, especially when bias is False, indicates a distribution similar to a normal distribution in terms of kurtosis.

Note

The bias parameter affects the calculation of kurtosis. If bias is False, the result is adjusted for bias, making it more representative for samples from a larger population. If bias is True (default), the kurtosis is calculated without any adjustments. The adjustment for bias involves a correction factor based on the number of samples, which corrects the result for the tendency of small samples to underestimate kurtosis.

statds.normality.kurtosis_test(b2: float, n: int)

Perform a kurtosis test to assess the ‘tailedness’ or peakedness of the probability distribution of a dataset. This test calculates a z-score for the kurtosis and the corresponding p-value to determine the statistical significance of the kurtosis.

Parameters

b2float

The squared sample kurtosis.

nint

The sample size.

Returns

z_b2float

The z-score for the kurtosis test. This score indicates the degree of peakedness in the distribution.

p_valuefloat

The p-value corresponding to the z-score. A small p-value (typically ≤ 0.05) suggests that the distribution of the data has significant kurtosis, differing from a normal distribution.

Note

The kurtosis test is used to determine if a dataset has heavier or lighter tails compared to a normal distribution. The test involves calculating the mean and variance of b2, the standardized version of b2, and then computing the standardized moment of b2. The z-score and p-value help assess whether the kurtosis of the dataset significantly deviates from that of a normal distribution, where the kurtosis is expected to be around 0.

statds.normality.pp_plot(data: array)

Generate a Probability-Probability (PP) plot for a given dataset. A PP plot is a graphical technique for assessing how closely a set of data follows a given distribution, typically the normal distribution. It compares the empirical cumulative distribution function (CDF) of the data to the theoretical CDF of the specified distribution.

Parameters

datanumpy.array

A numpy array of sample data to be analyzed.

Returns

matplotlib.figure.Figure

A matplotlib figure object that contains the PP plot.

Note

In a PP plot, the y-axis shows the empirical CDF of the data, and the x-axis displays the theoretical CDF of the distribution being tested (normal distribution in this case). A 45-degree reference line is added to the plot. If the data follow the specified distribution, the plot will align closely with this line. The PP plot is useful for assessing the goodness of fit of a distribution and is particularly helpful for determining if data follow a normal distribution, which is a common assumption in various statistical tests.

statds.normality.qq_plot(data: array)

Generate a Quantile-Quantile (QQ) plot for a given dataset. A QQ plot is a graphical tool to help assess if a dataset follows a particular distribution, such as a normal distribution. It compares the quantiles of the data to the quantiles of a theoretical distribution.

Parameters

datanumpy.array

A numpy array of sample data to be analyzed.

Returns

matplotlib.figure.Figure

A matplotlib figure object that contains the QQ plot.

Note

In the QQ plot, the quantiles of the data are plotted against the quantiles of a theoretical distribution (in this case, the normal distribution). If the data follow the theoretical distribution, the points on the QQ plot will approximately lie on the line y = x. Departures from this line indicate departures from the theoretical distribution. The plot helps in visually assessing normality, which is a common assumption in many statistical tests.

statds.normality.shapiro_wilk_normality(data: array, alpha: float = 0.05)

Performs the Shapiro-Wilk test for normality. This test assesses the null hypothesis that the data was drawn from a normal distribution.

Parameters

datanumpy.array

Array of sample data. It should be a one-dimensional numpy array.

alphafloat, optional

The significance level for test analysis. Default is 0.05.

Returns

statistics_wfloat

The W statistic for the test, a measure of normality.

p_valuefloat

The p-value for the hypothesis test. A small p-value (typically ≤ 0.05) rejects the null hypothesis, indicating the data is not normally distributed.

cv_valuefloat

Critical value for the Shapiro-Wilk test. This is currently set to None.

hypothesisstr

A string stating the conclusion of the test based on the p-value and alpha. It indicates whether the null hypothesis can be rejected or not.

statds.normality.skewness(data: array, bias: bool = True)

Calculate the skewness of the given data. Skewness is a measure of the asymmetry of the probability distribution of a real-valued random variable about its mean. Positive skewness indicates a distribution with an asymmetric tail extending towards more positive values, while negative skewness indicates a distribution with an asymmetric tail extending towards more negative values.

Parameters

datanumpy.array

Array of sample data. It should be a one-dimensional numpy array.

biasbool, optional

A boolean indicating whether to correct for statistical bias. If False, calculations are corrected for bias. Default is True, meaning no bias correction is applied.

