ppt anova analysis of varian presentation

ANOVA

1. Introduction to ANOVA ANOVA, or Analysis of Variance, is a statistical technique used to compare the means of two or more groups. It helps determine if there are significant differences between the groups and identifies the sources of variation. By: Bunga Satya Hardika Esti Sapta Lestari Fajriati Selza Wahyu

2. Assumptions of ANOVA 1 Normality The data in each group should follow a normal distribution. 2 Independence The observations in each group should be independent of each other. 3 Homogeneity of Variance The variances of the groups should be equal. Random Sampling 4 The data should be collected through a process of random sampling to ensure that the sample represents the population from which it was drawn. 5 Additivity The model assumes that the effect of the different factors is additive. This means that the combined effect of different factors is equal to the sum of their individual effects.

3. Here is a simple example of how ANOVA is used and how the assumptions are checked: Suppose we want to find out if there is a difference in average test scores between three different classes. We have test score data from 30 students divided into three classes (A, B, and C) with 10 students each per class. Step 1: Collecting Data Suppose the exam score data is as follows: Class A: 75, 80, 85, 70, 90, 95, 85, 80, 75, 85 Class B: 65, 70, 75, 60, 85, 70, 80, 75, 65, 70 Class C: 85, 90, 95, 80, 75, 85, 90, 85, 80, 75 Step 2: Checking Assumptions Independence of Observations: The scores of each student in different classes are assumed to be independent. For example, the score of a student in Class A is not influenced by the score of a student in Class B or C. 2. Normality: We check normality using the Shapiro-Wilk test or by looking at the Q-Q plot. 3. Homogeneity of Variance: We check homogeneity of variance using Levene's or Bartlett's test. 4. Random Sampling: Data is considered to be randomly drawn from the population of students taking the exam. 5. Additivity: It is assumed that the effect of class on test scores is additive. Step 3: Performing ANOVA We will use statistical software (such as Python, R, or SPSS) to perform the ANOVA. Step 4: Interpretation of Results If the p-value of the Shapiro-Wilk test for each class is greater than 0.05, the normality assumption is met. If the p-value of the Levene's test is greater than 0.05, the assumption of homogeneity of variance is met. The ANOVA results will show whether there is a significant difference between the mean exam scores in the three classes. If the p-value of the ANOVA result is smaller than 0.05, we conclude that there is a significant difference between the mean test scores in at least two classes. Thus, these steps will help us understand how to use ANOVA and ensure that the necessary assumptions are met.

4. One-way ANOVA 1 Independent Variable One categorical independent variable with two or more levels. 2 Dependent Variable One continuous dependent variable. 3 Hypothesis Testing Compares the means of two or more groups to determine if they are significantly different.

5. Two-way ANOVA Independent Variables Two categorical independent variables, each with two or more levels. Dependent Variable One continuous dependent variable. Interaction Effects Examines the combined effect of the two independent variables on the dependent variable.

6. Interpreting ANOVA Results F-statistic Compares the variance between groups to the variance within groups. p-value Determines the statistical significance of the differences between groups. Effect Size Quantifies the magnitude of the difference between groups. Interaction Effects Indicates if the effect of one independent variable depends on the level of the other independent variable.

7. Post-hoc Tests Pairwise Comparisons Identifies which specific groups differ significantly from each other. Bonferroni Correction Adjusts the p-value to account for multiple comparisons and control the family-wise error rate. Tukey's HSD A common post-hoc test that performs pairwise comparisons while controlling the Type I error rate.

8. Effect Size and Statistical Power Effect Size Quantifies the magnitude of the difference between groups, independent of sample size. Statistical Power The probability of detecting an effect if it truly exists. Helps determine the appropriate sample size. Interpreting Results Considering both statistical significance and effect size provides a more complete understanding of the findings.

9. Applications and Limitations of ANOVA Applications Limitations Comparing means of multiple groups Assumes normality, independence, and homogeneity of variance Identifying significant factors and their interactions Sensitive to violations of assumptions, which can lead to inaccurate conclusions Analyzing experimental and observational data Cannot determine the direction or magnitude of differences between groups