Inferential statistics

General concepts

See also: https://en.wikipedia.org/wiki/Power_of_a_test

See also: https://en.wikipedia.org/wiki/Sample_size_determination

Inferential statistics

• Basic classical statistical tests (stratified)
  • Student t-test for 1 sample: tests (p-values) and confidence intervals
    • ctx.student_t_1sample_test()
  • Student t-test for 1 sample: power calculations
    • ctx.student_t_1sample_power()
  • Student t-test for 1 sample: sample size calculation
    • ctx.student_t_1sample_samplesize()
  • Chi-squared-test for the variance of 1 sample: tests (p-values)
    • ctx.chi2_variance_1sample_test()
  • Chi-squared-test for the variance of 1 sample: confidence intervals
    • ctx.chi2_variance_1sample_ci()
  • Chi-squared-test for the variance of 1 sample: power
    • ctx.chi2_variance_1sample_power()
  • Chi-squared-test for the variance of 1 sample: sample size
    • ctx.chi2_variance_1sample_samplesize()
• Basic classical statistical tests for 2 independent samples (stratified)
  • Student t-test for 2 independent samples: tests (p-values)
    • ctx.studentt_2isamples_test()
  • Student t-test for 2 independent samples: confidence intervals
    • ctx.studentt_2isamples_ci()
  • Student t-test for 2 independent samples: power
    • ctx.studentt_2isamples_power()
  • Student t-test for 2 independent samples: sample size calculation
    • ctx.studentt_2isamples_samplesize()
  • Student t-test for 2 independent samples: power and sample size: failure to stratify
    • ctx.studentt_2isamples_power2()
  • Student t-test for 2 independent samples: equivalence and non-inferiority
    • ctx.studentt_2isamples_equivalence()
  • F-test for the variances of 2 independent samples: tests (p-values)
    • ctx.fratio_variance_2isamples_test()
  • F-test for the variances of 2 independent samples: confidence intervals
    • ctx.fratio_variance_2isamples_ci()
  • F-test for the variances of 2 independent samples: power
    • ctx.fratio_variance_2isamples_power()
  • F-test for the variances of 2 independent samples: sample size
    • ctx.fratio_variance_2isamples_samplesize()
• Basic classical statistical tests for 2 correlated samples (stratified)
  • Student t-test for 2 correlated samples: tests (p-values)
    • ctx.studentt_2csamples_test()
  • Student t-test for 2 correlated samples: confidence intervals
    • ctx.studentt_2csamples_ci()
  • Student t-test for 2 correlated samples: power
    • ctx.studentt_2csamples_power()
  • Student t-test for 2 correlated samples: sample size calculation
    • ctx.studentt_2csamples_samplesize()
  • Morgan-Pitman test for the variances of 2 correlated samples: tests (p-values)
    • ctx.fratio_variance_2csamples_test()
  • Morgan-Pitman test for the variances of 2 correlated samples: confidence intervals
    • ctx.fratio_variance_2csamples_ci()
  • Morgan-Pitman test for the variances of 2 correlated samples: power
    • ctx.fratio_variance_2csamples_power()
  • Morgan-Pitman test for the variances of 2 correlated samples: sample size
    • ctx.fratio_variance_2csamples_samplesize()
  • Pearson’s rho, 2 correlated samples: tests (p-values)
    • ctx.pearson_rho_test()
  • Pearson’s rho, 2 correlated samples: confidence intervals
    • ctx.pearson_rho_ci()
  • Pearson’s rho, 2 correlated samples:: power
    • ctx.pearson_rho_power()
  • Pearson’s rho, 2 correlated samples:: sample size calculation
    • ctx.pearson_rho_samplesize()
• Analysis of variance (ANOVA), orthogonal polynomials, and analysis of means (AOM)
  • Literature
  • Anova: overview
  • Anova (completely randomized and randomized blocks): p-value
    • ctx.anova_test()
  • Anova (completely randomized and randomized blocks): power
    • ctx.anova_power()
  • Anova (completely randomized and randomized blocks): sample size
    • ctx.anova_samplesize()
  • Anova, trend tests using orthogonal polynomials: p-value
    • ctx.orthogonal_poly_test()
  • Anova, trend tests using orthogonal polynomials: confidence interval
    • ctx.orthogonal_poly_ci()
  • Anova, trend tests using orthogonal polynomials: power
    • ctx.orthogonal_poly_power()
  • Anova, trend tests using orthogonal polynomials: sample size
    • ctx.orthogonal_poly_samplesize()
  • Analysis of means (ANOM): p-value
    • ctx.anom_test()
  • Distribution fitting
    • ctx.dist_fit()
  • Additional info: Narula’s algorithm
• Multiple comparisons of means
