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 variances are equal across groups. They are powerful tools for analyzing relationships and differences between variables, particularly when certain conditions about the data are met.

5 Must Know Facts For Your Next Test

1. Parametric tests require that data be measured at least at an interval level, meaning they need meaningful intervals between values.
2. The validity of parametric tests relies heavily on the assumption of normality; if this assumption is violated, results may not be reliable.
3. Common examples of parametric tests include the t-test and ANOVA, which analyze differences in means across groups.
4. Parametric tests tend to be more powerful than non-parametric tests when their assumptions are met, meaning they have a higher chance of detecting a true effect.
5. Sample size plays a crucial role in parametric testing; larger samples can provide more reliable estimates of population parameters.

Review Questions

• What assumptions must be met for parametric tests to be valid, and why are these assumptions important?
  • For parametric tests to be valid, the data must meet several assumptions including normality, homogeneity of variance, and interval level measurement. These assumptions are important because they ensure that the statistical methods being used yield accurate and reliable results. If these assumptions are violated, it can lead to incorrect conclusions about the data.
• How do parametric tests differ from non-parametric tests in terms of their underlying assumptions and applications?
  • Parametric tests differ from non-parametric tests primarily in their assumptions about data distribution. Parametric tests assume that the data follows a normal distribution and requires interval or ratio scales. In contrast, non-parametric tests do not make such stringent assumptions, allowing them to be used with ordinal or nominal data. Consequently, while parametric tests are more powerful when their assumptions hold true, non-parametric tests offer flexibility in handling various types of data distributions.
• Evaluate the significance of sample size when applying parametric tests and how it impacts statistical power.
  • Sample size plays a critical role in applying parametric tests because larger samples can provide a better estimate of population parameters and enhance the reliability of test results. A larger sample size increases statistical power, meaning there's a greater likelihood of detecting an actual effect if it exists. Conversely, small samples can lead to misleading results due to increased variability and reduced power, potentially resulting in Type II errors where true effects go undetected.

Related terms

Normal Distribution: A probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean.

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 test used to compare the means of three or more groups to assess whether at least one group mean is statistically different from the others.