Returns

float

The skewness of the data, indicating the degree of asymmetry in the distribution: - A value close to 0 indicates a symmetric distribution. - A positive value indicates a distribution that is skewed to the right. - A negative value indicates a distribution that is skewed to the left.

Note

The bias parameter affects the calculation of skewness. If bias is False, the result is adjusted for bias, making it suitable for samples from a larger population. If bias is True (default), the skewness of the sample is calculated without any adjustments.

statds.normality.skewness_test(b2, n)

Perform a skewness test to assess the asymmetry of the probability distribution of a dataset. This test calculates a z-score for the skewness and the corresponding p-value to determine the statistical significance of the skewness.

Parameters

b2float

The squared sample skewness.

nint

The sample size.

Returns

z_b1float

The z-score for the skewness test. A higher absolute value indicates greater skewness.

p_valuefloat

The p-value corresponding to the z-score. A small p-value (typically ≤ 0.05) suggests that the distribution of the data is significantly skewed.

Note

The skewness test is a hypothesis test that evaluates whether the skewness of the data differs significantly from 0, which would indicate a symmetric distribution. The test uses the sample size and the squared skewness to compute the test statistic. It’s particularly useful for determining if a distribution departs from normality, where skewness is expected to be about 0.

statds.parametrics module

statds.parametrics.anova_cases(dataset: DataFrame, alpha: float = 0.05)

Perform an ANOVA (Analysis of Variance) test. This statistical test is used to compare the means of two or more groups to determine if at least one group mean is significantly different from the others. It’s commonly used when there are three or more groups.

Parameters

datasetpandas.DataFrame

A DataFrame where each column represents a different group/sample. The first column is ignored.

alphafloat, optional

The significance level for the test. Default is 0.05.

Returns

summary_resultspandas.DataFrame

A DataFrame with a summary of each group’s mean, standard deviation, and standard error.

anova_resultspandas.DataFrame

A DataFrame with the ANOVA results, including degrees of freedom, sum of squares, mean square, F-statistic, and rejected value for between groups and within groups.

statistical_f_anovafloat

The F-statistic for the ANOVA test. A higher value suggests a greater difference between group means.

p_valuefloat

The p-value for the hypothesis test (currently not calculated and set to None).

rejected_valuefloat

The critical value for the test at the specified alpha level.

hypothesisstr

A string stating the conclusion of the test based on the F-statistic and alpha.

Note

ANOVA tests the null hypothesis that all group means are equal. The test assumes that the groups are sampled from populations with normal distributions and equal variances. The F-statistic is calculated based on the ratio of variance between the groups to the variance within the groups. A significant F-statistic (p-value less than alpha) indicates that at least one group mean is significantly different.

statds.parametrics.anova_within_cases(dataset: DataFrame, alpha: float = 0.05)

Perform a within-subject ANOVA (Analysis of Variance). This type of ANOVA is used when the same subjects are used for each treatment (i.e., the subjects are subjected to repeated measures). This test is beneficial for analyzing the effects of different conditions or treatments on a single group of subjects.

Parameters

datasetpandas.DataFrame

A DataFrame where each column represents a different condition/treatment for the same subjects. The first column is typically used for subject identification and is ignored in the analysis.

alphafloat, optional

The significance level for the test. Default is 0.05.

Returns

summary_resultspandas.DataFrame

A DataFrame with a summary of each group’s mean, standard deviation, and standard error.

anova_resultspandas.DataFrame

A DataFrame with the ANOVA results, including degrees of freedom, sum of squares, mean square, F-statistic, and rejected value for different sources of variance (between conditions, between subjects, etc.).

statistical_f_anovafloat

The F-statistic for the ANOVA test. A higher value suggests a significant differensce between conditions or treatments.

p_valuefloat

The p-value for the hypothesis test (currently not calculated and set to None).

rejected_valuefloat

The critical value for the test at the specified alpha level.

hypothesisstr

A string stating the conclusion of the test based on the F-statistic and alpha.

Note

Within-subject ANOVA controls for potential variability among subjects, as each subject serves as their own control. This test separates the variance due to the interaction between subjects and conditions from the variance due to differences between conditions and residual variance. It assumes sphericity, which implies that the variances of the differences between all possible pairs of conditions are equal.

statds.parametrics.t_test_paired(dataset: DataFrame, alpha: float = 0.05, verbose: bool = False)

Perform a paired t-test. This statistical test is used to compare the means of two related groups of samples, typically before and after a specific treatment or intervention. The test assumes that the differences between pairs are normally distributed.