  • Scheffé F-test: p-value
    • ctx.scheffe_test()
  • Scheffé F-test: power
    • ctx.scheffe_power()
  • Scheffé F-test: sample size
    • ctx.scheffe_samplesize()
  • Tukey-Kramer q-test: p-value
    • ctx.tukey_kramer_test()
  • Tukey-Kramer q-test: confidence interval
    • ctx.tukey_kramer_ci()
  • Tukey-Kramer q-test: power
    • ctx.tukey_kramer_power()
  • Tukey-Kramer q-test: sample size
    • ctx.tukey_kramer_samplesize()
  • Fisher-Hayter test: p-value
    • ctx.fisher_hayter_test()
  • REGWQ test (CR only): p-value
    • ctx.rEGWQ_test()
  • Newman-Keuls test (CR only): p-value
    • ctx.newman_keuls_test()
  • Duncan-test (CR only): p-value
    • ctx.duncan_test()
  • Dunnett t-test: p-value
    • ctx.dunnett_test()
  • Dunnett t-test: confidence interval
    • ctx.dunnett_ci()
  • Dunnett t-test: power
    • ctx.dunnett_power()
  • Dunnett t-test: sample size
    • ctx.dunnett_sample_size()
  • Marcus test: p-value
    • ctx.marcus_test()
  • Hsu test: p-value
    • ctx.hsu_test()
• Nonparametric statistical tests, 1 or 2 samples
  • Sign test: p-value and confidence interval
    • ctx.sign_test()
  • Sign test: power and sample size
    • ctx.sign_test_power()
  • Brown-Mood median test for 2 independent samples: p-value and confidence interval
    • ctx.brown_mood_test()
  • Brown-Mood median test for 2 independent samples: power and sample size
    • ctx.brown_mood_power()
  • Wilcoxon’s signed rank \(T\) test: p-value and confidence interval, continuous data
    • ctx.signed_rank_test()
  • Wilcoxon’s signed rank test \(T\) (Bennett alternatives): power and sample size
    • ctx.signed_rank_power()
  • Mann-Whitney \(U\) test (stratified): p-value and confidence interval, continuous data
    • ctx.mannwhitney_test()
  • Mann-Whitney \(U\) test: (Lehmann alternatives): power and sample size
    • ctx.mannwhitney_power_lehmann()
  • Mann-Whitney \(U\) test: (Milton alternatives): power and sample size
    • ctx.mannwhitney_power_milton()
  • Siegel-Tukey test: p-value and confidence interval
    • ctx.siegel_tukey_test()
  • Kendall test for 2 correlated samples: p-value
    • ctx.kendall_test()
  • Theill test for 2 correlated samples: p-value and confidence interals
    • ctx.theill_test()
• Nonparametric statistical tests, k samples
  • Jonckheere-Terpsta \(S\) test: p-value and confidence interval, continuous data
    • ctx.jterpsta_test()
  • Jonckheere-Terpsta \(S\) test, Shorack alternatives: power and sample size
    • ctx.jterpsta_power_shorack()
  • Jonckheere-Terpsta \(S\) test (stratified), Milton alternatives: power and sample size
    • ctx.jterpsta_power_milton()
  • Spearman test for 2 correlated samples: p-value
    • ctx.spearman_test()
  • Generalized Page \(L\) test: p-value
    • ctx.page_l_test()
  • Generalized Page \(L\) test, Milton alternatives: power and sample size
    • ctx.page_l_milton_power()
  • Generalized Quade \(L\) test: p-value
    • ctx.quade_l_test()
  • Friedman’s S, and related linear rank statistics
    • ctx.friedman_test()
  • Kruskal-Wallis’ H, and related linear rank statistics
    • ctx.kruskal_wallis_test()
• Multivariate statistical tests
  • Multiple linear regression: p-value and confidence interval
    • ctx.multlinreg_test()
  • Multiple linear regression Type I: power and sample size
    • ctx.multlinreg_type1_power()
  • Multiple linear regression Type II: power and sample size
    • ctx.multlinreg_type2_power()
  • Hotelling’s \(T^2\) test for 1 sample: p-value and confidence interval
    • ctx.hotelling_1sample_test()
  • Hotelling’s \(T^2\) test for 1 sample: power and sample size
    • ctx.hotelling_1sample_power()
  • Hotelling’s \(T^2\) test for 2 independent samples: p-value and confidence interval
    • ctx.hotelling_2isamples_test()
  • Hotelling’s \(T^2\) test for 2 independent samples: power and sample size
    • ctx.hotelling_2isamples_power()
  • Overview: 4 test criteria for 3 hypotheses
  • MANOVA: Wilks \(\Lambda\), Pillai’s \(V\), Hotelling’s \(T^2\), Roy’s largest root \(\theta\)
    • ctx.four_tests_glm_test()
  • Canonical correlation: Wilks \(\Lambda\), Pillai’s \(V\), Hotelling’s \(T^2\), Roy’s largest root \(\theta\)
    • ctx.four_tests_ind_test()
  • Power estimates of 4 tests in MANOVA
    • ctx.four_tests_glm_power()
  • Power estimates of 4 tests in canonical correlation (Type I)
    • ctx.four_tests_ind_power()