ANOVA: Introduction & Analysis PDF

Parametric-tests Introduction to ANOVA (Analysis of Variance) Biostatistics for Pharmaceutical Sciences - PHRM 103 – Lecture 2 Dr. Mansour Adam Mahmoud, PhD, CSPP Associate Professor Department of Pharmacy Practice, Col...

Parametric-tests Introduction to ANOVA (Analysis of Variance) Biostatistics for Pharmaceutical Sciences - PHRM 103 – Lecture 2 Dr. Mansour Adam Mahmoud, PhD, CSPP Associate Professor Department of Pharmacy Practice, College of Pharmacy, Taibah University 2024-1446 1  Learning Objectives 1. Understand the basics of what ANOVA is?. 2. Know when and why ANOVA is used in research. 3. Learn how to interpret the results of an ANOVA test. 4. Understand how ANOVA applies to pharmacy and clinical research. 2 What is ANOVA? Definition: ANOVA is a statistical method used to compare the means of three or more groups. It tells us if the differences in group means are significant or due to random chance. Example: Comparing the effectiveness of three different drugs. 3 Why Do We Use ANOVA? When there are more than two groups, a t-test isn’t appropriate. Multiple Comparisons: If we used multiple t-tests, the chance of making an error increases. ANOVA avoids this by testing all groups simultaneously. Application in Pharmacy: Used to compare drug efficacy, side effects, or patient outcomes across different treatment groups. 4  Feature T-test ANOVA Compares means between two Compares means between three Purpose groups or more groups Number of Groups Only 2 groups 3 or more groups Increases with multiple Controls the error rate by testing Error Rate comparisons all groups simultaneously Comparing blood pressure Comparing blood pressure across Example between two drug treatments three drug treatments (Drug A, B, (Drug A vs. Drug B) and C) Tests whether all group means are Tests whether two group means Hypothesis equal (or if at least one is are equal different) Statistical Test t-statistic F-statistic 5  Key Terms Groups (or Treatments): Different categories being tested (e.g., Medication A, B, and C). Mean: The average value within each group (e.g., average blood pressure in each medication group). Variance: The spread of data points around the mean within each group. Example: Three blood pressure medications being compared for their effectiveness. 6  Real-World Example in Pharmacy Imagine you want to study the effectiveness of three drugs for treating high blood pressure. You measure the reduction in systolic blood pressure for each patient after 30 days of treatment. Group 1: Patients on Drug A. Group 2: Patients on Drug B. Group 3: Patients on Drug C. ANOVA will help us determine if the differences in blood pressure reduction between these groups are significant. 7 8  Types of ANOVA One-Way ANOVA: Compares means of three or more groups based on one factor. Example: Comparing the effectiveness of three different medications. Two-Way ANOVA: Compares means based on two factors (e.g., medication type and dosage). Example: Comparing drug efficacy across different dosages and genders. 9 Feature One-Way ANOVA Two-Way ANOVA Compares the means based on two independent Compares the means of three or more groups based on Definition variables (factors), examining their individual and one independent variable (factor). interaction effects. Two independent variables (e.g., Drug type and Number of Factors One independent variable (e.g., Drug type). Dosage). Purpose Determines if there is a statistically significant Determines the effects of two factors on the difference between the means of multiple groups. dependent variable and if there is any interaction between them. - Normal distribution of data Same as One-Way ANOVA, but also considers Assumptions - Homogeneity of variances interactions between factors. - Independent observations Hypothesis - Null Hypothesis (H₀): All group means are equal - Null Hypothesis (H₀): No effect of factor A, no - Alternative Hypothesis (H₁): At least one group mean effect of factor B, and no interaction is different - Alternative Hypothesis (H₁): At least one factor affects the outcome or there's an interaction effect. Example One-Way ANOVA: Comparing the effectiveness of three Two-Way ANOVA: Comparing the effectiveness of drugs (Drug A, Drug B, Drug C) on reducing cholesterol three drugs (Drug A, Drug B, Drug C) at two levels. different dosages (Low and High) on reducing cholesterol levels. Output Produces one F-statistic for the independent variable Produces F-statistics for each factor (e.g., Drug (e.g., Drug type). type and Dosage) and their interaction. Interaction Effect No interaction Tests if the combination of factors (e.g., Drug type and Dosage) affects the outcome. 10  Assumptions of ANOVA For ANOVA to work properly, a few assumptions must be met: 1.Normality: The data in each group should follow a normal distribution. 2.Homogeneity of Variance: The variance across groups should be similar. 3.Independence: Observations must be independent of each other (no overlap between groups). 11 Hypothesis in ANOVA Null Hypothesis (H0): The means of all groups are equal (no difference). E.g., Drug A, B, and C have the same effect. Alternative Hypothesis (H1): At least one group mean is different. E.g., One drug reduces blood pressure significantly more or less than the 12  F-Statistic ANOVA calculates an F-statistic, which is the ratio of variability between group means to the variability within the groups. Interpretation: A large F-statistic indicates the group means are different. A small F-statistic suggests the group means are similar. Formula: F=Variance between groups/Variance within groups 13  P-Value The P-value tells us whether the F-statistic is significant. P < 0.05: Significant difference between groups. P ≥ 0.05: No significant difference. Significance Level (α): Usually set at 0.05. Example: If P = 0.03, we reject the null hypothesis and conclude there is a difference between the groups. 14 One-Way ANOVA Example Study Example: You test three medications for reducing cholesterol. Group 1: Drug A. Group 2: Drug B. Group 3: Drug C. After measuring cholesterol levels, you run ANOVA to see if any drug performs significantly better. 15  Steps to Perform ANOVA 1.Formulate Hypotheses: Null and alternative. 2.Collect Data: Measure outcomes for each group. 3.Calculate the F-Statistic: Using software like SPSS. 4.Compare P-value: Is it less than 0.05? 5.Make a Conclusion: Reject or fail to reject the null hypothesis. 16  Interpreting ANOVA Results Significant Result (P < 0.05): One or more group means are different. Follow up with post hoc tests to determine which groups differ. Non-Significant Result (P ≥ 0.05): No evidence that the group means are different. This doesn't mean they are exactly the same, just that there is no statistical evidence of a difference. 17  Post Hoc Tests Purpose: If ANOVA shows significant differences, post hoc tests (e.g., Tukey’s, Bonferroni) help identify which specific groups differ. Example: After finding that the blood pressure medications are different, post hoc tests show that Drug A and Drug C are significantly different, but Drug B is not. 18  Pharmacy Research Applications Clinical Trials: Comparing different treatments. Drug Comparisons: Evaluating side effects or effectiveness. Patient Outcomes: Analyzing results based on different interventions. Example: Comparing three diabetes medications in a clinical trial using ANOVA to assess their impact on HbA1c levels. 19 20