Test statistic

Definition

A test statistic is a standardized value used in statistical hypothesis testing to determine whether to reject the null hypothesis. It quantifies the difference between the observed data and what is expected under the null hypothesis, allowing researchers to make inferences about the population based on sample data. The value of the test statistic helps in assessing the significance of the results and is central to various statistical tests.

5 Must Know Facts For Your Next Test

1. The value of the test statistic varies based on the type of statistical test being performed, such as t-tests or z-tests.
2. Common distributions used to interpret test statistics include the normal distribution, t-distribution, chi-square distribution, and F-distribution.
3. The larger the absolute value of the test statistic, the more evidence there is against the null hypothesis.
4. Test statistics are calculated using sample data and are compared against critical values derived from statistical distributions to determine significance.
5. In most tests, if the test statistic exceeds a certain critical value determined by the significance level, the null hypothesis is rejected.

Review Questions

• How does a test statistic assist researchers in making decisions about a null hypothesis?
  • A test statistic provides a numerical representation of how far an observed sample outcome deviates from what is expected under the null hypothesis. By calculating this value, researchers can compare it against critical values from statistical distributions. If the test statistic indicates a significant deviation, it suggests strong evidence against the null hypothesis, guiding researchers to either reject or fail to reject it.
• In what ways do different types of test statistics affect conclusions drawn in hypothesis testing?
  • Different types of test statistics correspond to different statistical tests designed for specific data types and conditions. For example, a t-test statistic is suitable for smaller sample sizes and unknown population variances, while a z-test statistic applies to larger samples with known variances. The choice of test statistic affects how results are interpreted and can lead to varying conclusions about whether or not to reject the null hypothesis based on the context of the data.
• Evaluate how changes in significance level can impact the interpretation of a test statistic and subsequent decisions about hypotheses.
  • Changing the significance level affects how critical values are set for test statistics, which in turn influences whether a null hypothesis is rejected or not. A lower significance level (e.g., 0.01 instead of 0.05) means stricter criteria for rejecting the null hypothesis. Consequently, even with a substantial test statistic, researchers may fail to reject the null if it does not exceed this new threshold. This adjustment highlights how subjective choices regarding significance levels can lead to different conclusions about research findings and their implications.

Related terms

null hypothesis: A statement asserting that there is no effect or no difference, serving as the default assumption in hypothesis testing.

p-value: The probability of observing a test statistic as extreme as, or more extreme than, the value computed from the sample data, assuming that the null hypothesis is true.

significance level: A threshold set before testing that defines the probability of rejecting the null hypothesis when it is actually true, often denoted as alpha (α).