Parametric and non-parametric tests

1. Assumptions: Parametric tests have stricter assumptions about the population distribution, while non-parametric tests are more flexible and make fewer distributional assumptions.
2. Type of Data: Parametric tests are often used for interval or ratio data, whereas non-parametric tests can handle a wider range of data types, including ordinal data.
3. Efficiency: Parametric tests can be more powerful when assumptions are met, but non-parametric tests are more robust in the presence of violations of assumptions.
4. Examples: t-tests and ANOVA are examples of parametric tests, while Mann-Whitney U test and Wilcoxon signed-rank test are examples of non-parametric tests.

z**-test**

When to use: Used to compare means between two groups, means when the population standard deviation is known

Example (One-Tailed): Determine if New Jersey receives significantly more public school funding (per student) than the USA average. You know that the USA mean public school yearly funding is $6300 per student per year, with a standard deviation of $400. Next, suppose you collect a sample (n = 100) and determine that the sample mean for New Jersey (per student per year) is $8801. Use the z-test and the correct Ho and Ha to run a hypothesis test to determine if New Jersey receives significantly more funding for public school education (per student per year).

Ho: mean funding for New Jersey = mean funding for the USA

Ha: mean funding for New Jersey > mean funding for the USA

The Ho is the null hypothesis and so always contains the equal sign, as it is the case for which there is no significant difference between the two groups

Types:

1. One tailed
2. Two tailed

t-test

(Video1, Video2)