# Tarone-Ware Test

The Tarone-Ware test is a variant of the log rank test. It is used in survival analysis to compare two different survival distributions.

The test can be used to compare a variety of different situations, including:

• Two treatment groups in a medical study,
• Drivers in two different car models in a series of crash tests,
• A project comparing compliance in ground water between a background location and test location.

## Assumptions of the Tarone-Ware Test

To use the Tarone-Ware test you must assume that your two populations are identically distributed and also have equal variance. You also need to assume temporal stability (no drastic change over time) and no spatial variability (consistent data over the test site).

## Strengths and Weaknesses of the Tarone-Ware test

The Tarone-Ware test is non-ideal for very small samples; 8 to 10 measurements is usually recommended. It doesn’t require normality in the data set, though data that is very far from a norm may possibly produce slightly skewed results.

## Similar Tests

Other tests used to compare survival distributions, like the Log rank test and Wilcoxon test, are good for particular survival times (the log rank test for longer survival times, the Wilcoxon tests shorter survival times). One strength of the Tarone-Ware test is that in includes a ‘tuning parameter‘, k, with values between 0 and 1 which can be used to set up the test to emphasize long, short, or intermediate survival times.

• With k = 0, longer survival times are emphasized,
• If k = 0.5, intermediate survival time is emphasized,
• With k = 1, the emphasis is on shorter times.

## Performing a Tarone-Ware Test

To perform a Tarone-Ware Test, simply go through the steps for the Wilcoxon test, but weight your result with W(tj) = √nj rather than the weight of W(tj) = nj used for a Wilcoxon test.

## References

Chang, Guang-Hwa. Statistics 5817 Lecture Notes: Survival Analysis.

ITRC (Interstate Technology & Regulatory Council). 2013. Groundwater Statistics and Monitoring Compliance, Statistical Tools for the Project Life Cycle. Two Sample Tests.

Hazra & Gogtay, Biostatistics Series Module 9: Survival Analysis. Indian J Dermatol. 2017 May-Jun; 62(3): 251–257. doi: 10.4103/ijd.IJD_201_17