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Welcome to our CFA Level 1 tutorial on Parametric versus Nonparametric tests! Statistical hypothesis testing is a fundamental tool that helps us make inferences about populations based on sample data. There are two main categories of statistical tests: Parametric tests and Nonparametric tests. Understanding when to use each type is crucial for proper data analysis in finance and investment research. Let's explore the key differences between these two approaches! Parametric tests are statistical procedures that make specific assumptions about the population parameters and the distribution of the data. The first key assumption is that data follows a specific distribution, most commonly the normal distribution, which appears as this bell-shaped curve. The second assumption is that data must be measured on an interval or ratio scale, meaning the numerical differences and ratios between values are meaningful. The third assumption often required is equal variances between groups being compared. Common parametric tests include t-tests for comparing means between two groups, ANOVA for comparing multiple groups, and Z-tests for large sample means. These tests are powerful when their assumptions are met. Nonparametric tests are statistical procedures that do NOT make specific assumptions about population parameters or the distribution of the data. They are used when parametric assumptions are violated, such as when data is not normally distributed, when sample sizes are small, or when working with ordinal or nominal data. The key feature of nonparametric tests is that they often work with ranks or signs of data rather than the raw values themselves. This makes them more flexible but generally less powerful than parametric tests when parametric assumptions are met. As shown here, original data values are converted to ranks for analysis. Common nonparametric tests include the Mann-Whitney U test as an alternative to the independent t-test, the Kruskal-Wallis test as an alternative to ANOVA, and the Chi-Square test for categorical data analysis. Now let's compare these two approaches and understand when to use each. The key decision factors include data distribution, sample size, data type, and desired statistical power. If your data follows a normal distribution, use parametric tests. If it's non-normal or unknown, choose nonparametric. For large samples, parametric tests are generally preferred, while small samples are safer with nonparametric approaches. Interval or ratio data suits parametric tests, while ordinal or nominal data requires nonparametric methods. Parametric tests offer higher statistical power when their assumptions are met, but nonparametric tests provide more flexibility when assumptions are violated. The choice ultimately depends on your data characteristics and whether parametric assumptions can be reasonably satisfied. Let's summarize the key takeaways. Parametric tests assume specific distributions and are more powerful when their assumptions are met, but they require interval or ratio data. Nonparametric tests are distribution-free, more flexible and robust, and can work with any data type. For CFA Level 1, understanding these concepts is essential for proper financial data analysis. Always choose your test based on data characteristics and validate assumptions before testing. Remember this decision framework: first check data distribution, then assess sample size, identify your data type, and finally select the appropriate test. This knowledge will serve you well in analyzing financial markets and investment data. Thank you for learning about parametric versus nonparametric tests with us today!