Non-Parametric Tests PDF

Non-Parametric tests Biostatistics for Pharmaceutical Sciences - PHRM 103 – Theory Department of Pharmacy Practice, College of Pharmacy, Taibah University 2024-1446...

Non-Parametric tests Biostatistics for Pharmaceutical Sciences - PHRM 103 – Theory Department of Pharmacy Practice, College of Pharmacy, Taibah University 2024-1446 1  Learning Objectives Learning Objectives: 1. Understand the fundamental principles and applications of nonparametric tests. 2. Identify when to use nonparametric tests versus parametric tests. 3. Apply basic nonparametric tests such as Wilcoxon Signed-Rank, Mann-Whitney U, Kruskal-Wallis, and Spearman’s Rank Correlation. 4. Interpret the results of nonparametric tests and understand their implications in real-world pharmacy research. 5. Develop the ability to report nonparametric test outcomes in a clear and structured manner. 2 3  Introduction to Nonparametric Tests Definition: Nonparametric tests are statistical tests that do not assume a specific distribution for the data. Purpose: Used when data do not meet the assumptions required for parametric tests (e.g., normal distribution). Examples in Pharmacy: Comparing patient satisfaction scores, analyzing treatment effects where data are not normally distributed. 4  Parametric vs. Nonparametric Tests Parametric Tests: Require assumptions like normal distribution and homogeneity of variance (e.g., t-test, ANOVA). Nonparametric Tests: Do not require these assumptions and can be used with ordinal data or small sample sizes. 5  Advantages of Nonparametric Tests Flexibility: Suitable for non-normal data and ordinal data. Robustness: Not affected by outliers as much as parametric tests. Ease of Use: Often simpler to apply and interpret. 6 Common Nonparametric Tests Overview Wilcoxon Signed-Rank Test: For paired or related samples. Mann-Whitney U Test: For comparing two independent groups. Kruskal-Wallis Test: For comparing more than two independent groups. Ch-square test: Used to test relationships between categorical variables. Spearman’s Rank Correlation: Measures the strength of association between two variables. 7  Wilcoxon Signed-Rank Test Purpose: Compares the median differences between paired observations. Example: Comparing blood pressure readings before and after treatment in the same patients. How It Works: Calculate the differences between paired observations. Rank the absolute differences. Sum the ranks of positive and negative differences separately. Determine significance using the test statistic. 8  Mann-Whitney U Test Purpose: Compares two independent groups to determine if their distributions are different. Example: Comparing test scores between two groups of pharmacy students. Steps: Rank all data points across both groups together. Calculate the sum of ranks for each group. Use the U statistic to determine significance. Interpretation: If the p-value < 0.05, conclude that there is a significant difference between the two groups. 9  Kruskal-Wallis Test Purpose: Extension of the Mann-Whitney U Test for comparing more than two independent groups. Example: Comparing satisfaction scores of patients across three different pharmacies. Steps: Rank all data points together. Calculate the sum of ranks for each group. Compute the Kruskal-Wallis H statistic. Interpretation: If p-value < 0.05, at least one group differs significantly. 10  Spearman’s Rank Correlation Purpose: Measures the strength and direction of association between two variables. Example: Relationship between patient age and adherence to medication. How to Calculate: Rank the data points for both variables. Compute the differences between the ranks. Calculate Spearman’s rho using the formula. Interpretation: Rho value close to +1 or -1 indicates strong correlation, while 0 indicates no correlation. 11  Ch-square test Purpose: The Chi-Square Test is primarily used to: Test for independence: Determine if there is an association between two categorical variables. Test for goodness of fit: Assess whether observed data matches an expected distribution. Example: A hospital wants to find out if patient satisfaction (categorized as “Satisfied,” “Neutral,” “Dissatisfied”) is associated with the type of service received (e.g., “In-person” or “Online”). 12  Ch-square test Interpretation: If the p-value is less than 0.05, it indicates that the difference in patient satisfaction levels between in-person and online services is statistically significant, suggesting that the type of service impacts patient satisfaction. If the p-value is greater than 0.05, there is not enough evidence to say that patient satisfaction is related to service type. 13  Real-Life Applications in Pharmacy Scenario: A pharmacy wants to assess whether a new service (e.g., a medication counseling program) has improved patient satisfaction. Appropriate Test: Use the Wilcoxon Signed-Rank Test since it is designed for paired samples where the distribution of the differences between pre- and post-service satisfaction scores may not be normal. Interpretation: If the p-value < 0.05, conclude that the new service significantly impacted adherence rates. 14  Real-Life Applications in Pharmacy Scenario: A study aims to analyze whether adherence rates to a chronic medication differ between two age groups (e.g., patients under 50 and those 50+). Appropriate Test: Use the Mann-Whitney U Test to compare the two independent groups because adherence rates may not follow a normal distribution. 15  Real-Life Applications in Pharmacy Scenario: A study investigates whether patient satisfaction scores differ across three pharmacy branches (A, B, and C) offering varying levels of service. Appropriate Test: Use the Kruskal-Wallis Test to compare more than two independent groups where data distribution might not be normal. Interpretation: If the p-value < 0.05, there is a significant difference in satisfaction scores between the branches, suggesting that at least one branch has a different satisfaction level from the others. 16  Real-Life Applications in Pharmacy Scenario: A study aims to determine the relationship between the number of pharmacist consultations a patient receives and their medication adherence level. Appropriate Test: Use Spearman’s Rank Correlation to measure the strength and direction of the association between these two variables, especially when the relationship is not linear. Interpretation: A positive rho close to +1 indicates a strong positive correlation, meaning that more consultations are associated with better adherence. 17 Purpose Parametric Test Nonparametric Test Comments Comparing two t-test (independent Mann-Whitney U Test Use the Mann-Whitney U independent groups samples) Test when data is not normally distributed or for ordinal data. Comparing two Paired t-test Wilcoxon Signed-Rank Test Wilcoxon is suitable for related/paired samples paired observations with non-normal data. Comparing more than two One-way ANOVA Kruskal-Wallis Test Use Kruskal-Wallis when independent groups data is not normally distributed across groups. Measuring the association Pearson’s Correlation Spearman’s Rank Spearman’s is used for between two variables Correlation ordinal data or non-linear relationships. 18