The __Biostatistics, Epidemiology, and Research Design__ team at NYU Langone’s Clinical and Translational Science Institute have compiled useful biostatistics tools for statistical analyses.

The tools include calculators for study design, such as power and sample size calculation, and calculators for data analysis such as *t* test, chi-square test, Pearson correlation coefficient, linear regression, and receiver operating characteristic (ROC) curve. If you need additional research advice, please submit our online form to request a consultation.

## Tools for Study Design

Several online tools are available for researchers to calculate statistical powers or sample sizes during the study design phase.

### Power Calculator

When a study sample size is determined, researchers may wish to calculate the statistical power of the statistical hypothesis for the given study sample size. Inputs typically contain sample size (n), the effect size, the number of groups, and the desired type I error rate (the probability of rejecting the null hypothesis when it is true, typically set at 0.05 when there is no multiple testing corrections), and one-sided or two-sided test.

For continuous outcomes, use the two-sample unpaired *t*-test power calculator to test the hypothesis that the outcome has the same mean between two groups or the analysis of variance (ANOVA) power calculator to test to test the hypothesis that the outcome has the same mean between multiple groups.

For categorical outcomes, use the chi-squared test power calculator to test the hypothesis that the probability of outcome is the same across groups. For continuous outcome and continuous exposure, use the linear regression power calculator to test the hypothesis that the outcome is independent of the exposure, with or without covariates adjusted.

### Sample Size Calculator

When the target statistical power is determined, researchers may wish to estimate how many samples are needed for a study. Inputs typically contain desired power (typically at minimum 80 percent), the effect size, the number of groups, and the desired type I error rate (the probability of rejecting the null hypothesis when it is true, typically set at 0.05 when there is no multiple testing corrections), and one-sided or two-sided test.

When the outcome is continuous, use the two-sample unpaired *t*-test sample size calculator to test the hypothesis that the outcome has the same mean between two groups or the ANOVA sample size calculator to test the hypothesis that the outcome has the same mean between multiple groups.

For categorical outcomes, use the chi-squared test sample size calculator to test the hypothesis that the probability of outcome is the same across groups. For continuous outcome and continuous exposure, use the linear regression sample size calculator to test the hypothesis that the outcome is independent of the exposure, with or without covariates adjusted.

## Tools for Data Analysis

Several online tools are available for researchers to implement analyses once data are collected. These include calculators to compare continuous outcome between exposure groups, to compare categorical outcome between exposure groups, to test correlation between exposure and outcome, and for data diagnosis or prediction.

### Comparing Continuous Outcome Between Groups

When the outcome is continuous and normally distributed or the sample size is sufficiently large, use the unpaired two-sample *t*-test calculator to compare the means of a continuous outcome between two independently sampled groups or the one-way ANOVA calculator to compare the means of two or more groups.

Use the paired *t*-test calculator to compare the means of a continuous outcome between two correlated groups (e.g., compare between siblings, matched pairs, before and after samples of the same subjects).

When the outcome is not normally distributed, or has outliers, or sample size is small, we typically recommend the following nonparametric analytical techniques:

- Wilcoxon rank-sum test (also known as the Mann Whitney
*U*test): a nonparametric test alternative to the two-sample*t*test, comparing the overall distribution of a continuous outcome between two independent groups - Wilcoxon signed-rank test: a nonparametric test alternative to the paired two-sample
*t*test - Kruskal-Wallis test: a nonparametric test alternative to ANOVA

### Comparing Categorical Outcome Between Groups

When the outcome is categorical, use the two-sample proportion *z* test to compare the probability of the outcome between two independent groups, or the chi-squared test to compare the probability of the outcome between two or more independent groups.

When the sample size is small or events are rare, consider Fisher’s exact test as an alternative to the chi-squared test. For matched case-control data, McNemar’s test can be used as an alternative to the chi-squared test.

### Testing Correlations Between Exposure and Outcome

When the outcome is continuous and normally distributed, consider the following tools:

- The Pearson correlation coefficient calculator determines the linear correlation between two continuous variables.
- A simple linear regression calculator is appropriate when there is only one predictor for a continuous outcome.
- A multivariable linear regression calculator is appropriate to test the correlation between the outcome and the exposure variable while adjusting other covariates in the model.

When the outcome is 0/1, denoting success or failure, case or control, a logistic regression calculator is appropriate for binary outcome. Learn more about the logistic regression method.

When the outcome is time-to-event, consider Kaplan Meier curves and log-rank tests, as well as Cox proportional hazards regression. Learn more about survival analysis.

### Diagnosis or Prediction

A receiver operating characteristic curve, or ROC curve, is a graphical plot that illustrates the diagnostic ability of a binary classifier system as its discrimination threshold is varied. Access the easyROC web tool for ROC analysis.

Concordance probability and discriminatory power is a metric similar to area under the curve (AUC) that researchers can use to calculate time-to-event outcomes in proportional hazards regressions.