Parametric and Non-Parametric Tests Quiz

Parametric and Non-Parametric Tests

• Statistical methods used to reject or not reject a null hypothesis
• Based on probability distributions
• Can be one-tailed or two-tailed, depending on the research hypotheses

Parametric Tests

• Statistical tests assuming data approximately follows a normal distribution
• Include z-tests, t-tests, and ANOVA
• Crucial assumption: the entire population, not just the sample, follows a normal distribution.

Non-Parametric Tests

• Statistical tests not assuming any specific distribution for the data
• Also called distribution-free tests
• Examples include Chi-square tests, Mann-Whitney U tests
• Based on ranks of data points

Parametric Test Examples

• Paired t-test
• Unpaired t-test
• One-way ANOVA
• Pearson's correlation coefficient

Non-Parametric Test Examples

• Wilcoxon signed-rank test
• Mann-Whitney U test
• Kruskal-Wallis H test
• Spearman's rank correlation coefficient

Parametric Test Focus

• Analyzing and comparing the mean or variance of data.
• Mean is a common measure of central tendency, but it's sensitive to outliers.
• Data analysis should consider outliers when using means.

Parametric Test Assumptions

• Normality: Sample data originates from a normally distributed population.
• Homogeneity of variance: Sampled data comes from populations with equal variances.
• Independence: Observations are independent of each other.
• Outliers: Absence of extreme outliers in the sample.

Degrees of Freedom

• Essentially the number of independent values that can differ within a data set while measuring statistical parameters.

Comparing Means using T-Tests

• One-sample t-test: Compares a sample to a population standard value. Does the sample behave differently than the population?
• Two-sample t-test: Compares two separate samples. Both samples must be randomly selected from the population, with independent observations.

Choosing Between Z-test and T-test

• Known Population Variance and Large Sample: Use z-test (sample size ≥ 30).
• Known Population Variance and Small Sample: Use either z-test or t-test.
• Unknown Population Variance and Small Sample: Use t-test.
• Unknown Population Variance and Large Sample: Use t-test.

T-test for Independent Samples

• Used to determine if there's a difference between two independent groups' means.
• Data should be normally distributed, have equal variances, and be in interval or ratio form.
• Sample size should be less than 30.

T-test Usefulness

• More powerful than other tests for evaluating differences between independent groups.

Example Data and Problem

• Provided data tables show hours of overtime per week for male and female nurses. The goal is to determine if there's a significant difference in their overtime performance.

Steps for Solving a T-Test Problem

• Establish the problem: Determine if there's a significant difference
• Develop Hypotheses:
  • Null Hypothesis (H₀): No significant difference in overtime performance between groups.
  • Alternative Hypothesis (H₁): A significant difference exists in overtime performance.
• Assess Level of Significance
• Perform Statistical calculations using the formula(s).
• Decide based on computed and critical values if t-computed > t-critical.
• Final result: State the conclusion