What is the purpose of a test statistic?

The purpose of a test statistic is primarily to summarize the entire data set in one value, which is generally used to determine whether to reject the null hypothesis in hypothesis testing. This single value condenses the information of the data set into a metric that can be compared against a critical value or used to compute a p-value, which in turn indicates the statistical significance of the observed results.

In this context, the test statistic plays a critical role in data analysis by providing the necessary framework for making informed decisions based on the underlying data. It encapsulates key information, such as mean differences or proportions, and helps verify if the data aligns with established expectations or models. This simplifies the complexity of analyzing an entire data set, enabling analysts to focus on this single, pivotal number when assessing their hypotheses.

The other options do not accurately capture the core function of a test statistic. While documenting errors, presenting raw data, and visualizing data trends are all important aspects of data analysis, they serve different purposes and do not encapsulate the essence of what a test statistic is designed to achieve in hypothesis testing.