Parameters

datasetpandas.DataFrame

A DataFrame with exactly two columns, each representing a different group/sample. These groups must be related or paired in some way (e.g., measurements before and after an intervention).

alphafloat, optional

The significance level for the test. Default is 0.05.

verbosebool, optional

A boolean indicating whether to print detailed results. If True, prints the test statistic, rejected value, p-value, and hypothesis. Default is False.

Returns

statistical_tfloat

The t-test statistic. A higher absolute value indicates a greater difference between the paired groups.

p_valuefloat

The p-value for the hypothesis test (currently not calculated and set to None).

rejected_valuefloat

The critical value for the test at the specified alpha level.

hypothesisstr

A string stating the conclusion of the test based on the test statistic and alpha. It indicates whether the null hypothesis (no difference between means) can be rejected or not.

Note

The paired t-test is appropriate for comparing two means from the same group or individual under two different conditions. The test statistic is calculated by dividing the mean difference between paired observations by the standard error of the mean difference. The test is sensitive to the normality assumption of the differences between pairs.

statds.parametrics.t_test_unpaired(dataset: DataFrame, alpha: float = 0.05, verbose: bool = False)

Perform an unpaired (independent) t-test. This statistical test is used to compare the means of two unrelated groups of samples to determine if there is a statistically significant difference between the two means. It’s appropriate when the two groups are independent of each other.

Parameters

datasetpandas.DataFrame

A DataFrame with exactly two columns, each representing a different group/sample. These groups must be independent or unpaired.

alphafloat, optional

The significance level for the test. Default is 0.05.

verbosebool, optional

A boolean indicating whether to print detailed results. If True, prints the test statistic, rejected value, p-value, and hypothesis. Default is False.

Returns

statistical_tfloat

The t-test statistic. A higher absolute value indicates a greater difference between the group means.

p_valuefloat

The p-value for the hypothesis test (currently not calculated and set to None).

rejected_valuefloat

The critical value for the test at the specified alpha level.

hypothesisstr

A string stating the conclusion of the test based on the test statistic and alpha. It indicates whether the null hypothesis (no difference between means) can be rejected or not.

Note

The unpaired t-test assumes that the two groups have equal variances and that the samples are randomly drawn. The test statistic is calculated by taking the difference between the two group means and dividing by the standard error of the mean difference. The test is sensitive to the normality assumption of the sample data.

statds.stats module

statds.stats.binomial_coef(n: int, k: int)

Calculate the binomial coefficient (n choose k).

Parameters

nint

The total number of items.

kint

The number of items to be chosen.

Returns

int

The binomial coefficient value (n choose k).

statds.stats.get_cdf_normal(z_value)

Calculate the cumulative distribution function (CDF) of the standard normal distribution.

Parameters

z_valuefloat

The z-value for which the CDF is calculated.

Returns

float

The CDF value for the given z-value.

statds.stats.get_cv_f_distribution(df_numerator: int, df_denominator: int, alpha: float)

Retrieve the critical value from an F-distribution critical values table for given degrees of freedom and alpha. This function reads an F-distribution critical values table from a CSV file, which contains critical values for different degrees of freedom for the numerator and denominator, as well as significance levels (alpha). It selects the critical value based on the provided degrees of freedom for the numerator (df_numerator), degrees of freedom for the denominator (df_denominator), and significance level (alpha).

Parameters

df_numeratorint

Degrees of freedom for the numerator.

df_denominatorint

Degrees of freedom for the denominator.

alphafloat

The significance level for which the critical value is needed.

Returns

float

The critical value corresponding to the input degrees of freedom and alpha.

statds.stats.get_cv_q_distribution(k_degrees_of_freedom: int, num_alg: int, alpha: float)

Retrieve the critical value from a Q-table for a given chi-squared distribution. This function reads a Q-table from a CSV file, which contains critical values for various degrees of freedom, numerator degrees of freedom, and numbers of algorithms. It selects the critical value based on the provided degrees of freedom (k_degrees_of_freedom), number of algorithms (num_alg), and significance level (alpha).

