Sample Size Tables

Means | Proportions | Survival Analysis | Agreement/Correlation | Regression

One-group, paired and repeated measures tests and confidence intervals for means

One group t test that a mean equals a user-specified value  (MOT0)
Confidence interval for mean based on z (n large)  (MOC0)
Confidence interval for mean based on t (with coverage probability) (MOC1)
Confidence interval for percentile of a normal distribution (MOC5)

Paired t test of mean difference equal to zero (MOT1)
Univariate one-way repeated measures analysis of variance (constant correlation) (MOT2)
One-way repeated measures contrast (constant correlation) (MOT3)
Univariate one-way repeated measures analysis of variance (Greenhouse-Geisser approximation) (MOT4)
Confidence interval for difference in paired means based on z (n large) (MOC2)
Confidence interval for difference in paired means based on t (coverage probability) (MOC3)
Confidence interval for one-way repeated measures contrast (constant correlation) (MOC4)
Two-group tests and confidence intervals for means

Two group t-test of equal means (MTT0)
Two group Satterthwaite t-test of equal means (unequal variances)  (MTT0uv)
Two group t-test for fold change assuming log-normal distribution (MTT0cv)
Two group t-test of equal fold change with fold change threshold (MTT0fct)
Wilcoxon (Mann-Whitney) rank-sum test that P (X less than Y)=0.5 (continous outcome) (MTT1)
Wilcoxon (Mann-Whitney) rank-sum test that P(X less than Y)=0.5 (ordered categories) (MTT2)

Confidence interval for difference of two means based on z (MTC0)
Confidence interval for difference of two means (coverage probability) (MTC1)

Two-group univariate repeated measures analysis of variance (Greenhouse-Geisser correction) (MTT3)
t-test (ANOVA) for difference in means in a 2 x 2 crossover design (MTT4)

One and two group and crossover designs, non-inferiority and equivalence tests

Paired t test of equivalence of means (MOE0)
Two-group t test of equivalence in means (non-inferiority) (MTE0)
Two one-sided equivalence tests (TOST) for two group design (MTE1tg)
Two one-sided equivalence tests (TOST) for crossover design (MTE1co)*
Two-group t-tests (TOST) for ratio of means (log scale) (MTE2tg)*
t-tests (TOST) for ratio of means for crossover design (log scale) (MTE2co)*
Two-group t-tests (TOST) for ratio of means (using original scale) (MTE3)*
Crossover design TOST for ratio of means (using original scale) (MTE4)*

*Can be used for non-inferiority tests

Multiple group tests and confidence intervals for means

One-way analysis of variance (MGT0)
Single One-way between means contrast (MGT1)
Two-way analysis of variance  (MGT2)
Confidence interval contrast between means (large n’s) (MGC0)
Confidence interval for one-way contrast (with coverage probability) (MGC1)

One-group and paired tests and confidence intervals for proportions

One group χ 2 test that proportion equals user specified value (normal approximation) (POT0)
Exact test for single proportion (POT0x)
McNemar’s Test (χ 2) of equality of paired proportions (POT1)
Exact sign test of equality of paired proportions (POT1x)
Chi-square test of specified proportions in C categories (POT2)
Confidence interval for proportion using normal approximation (n large)(POC0)
Confidence interval for ln(ψМ), odds ratio for paired proportions (n large) (POC1)
Confidence interval for probability of observing a rare event (POC2)

Two-group tests and confidence intervals for proportions

Two group χ 2 test of equal proportions (odds ratio = 1) (Compute power or sample size) (PTT0)
Two group  χ 2 test of equal proportions (Compute a proportion) (PTT0p)
Two group continuity corrected χ 2 test of equal proportions (odds ratio = 1) (Compute power or sample size) (PTT1)
Two group continuity corrected χ 2 test of equal proportions (Compute a proportion) (PTT1p)
Two-group Fisher’s exact test of equal proportions (odds ratio=1) (PTT2)
Two-group Chi-square test comparing proportions in C categories (PTT3)
Mantel-Haenszel (Cochran) test of OR=1 for 2×2 tables in S strata (PTT4)
Mantel-Haenszel (Cochran) test of OR=1 for 2×2 tables in S strata (Continuity Corrected) (PTT4cc)

Confidence interval for difference of two proportions (PTC0)
Confidence interval for difference of two proportions (continuity corrected) (PTC1)
Confidence interval for ln(odds ratio) (PTC2)
Confidence interval for relative risk (ratio of two proportions) (PTC3)
One and two group non-inferiority and equivalence tests

Paired test of non-inferiority of proportions (n large) (POE0)
Paired test of equivalence in proportions using confidence interval (simulation):
Lower confidence limit for difference in paired proportions (POE1a)
Upper confidence limit for difference in paired proportions (POE1b)
Two-sided confidence limits for difference in paired proportions (POE1c)
Two-group test of non-inferiority in proportions (large n) (PTE0)
Two group test of equivalence in proportions using confidence interval (simulation):
Lower confidence limit for difference in proportions (PTE1a)
Upper confidence limit for difference in proportions (PTE1b)
Two-sided confidence limits for difference in proportions (PTE1c)

Multiple group tests

χ 2 test of equal proportions in G groups (PGT0)
Trend across proportions, logistic model (PGT1)
G group Chi-square test comparing proportions in C categories (PGT2)

Tests Comparing Two Survival Curves

Log-rank test for equality of survival curves (STT0)
Test based on exponential survival, accrual period (STT1)
Test based on exponential survival, accrual period, dropouts (STT2)
Log-rank test with user specified survival, hazard, accrual, dropout rates, simulation (STT3 )

One-sided non-inferiority tests for survival hazard ratio

Non-inferiority test for two exponential survival curves (STE0)

Dichotomous outcome methods using Intraclass Kappa

Agreement between two dichotomous ratings (intraclass kappa) (AOT0)
Confidence interval for intraclass kappa (n large) (AOC0)

Continuous outcome methods using Pearson r

Correlation test that r = r0 for x and y bivariate normal (AOT1)
One-sided confidence interval for r for x and y bivariate normal (AOC1)
Continuous outcome methods using Lin’s concordance coefficient

Large sample test that Lin’s concordance coefficient = K0 (AOT2)
One-sided large sample confidence interval for Lin’s concordance coefficient (AOC2)
Continuous outcome methods using intraclass correlation

Confidence interval for intraclass correlation for k measurements (AOC3)

Logistic Regression

Trend across proportions (logistic model) (PGT1)
Logistic regression test that β = 0 for one normally distributed covariate, x (ROT0)
Logistic regression test that β = 0 for one normal covariate x, adjusting for prior covariates (ROT1)

Linear Regression

Linear regression test that ρ = 0 for one normally distributed covariate, x (ROT2)
Correlation test that ρ=ρ0 for x and y bivariate normal (AOT1)
One-sided confidence interval for ρ for x and y bivariate normal (AOC1)
Linear regression test that β=β0 for one x (ROT5)
Linear regression confidence interval for β (ROC0)
Linear regression test that β1=β2 for one x (RTT0)
Linear regression confidence interval for β1 -β2 (RTC0)
Multiple linear regression test that R2 = 0 for k normally distributed covariates. (ROT3)
Multiple regression, test 0 increase in R2 for B covariates adjusted for A covariates. (ROT4 )