Special Cases
In many situations, the score statistic reduces to another commonly used statistic.
When the data follows a normal distribution, the score statistic is the same as the t statistic.
When the data consists of binary observations, the score statistic is the same as the chi-squared statistic in the Pearson's chi-squared test.
When the data consists of failure time data in two groups, the score statistic for the Cox partial likelihood is the same as the log-rank statistic in the log-rank test. Hence the log-rank test for difference in survival between two groups is most powerful when the proportional hazards assumption holds.
Read more about this topic: Score Test
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