Parametric Tests

Definition

Parametric tests are statistical methods that assume the data follows a specific distribution, typically a normal distribution. These tests rely on certain parameters, such as mean and standard deviation, to make inferences about the population from which the sample is drawn. Because they assume underlying statistical properties, they can be more powerful than non-parametric tests when those assumptions are met.

5 Must Know Facts For Your Next Test

1. Parametric tests require data to meet specific assumptions, including normality, homogeneity of variance, and independence of observations.
2. Common examples of parametric tests include t-tests, ANOVA, and regression analysis.
3. Parametric tests generally have more statistical power than non-parametric tests, meaning they can detect smaller effects if assumptions are satisfied.
4. If data do not meet parametric assumptions, researchers may opt for non-parametric tests which do not rely on these assumptions.
5. The results of parametric tests often provide confidence intervals and effect sizes, which give additional context beyond just p-values.

Review Questions

• What are the key assumptions that must be met for a parametric test to be valid?
  • For a parametric test to be valid, several key assumptions must be met. These include the assumption of normality, where the data should follow a normal distribution; homogeneity of variance, meaning that different groups should have similar variances; and independence of observations, indicating that the data collected from different subjects or groups should not influence each other. If these assumptions are violated, the results may not be reliable.
• Compare and contrast parametric tests with non-parametric tests in terms of their application and requirements.
  • Parametric tests are used when data meets certain assumptions such as normality and equal variances, allowing for more powerful analyses. Examples include t-tests and ANOVA. Non-parametric tests, on the other hand, do not assume a specific distribution and can be used with ordinal data or when the sample size is small. While non-parametric tests can be less powerful due to fewer assumptions about the data structure, they offer flexibility when conditions for parametric testing cannot be satisfied.
• Evaluate how the choice between using a parametric or non-parametric test can impact research findings and conclusions.
  • Choosing between a parametric and a non-parametric test can significantly impact research findings. If researchers incorrectly apply a parametric test when data does not meet its assumptions, it could lead to inaccurate conclusions about differences or relationships within the data. Conversely, using non-parametric tests can provide valid insights when assumptions for parametric tests are violated but may miss detecting smaller effects due to lower power. Therefore, understanding the characteristics of the data and the implications of these choices is crucial for drawing reliable conclusions.

Related terms

Normal Distribution: A probability distribution that is symmetric about the mean, where most of the observations cluster around the central peak and probabilities for values further away from the mean taper off equally in both directions.

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

ANOVA (Analysis of Variance): A parametric statistical method used to determine if there are any statistically significant differences between the means of three or more independent groups.