Parameters

k_degrees_of_freedomint

The degrees of freedom of the chi-squared distribution.

num_algint

The number of algorithms.

alphafloat

The significance level for which the critical value is needed.

Returns

float

The critical value corresponding to the input degrees of freedom, number of algorithms, and alpha.

statds.stats.get_cv_t_distribution(k_degrees_of_freedom: int, alpha: float)

Retrieve the critical value from a t-distribution critical values table for a given degrees of freedom and alpha. This function reads a t-distribution critical values table from a CSV file, which contains critical values for different degrees of freedom and significance levels (alpha). It selects the critical value based on the provided degrees of freedom (k_degrees_of_freedom) and significance level (alpha).

Parameters

k_degrees_of_freedomint

Degrees of freedom for the t-distribution.

alphafloat

The significance level for which the critical value is needed.

Returns

float

The critical value corresponding to the input degrees of freedom and alpha.

statds.stats.get_cv_willcoxon(num_problems: int, alpha: float)

Retrieve the critical value from a Wilcoxon signed-rank test critical values table for a given number of samples and alpha. This function reads a Wilcoxon signed-rank test critical values table from a CSV file, which contains critical values for different numbers of samples and significance levels (alpha). It selects the critical value based on the provided number of samples (num_problems) and significance level (alpha).

Parameters

num_problemsint

The number of samples for which the critical value is needed.

alphafloat

The significance level for which the critical value is needed.

Returns

int

The critical value corresponding to the input number of samples and alpha.

statds.stats.get_p_value_binomial(num: int, statistical: int, probability: float = 0.5)

Calculate the p-value of a binomial distribution.

Parameters

numint

The number of trials in the binomial distribution.

statisticalint

The number of successful trials.

probabilityfloat, optional

The probability of success in each trial. Default is 0.5.

Returns

float

The p-value associated with the given values.

statds.stats.get_p_value_chi2(z_value: float, k_degrees_of_freedom: int, alpha: float)

Calculate the p-value of a binomial distribution.

Parameters

z_valuefloat

The z-value for which the CDF is calculated.

k_degrees_of_freedomint

The degrees of freedom of the chi-squared distribution.

alphafloat

The significance level for which the critical value is needed.

Returns

p_valuefloat

The p-value associated with the given z-value.

cv_to_alphafloat

The critical value corresponding to the specified alpha.

statds.stats.get_p_value_f(value: float, df_numerator: int, df_denominator: int)

Calculate the p-value for a given F-statistic using the F-distribution. This function is used to determine the significance of a test statistic from an ANOVA test, comparing the ratio of variances between and within groups.

Parameters

valuefloat

The F-statistic value for which the p-value is to be calculated.

df_numeratorint

The degrees of freedom for the numerator, often corresponding to the number of groups minus one.

df_denominatorint

The degrees of freedom for the denominator, usually related to the total number of observations minus the number of groups.

Returns

float

The p-value corresponding to the given F-statistic and degrees of freedom. This p-value indicates the probability of observing a value at least as extreme as the F-statistic under the null hypothesis.

Note

The calculation of the p-value depends on the degrees of freedom for both the numerator and the denominator, and the F-statistic itself.

statds.stats.get_p_value_normal(z_value)

Calculate the p-value for a given z-value in a standard normal distribution.

Parameters

z_valuefloat

The z-value for which the p-value is calculated.

Returns

float

The p-value associated with the given z-value.

statds.stats.get_p_value_shapier(num_samples: int, statistics_w: float)

Retrieve the p-value from a Shapiro-Wilk test for a given number of samples and statistics.

Parameters

num_samplesint

The number of samples for which the critical value is needed.

statistics_wfloat

The statistics for which the p-value is calculated.

Returns

float

The p-value from the Shapiro-Wilk test.

statds.stats.get_p_value_t(z_value: float, k_degrees_of_freedom: int, inf_approx=100, steps=1000000)

Calculate the p-value associated with a given z-value and degrees of freedom using the t-distribution. This function approximates the p-value by converting the z-value to a t-value and then integrating over the t-distribution to find the area under the curve.

Parameters

z_valuefloat

The z-value for which the p-value is to be calculated.

k_degrees_of_freedomint

The degrees of freedom for the t-distribution.

inf_approxint, optional

The upper limit for the integral approximation, default is 100.

stepsint, optional

The number of steps to use in the numerical approximation, default is 1,000,000.

