How to Perform a One-Way ANOVA by Hand.pptx

How to Perform a One-Way ANOVA by Hand

1. How to Perform a One-Way ANOVA by Hand

2. one-way ANOVA A one-way ANOVA (“analysis of variance”) compares the means of three or more independent groups to determine if there is a statistically significant difference between the corresponding population means.

3. Example: One-Way ANOVA by Hand Suppose we want to know whether or not three different exam prep programs lead to different mean scores on a certain exam. To test this, we recruit 30 students to participate in a study and split them into three groups . The students in each group are randomly assigned to use one of the three exam prep programs for the next three weeks to prepare for an exam. At the end of the three weeks, all of the students take the same exam.

4. Group 1 Group 2 Group 3 85 91 79 86 92 78 88 93 88 75 85 94 78 87 92 94 84 85 98 82 83 79 88 85 71 95 82 80 96 81

5. steps to perform a one-way ANOVA by hand Step 1: Calculate the group means and the overall mean . Step 2: Calculate SSR . Step 3: Calculate SSE . Step 4: Calculate SST . Step 5: Fill in the ANOVA table . Step 6: Interpret the results.

6. ANOVA table Source Sum of Squares (SS) Df Mean Squares (MS) F test Statistics Treatment SSR k – 1 SSR/ Df MS Treatment / MS Error Error SSE n – k SSE/ Df Total SST n – 1

7. Interpretation of the results If F test statistics is less than F critical value, FAILED TO REJECT the Null Hypothesis. If F test statistics is greater than F critical value, REJECT the Null Hypothesis .