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Mohsen Askar

API Reference

The package is broadly divided into:

Mixin Classes:

To handle specific assumption checks:

  • NormalityChecker class: Checks normality using Shapiro-Wilk test, skewness, and kurtosis.
  • HomoscedasticityChecker class: Checks homoscedasticity using Levene's test.
  • MonotonicityChecker class: Checks monotonic relationships using Spearman correlation.
  • PairedDataChecker class: Checks if data is properly paired.
  • CategoricalDataChecker class: Checks if variables are categorical.
  • MultivariateNormalityChecker class: Checks multivariate normality using Mardia's test.
  • SurvivalDataChecker class: Checks basic requirements for survival data.
  • ProportionalHazardsChecker class: Checks proportional hazards using Schoenfeld residuals.
  • PairedDifferenceChecker class: Checks properties of paired differences.

Specific Checkers:

Specific checkers for various statistical tests, each inheriting from AssumptionChecker and relevant mixins:

  • IndependentTTestChecker class: For Independent Samples t-test
  • RepeatedMeasuresANOVAChecker class: For Repeated ANOVA
  • LogisticRegressionChecker class: For Logistic Regression
  • PearsonCorrelationChecker class: For Pearson correlation
  • PairedTTestChecker class: For Paired t-test
  • ChiSquareIndependenceChecker class: For Chi-square independence test
  • MultipleRegressionChecker class: For Multiple Linear Regression
  • TwoWayANOVAChecker class: For Two-way ANOVA
  • KaplanMeierChecker class: For Kaplan-Meier
  • CoxPHChecker class: For
  • PoissonRegressionChecker class: For Cox Proportional Hazards
  • SpearmanCorrelationChecker class: For Spearman Corraletion
  • WilcoxonSignedRankChecker class: For Wilcoxon Signed-Rank Test
  • MANOVAChecker class: For MANOVA
  • OneWayANOVAChecker class: For One-way ANOVA
  • FactorialANOVAChecker class: For Factorial ANOVA
  • Main Class: StatisticalTestAssumptions is the main class that manages the assumption checkers. It allows checking assumptions for a specified test type and provides recommendations based on the results.

Inlcuded tests assumptions

Independent Samples t-test t_test_ind

  1. Normality: The dependent variable should be (approximately) normally distributed within each group.
  2. Homogeneity of Variances: The population variances in the two groups should be equal (often checked using Levene’s test).
  3. Independence of Observations: Each observation in one group is independent of any observation in the other group.

Repeated-Measures ANOVA repeated_anova

  1. Normality: The dependent variable should be (approximately) normally distributed at each time point or for each repeated measure.
  2. Sphericity: The variances of the differences between all possible pairs of repeated-measure conditions should be equal (often checked by Mauchly’s test).
  3. Independence of Observations: Observations from different subjects are assumed to be independent, although repeated measures on the same subject are inherently correlated.

Logistic Regression logistic

  1. Dependent Variable: Binary (two categories, e.g., “success/fail” or “disease/no disease”). Independence of Errors: Residuals (errors) should be independent across observations.
  2. Lack of Multicollinearity: Predictor variables should not be too highly correlated with each other.
  3. Linearity in the Logit: Although logistic regression is for categorical outcomes, continuous predictors should have a linear relationship with the log odds of the outcome.

Factorial ANOVA factorial_anova

  1. Normality: The dependent variable in each cell of the design should be (approximately) normally distributed.
  2. Homogeneity of Variances: The variance across all cells (factorial combinations of levels) should be equal.
  3. Independence of Observations: Observations in each cell are independent of those in other cells and within cells.

One-Way ANOVA one_way_anova

  1. Normality: The dependent variable should be (approximately) normally distributed in each group.
  2. Homogeneity of Variances: The variances in each of the groups are assumed to be equal.
  3. Independence of Observations: Observations in one group should be independent from those in other groups.

Pearson Correlation pearson_correlation

  1. Linearity: The relationship between the two variables should be linear.
  2. Normality (for Significance Testing): Each variable should be (approximately) normally distributed if you want to use significance tests and confidence intervals for r.
  3. Interval or Ratio Scale: Both variables are typically continuous and measured on an interval or ratio scale.
  4. Independence of Observations: Each pair of observations comes from independent subjects or units.

Paired t-test paired_ttest

  1. Normality of Difference Scores: The differences between the paired observations should be (approximately) normally distributed.
  2. Dependence of Observations: Each pair is taken from the same subject or matched subjects (hence, “paired”).
  3. No Significant Outliers: Extreme outliers in the difference scores can affect the test.

Chi-Square Test of Independence chi_square_independence

  1. Independence of Observations: Each subject or unit should be counted only once in the contingency table.
  2. Expected Cell Frequency: Each cell in the contingency table should have an expected count of at least 5 (rule of thumb for validity of p-values).
  3. Categorical Variables: Both variables should be categorical (nominal or ordinal).

