Parametric tests

Definition

Parametric tests are statistical tests that make certain assumptions about the parameters of the population distribution from which the samples are drawn. These tests typically assume that the data follows a normal distribution and that the samples have equal variances, allowing for more powerful inferences about population parameters, such as means. The use of parametric tests can provide more accurate results when the underlying assumptions are met, making them an essential part of hypothesis testing.

5 Must Know Facts For Your Next Test

1. Parametric tests are generally more powerful than non-parametric tests when their assumptions are satisfied, meaning they can detect differences more effectively.
2. Common examples of parametric tests include the t-test, ANOVA, and linear regression, each serving specific purposes based on the research question.
3. The assumptions of normality and homogeneity of variance must be checked before applying parametric tests to ensure valid results.
4. When sample sizes are large, the central limit theorem suggests that parametric tests can be robust even if normality is slightly violated.
5. If the assumptions for parametric tests are not met, non-parametric alternatives like Mann-Whitney U test or Kruskal-Wallis test should be considered.

Review Questions

• What assumptions must be met for parametric tests to yield valid results, and why is this important?
  • For parametric tests to provide valid results, the data should follow a normal distribution, and the variances of the samples should be equal. These assumptions are important because if they are violated, the conclusions drawn from the tests may not be reliable. For instance, if the data is not normally distributed, using a t-test could lead to incorrect inferences about group means.
• Compare and contrast parametric tests with non-parametric tests in terms of their application and assumptions.
  • Parametric tests rely on specific assumptions about the data distribution, including normality and equal variances. They are often more powerful when these conditions are met, making them suitable for analyzing data from well-understood populations. In contrast, non-parametric tests do not make strict assumptions about the underlying distribution and can be used with ordinal or non-normally distributed data. While non-parametric tests may have less power than parametric ones under ideal conditions, they provide flexibility when assumptions are violated.
• Evaluate the implications of using parametric tests in hypothesis testing and discuss what alternative methods can be employed if assumptions are violated.
  • Using parametric tests in hypothesis testing can lead to more precise estimates and greater statistical power when assumptions hold true. However, if these assumptions are violated, researchers might draw incorrect conclusions, which can undermine the validity of their findings. In such cases, alternative methods like non-parametric tests (e.g., Mann-Whitney U test) can be employed. These alternatives allow researchers to analyze data without relying on strict distributional assumptions, thus providing a safeguard against potential biases in results.

Related terms

Normal distribution: A symmetric, bell-shaped distribution characterized by its mean and standard deviation, often assumed in parametric tests.

T-test: A type of parametric test used to compare the means of two groups to determine if they are significantly different from each other.

ANOVA: Analysis of Variance (ANOVA) is a parametric test used to compare the means of three or more groups to assess if at least one group mean is different.