T-tests

Definition

t-tests are a type of statistical hypothesis test that is used to determine if the mean of a population is significantly different from a hypothesized value or the mean of another population. They are particularly useful when the sample size is small and the population standard deviation is unknown.

5 Must Know Facts For Your Next Test

1. t-tests are used when the population standard deviation is unknown, and the sample size is small (typically less than 30).
2. The t-statistic follows a t-distribution, which is similar to the normal distribution but has heavier tails.
3. The degrees of freedom for a t-test are equal to the sample size minus 1.
4. t-tests can be used to compare the mean of a single sample to a hypothesized value, or to compare the means of two independent samples.
5. The choice of a one-tailed or two-tailed t-test depends on the research question and the direction of the expected difference.

Review Questions

• Explain the purpose of t-tests in the context of hypothesis testing.
  • The purpose of t-tests in the context of hypothesis testing is to determine if the mean of a population is significantly different from a hypothesized value or the mean of another population. t-tests are particularly useful when the sample size is small and the population standard deviation is unknown. They allow researchers to make inferences about the population parameters based on the sample data and assess the statistical significance of the observed differences.
• Describe the relationship between t-tests and the t-distribution.
  • The t-statistic used in t-tests follows a t-distribution, which is similar to the normal distribution but has heavier tails. This distribution is used because the population standard deviation is unknown, and the t-statistic takes into account the uncertainty in the estimate of the standard deviation. The degrees of freedom for a t-test are equal to the sample size minus 1, which determines the shape of the t-distribution and the critical values used to evaluate the test statistic.
• Analyze the factors that influence the choice between a one-tailed or two-tailed t-test.
  • The choice between a one-tailed or two-tailed t-test depends on the research question and the direction of the expected difference. A one-tailed t-test is used when the researcher has a specific hypothesis about the direction of the difference (e.g., the mean is greater than or less than a hypothesized value). A two-tailed t-test is used when the researcher is interested in detecting any significant difference, regardless of the direction. The choice of the test affects the critical values used to evaluate the test statistic and the resulting p-value, which in turn influences the interpretation of the statistical significance of the findings.

Related terms

Hypothesis Testing: The process of using sample data to evaluate a hypothesis about a population parameter.

Confidence Interval: A range of values that is likely to contain an unknown population parameter with a certain level of confidence.

Degrees of Freedom: The number of values in the final calculation of a statistic that are free to vary.