Multiple Regression multiple_regression

  1. Linearity: The relationship between each predictor and the outcome (dependent variable) is assumed to be linear in the parameters.
  2. Independence of Errors: Residuals should be independent (often checked by plotting residuals vs. predicted values).
  3. Homoscedasticity: The variance of residuals is constant across all levels of the predictors (also checked by residual plots).
  4. Normality of Residuals: The residuals should be (approximately) normally distributed (checked with Q-Q plots).
  5. Lack of Multicollinearity: Predictors should not be too highly correlated with each other.

Two-Way ANOVA two_way_anova

  1. Normality: The dependent variable in each group (combination of two independent factors) should be (approximately) normally distributed.
  2. Homogeneity of Variances: The variances across all factor-level combinations should be equal (Levene’s test is common).
  3. Independence of Observations: Observations in one factor-level combination are independent from other factor-level combinations and within each combination.

Kaplan-Meier Analysis kaplan_meier

  1. Random Censoring: Assumes that censoring is non-informative (the reason an individual leaves the study or is censored is independent of their underlying risk).
  2. Independence of Survival Times: Each subject’s survival time is independent of others.
  3. Time-to-Event Data: Typically used when the outcome is the time until an event (e.g., death, relapse).

Cox Proportional Hazards Model cox_ph

  1. Proportional Hazards: The hazard functions for different groups (or at different levels of a covariate) are proportional over time (i.e., hazard ratios remain constant over time).
  2. Random/Non-Informative Censoring: Similar to Kaplan-Meier, censoring should not be related to the outcome.
  3. Linearity (for Continuous Covariates): Often assumed that continuous covariates have a log-linear relationship with the hazard.
  4. Independence of Observations: Each subject’s time-to-event is independent (unless modeling random effects or frailty for clustering).

Poisson Regression poisson

  1. Count Outcome Variable: The dependent variable is a count (e.g., number of doctor visits).
  2. Mean-Variance Relationship: The Poisson model assumes the mean and variance are equal. (If variance > mean significantly, a Negative Binomial model might be preferred.)
  3. Independence of Observations: Each count is assumed to be independent of the others.
  4. Linearity in the Log Link: The log of the expected count is assumed to be a linear combination of predictors.

Spearman Correlation spearman

  1. Monotonic Relationship: The relationship between the two variables should be monotonic (does not have to be linear).
  2. Ordinal or Interval/Ratio Data: Although often used for ordinal data, Spearman correlation can also handle interval/ratio data that fail Pearson’s normality assumption.
  3. Independence of Observations: Each pair of observations is assumed independent.

Wilcoxon Signed-Rank Test wilcoxon_signed_rank

  1. Paired or Matched Samples: The same subjects measured twice, or matched subjects.
  2. Ordinal or Continuous Data: Used when data are ordinal or not normally distributed, but we assume differences can be meaningfully ranked.
  3. Symmetry of Distribution of Differences (Ideal): While not as strict as the normality assumption, it is often assumed that the distribution of differences is symmetrical around the median.

MANOVA (Multivariate Analysis of Variance) manova

  1. Multivariate Normality: The combination of dependent variables follows a multivariate normal distribution within each group.
  2. Homogeneity of Variance-Covariance Matrices: The variance-covariance matrices for the dependent variables are the same in each group (Box’s M test).
  3. Independence of Observations: Observations across groups (and within groups) are independent.
  4. No Multicollinearity Among Dependent Variables: If the dependent variables are very highly correlated, MANOVA might not be the best approach.

Suggested test alternatives explanation

Independent T-Test:

  • Suggested Alternatives: Mann-Whitney U test, Welch's t-test

  • Explanation:

  • Mann-Whitney U test is a non-parametric alternative that does not assume normality.

  • Welch's t-test is used when the assumption of equal variances is violated.

Repeated Measures ANOVA:

  • Suggested Alternatives: Friedman test, Mixed-effects model

  • Explanation:

    • Friedman test is a non-parametric alternative for repeated measures.

    • Mixed-effects model can handle violations of sphericity and other complex data structures.

Logistic Regression:

  • Suggested Alternatives: Penalized regression (Ridge, Lasso), Decision trees

  • Explanation:

    • Penalized regression methods like Ridge and Lasso can handle multicollinearity.

    • Decision trees do not assume linearity or independence of errors.

Pearson Correlation:

  • Suggested Alternatives: Spearman rank correlation, Kendall rank correlation, Robust correlation methods

  • Explanation:

    • Spearman rank correlation and Kendall rank correlation are non-parametric and do not assume normality.

    • Robust correlation methods can handle outliers.

Paired T-Test:

  • Suggested Alternatives: Wilcoxon signed-rank test, Sign test, Randomization test

  • Explanation:

    • Wilcoxon signed-rank test is a non-parametric alternative for paired data.

    • Sign test is another non-parametric alternative.

    • Randomization test can be used when assumptions are severely violated.

Chi-Square Test of Independence:

  • Suggested Alternatives: Fisher's exact test, G-test of independence, Freeman-Halton test, Log-linear analysis

  • Explanation:

    • Fisher's exact test is used for small sample sizes.

