One-sample t-test

Definition

A one-sample t-test is a statistical method used to determine whether the mean of a single sample differs significantly from a known or hypothesized population mean. This test is essential for comparing the sample mean to a target value, helping researchers understand if their sample provides evidence for or against the population mean being equal to that target. It is a foundational concept in hypothesis testing and plays a vital role in analyzing experimental data.

5 Must Know Facts For Your Next Test

1. The one-sample t-test assumes that the sample data are drawn from a normally distributed population, especially important when sample sizes are small.
2. This test calculates the t-statistic, which measures how far the sample mean is from the hypothesized population mean in terms of standard error.
3. The degrees of freedom for a one-sample t-test is calculated as n - 1, where n is the sample size.
4. A significant result from a one-sample t-test indicates that there is enough evidence to reject the null hypothesis in favor of the alternative hypothesis.
5. One-sample t-tests can be conducted using both one-tailed and two-tailed approaches, depending on the research question being investigated.

Review Questions

• How does a one-sample t-test differ from other types of t-tests in terms of its application?
  • A one-sample t-test specifically compares the mean of a single sample to a known or hypothesized population mean, making it unique among t-tests. In contrast, independent two-sample t-tests compare means between two different groups, while paired sample t-tests assess means from related groups. Understanding these distinctions helps researchers choose the appropriate test based on their study design and data.
• Discuss the assumptions underlying the one-sample t-test and their implications for data analysis.
  • The one-sample t-test relies on several key assumptions: that the sample data are independently and randomly selected, that they follow a normal distribution, and that the sample size is sufficiently large (or the population distribution is normal if small). Violating these assumptions can lead to inaccurate results, so it's crucial for researchers to verify these conditions before applying the test. If assumptions are not met, alternative methods such as non-parametric tests may be considered.
• Evaluate how changes in sample size affect the outcome and interpretation of a one-sample t-test.
  • Changes in sample size significantly impact both the statistical power and precision of a one-sample t-test. A larger sample size generally increases power, reducing the likelihood of Type II errors (failing to reject a false null hypothesis), while also providing more reliable estimates of the population mean. On the other hand, smaller samples may result in wider confidence intervals and less certainty about whether the null hypothesis should be rejected. Thus, researchers must carefully consider sample size in their experimental design to ensure meaningful results.

Related terms

Hypothesis Testing: A statistical method that uses sample data to evaluate a hypothesis about a population parameter.

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

Confidence Interval: A range of values derived from sample statistics that is likely to contain the true population parameter with a specified level of confidence.