Test statistic

Definition

A test statistic is a standardized value that is calculated from sample data during a hypothesis test. It measures the degree to which the sample data deviates from the null hypothesis, providing a basis for deciding whether to reject it. The test statistic allows researchers to make inferences about a population based on sample information and is essential for assessing statistical significance.

5 Must Know Facts For Your Next Test

1. Test statistics can take various forms depending on the type of test being conducted, such as t-tests, z-tests, or chi-square tests.
2. The larger the absolute value of the test statistic, the more evidence there is against the null hypothesis.
3. Test statistics are used to calculate p-values, which help determine whether to reject or fail to reject the null hypothesis.
4. In hypothesis testing, comparing the test statistic to critical values helps establish rejection regions for decision making.
5. Different tests have different distributions (like normal or t-distribution) which influence how the test statistic is interpreted.

Review Questions

• How does a test statistic relate to hypothesis testing and what role does it play in decision making?
  • A test statistic quantifies how far sample data deviates from what is expected under the null hypothesis, serving as a key metric in hypothesis testing. When conducting a hypothesis test, researchers calculate the test statistic and compare it to critical values derived from probability distributions. This comparison helps decide whether to reject or fail to reject the null hypothesis, impacting conclusions drawn about the population.
• In what ways do different types of test statistics influence the choice of statistical tests in research?
  • Different types of test statistics correspond to specific statistical tests and are influenced by factors like sample size and data distribution. For example, a t-test uses a t-statistic for smaller samples, while a z-test uses a z-statistic for larger samples. Choosing the appropriate test statistic ensures that researchers accurately assess significance and maintain valid interpretations of their results.
• Evaluate how changes in sample size might affect the value of a test statistic and its implications for research conclusions.
  • As sample size increases, the variability of the sample mean decreases, often resulting in a more precise estimate of the population parameter. This can lead to larger absolute values of the test statistic when there is a real effect present because larger samples provide more reliable data. Consequently, researchers may be more likely to reject the null hypothesis with larger samples, potentially leading to different conclusions compared to analyses with smaller samples.

Related terms

p-value:

The p-value is the probability of obtaining test results at least as extreme as the observed results, assuming that the null hypothesis is true.

null hypothesis:

The null hypothesis is a statement that there is no effect or no difference, and it serves as the starting point for statistical testing.

confidence interval: A confidence interval is a range of values that is used to estimate the true parameter of a population with a specified level of confidence.