    • G-test is an alternative to the chi-square test.

    • Freeman-Halton test extends Fisher's test to larger tables.

    • Log-linear analysis is used for more complex categorical data.

Multiple Linear Regression:

  • Suggested Alternatives: Ridge Regression, Lasso Regression, Robust Regression, Quantile Regression, Non-linear regression models

  • Explanation:

    • Ridge and Lasso Regression address multicollinearity.

    • Robust Regression handles outliers.

    • Quantile Regression does not assume homoscedasticity.

    • Non-linear regression models are used when linearity is violated.

Two-Way ANOVA:

  • Suggested Alternatives: Non-parametric factorial analysis, Robust two-way ANOVA, Aligned Rank Transform ANOVA, Separate non-parametric tests with correction, Mixed-effects model

  • Explanation:

    • Non-parametric factorial analysis is used when assumptions are violated.

    • Robust ANOVA methods handle violations of assumptions.

    • Aligned Rank Transform ANOVA is a non-parametric alternative.

    • Mixed-effects model can handle complex designs.

Kaplan-Meier Survival Analysis:

  • Suggested Alternatives: Cox Proportional Hazards model, Parametric survival models, Competing risks analysis, Time-varying coefficient models

  • Explanation:

    • Cox Proportional Hazards model is more flexible.

    • Parametric survival models assume specific distributions.

    • Competing risks analysis is used when there are competing events.

    • Time-varying coefficient models handle time-dependent covariates.

Cox Proportional Hazards Regression:

  • Suggested Alternatives: Stratified Cox model, Time-varying coefficient Cox model, Parametric survival models, Additive hazards models

  • Explanation:

    • Stratified Cox model handles non-proportional hazards.

    • Time-varying coefficient models address time-dependent effects.

    • Parametric survival models assume specific distributions.

    • Additive hazards models are an alternative to proportional hazards.

Poisson Regression (continued):

  • Suggested Alternatives: Negative Binomial Regression, Zero-inflated Poisson Regression, Zero-inflated Negative Binomial Regression, Quasi-Poisson Regression

  • Explanation:

    • Negative Binomial Regression is suitable when there is overdispersion (variance greater than the mean) in count data.

    • Zero-inflated Poisson Regression is used when there are more zeros in the data than expected under a standard Poisson model.

    • Zero-inflated Negative Binomial Regression combines the handling of excess zeros and overdispersion.

    • Quasi-Poisson Regression is another approach to handle overdispersion by adjusting the variance function.

Spearman's Rank Correlation:

  • Suggested Alternatives: Kendall's tau, Kendall's tau-b (for ties), Pearson correlation (if relationship is linear), Distance correlation (for non-monotonic relationships)

  • Explanation:

    • Kendall's tau is a non-parametric measure of correlation that is less sensitive to ties than Spearman's.

    • Kendall's tau-b is specifically designed to handle ties in the data.

    • Pearson correlation can be used if the relationship is linear and assumptions of normality are met.

    • Distance correlation is a more general measure that can detect both linear and non-linear associations.

Wilcoxon Signed-Rank Test:

  • Suggested Alternatives: Sign test (for asymmetric differences), Paired t-test (if differences are normal), Permutation test, Bootstrap methods

  • Explanation:

    • Sign test is a simpler non-parametric test that can be used if the differences are not symmetrically distributed.

    • Paired t-test is appropriate if the differences are normally distributed.

    • Permutation test is a non-parametric method that does not rely on distributional assumptions.

    Bootstrap methods provide a flexible approach to estimate the sampling distribution of the test statistic.

MANOVA (Multivariate Analysis of Variance):

  • Suggested Alternatives: Separate univariate ANOVAs with Bonferroni correction, Robust MANOVA, Permutation MANOVA, Non-parametric multivariate tests (e.g., NPMANOVA), Linear Discriminant Analysis

  • Explanation:

    • Separate univariate ANOVAs with Bonferroni correction control for Type I error across multiple tests.

    • Robust MANOVA methods handle violations of assumptions such as multivariate normality.

    • Permutation MANOVA is a non-parametric alternative that does not assume normality.

    • Non-parametric multivariate tests like NPMANOVA are used when assumptions are violated.

    • Linear Discriminant Analysis can be used for classification purposes when MANOVA assumptions are not met.

One-Way ANOVA:

  • Suggested Alternatives: Kruskal-Wallis H-test, Welch's ANOVA, Brown-Forsythe test

  • Explanation:

    • Kruskal-Wallis H-test is a non-parametric alternative that does not assume normality.

    • Welch's ANOVA is used when the assumption of equal variances is violated.

    • Brown-Forsythe test is another alternative for testing equality of means when variances are unequal.

Factorial ANOVA:

  • Suggested Alternatives: Non-parametric factorial analysis, Mixed-effects model, Robust ANOVA

  • Explanation:

    • Non-parametric factorial analysis is used when assumptions of normality and homoscedasticity are violated.

    • Mixed-effects model can handle complex designs and violations of sphericity.