Returns

float

The p-value corresponding to the given z-value and degrees of freedom.

statds.stats.get_pdf_t(z_value: float, k_degrees_of_freedom: int)

Calculate the t value for a given z-value and degrees of freedom.

Parameters

z_valuefloat

The z-value for which the chi-squared value is calculated.

k_degrees_of_freedomint

The degrees of freedom for the chi-squared calculation.

Returns

float

The t value.

statds.stats.get_q_alpha_nemenyi(num_algorithm: int, alpha: float)

Retrieve the Q_alpha value from a Nemenyi critical values table for a given number of algorithms and alpha. This function reads a Nemenyi critical values table from a CSV file, which contains critical values for different numbers of algorithms and significance levels (alpha). It selects the Q_alpha value based on the provided number of algorithms (num_algorithm) and significance level (alpha).

Parameters

num_algorithmint

The number of algorithms for which the Q_alpha value is needed.

alphafloat

The significance level for which the Q_alpha value is needed.

Returns

float

The Q_alpha value corresponding to the input number of algorithms and alpha.

statds.stats.get_shapiro_weights(n_weights: int)

Retri: inteve weights a_i for any given sample size n_weights.

Parameters

n_weightsint

The number of samples.

Returns

list

Weights a_i list for the given number of samples.

statds.stats.inverse_gaussian_cdf(value, mu: float = 1.0, lamb: float = 1.0)

Calculate the cumulative distribution function (CDF) of the inverse Gaussian distribution.

Parameters

valuefloat

The value for which the CDF is calculated.

mufloat, optional

The mean parameter of the distribution. Default is 1.0.

lambfloat, optional

The lambda parameter of the distribution. Default is 1.0.

Returns

float

The CDF of the inverse Gaussian distribution for the given value.

statds.stats.kolmogorov_p_value(d, n)

Calcula el p-valor para el estadístico de Kolmogorov-Smirnov.

Parameters:

• d – El estadístico de Kolmogorov-Smirnov.

• n – El número de observaciones.

Returns:

El p-valor aproximado.

statds.utils module

exception statds.utils.LibraryError(message)

Bases: Exception

statds.utils.analysis_of_experiments(dataset, experiments: dict, generate_pdf: bool = False, name_pdf: str = 'inform.pdf')

Performs statistical analysis on experiments and optionally generates a PDF report.

Parameters

datasetpandas.DataFrame

The dataset containing the experimental data.

experimentsdict

A dictionary defining the experiments and their parameters.

generate_pdfbool, optional

Whether to generate a PDF report (default is False).

name_pdfstr, optional

Name of the PDF file (default is ‘inform.pdf’).

statds.utils.dataframe_to_latex(dataframe: DataFrame, caption: str | None = None, label: str | None = None)

Converts a pandas DataFrame into LaTeX code for table creation.

Parameters

dataframepandas.DataFrame

The pandas DataFrame to be converted.

captionstr, optional

The table caption in LaTeX.

labelstr, optional

The table label in LaTeX.

Returns

str

LaTeX code for creating a table.

statds.utils.generate_json(names_experiments: list, parameters_experiments: list)

Generates a JSON structure containing experiment parameters.

Parameters

names_experimentslist

List of experiment names.

parameters_experimentslist

List of dictionaries containing experiment parameters.

Returns

dict

A dictionary representing experiment parameters in a structured JSON format.

statds.utils.gets_args_functions(name_function)

Retrieves the arguments and their default values for a specified function.

Parameters

name_functionfunction

The function for which argument information is required.

Returns

dict

A dictionary containing argument names as keys and their default values as values.

statds.utils.print_results(title_experiment, title, test_subtitle, test_result, h_post_hoc, show_table, show_graph)

Prints the results and related information to the console.

Parameters

title_experimentstr

Title for the experiment section.

titlestr

Title for the document.

test_subtitlestr

Subtitle for the test section.

test_resultlist

List of test results to be printed.

h_post_hocstr

Post-hoc information or analysis to be included.

show_tablepandas.DataFrame

A DataFrame containing the test results.

show_graphstr

Name of the saved graph or None if no graph is available.

statds.utils.process_alpha_experiment(parameter)

Processes and validates experiment parameters, including alpha level and test details.

Parameters

parameterdict

A dictionary containing experiment parameters.

Returns

dict

A dictionary containing processed and validated experiment parameters.

Raises

LibraryError

If the provided parameters are invalid or missing.