I need to perform a One Way Anova for the following numbers:
Scores: are 1, 2, 3, 2,3,4,4,5,6
Group: are 1, 1, 1, 2,2,2,3,3,3
How do I do this?
I have the format but I don't know what numbers to put in for the samples,
To perform a One-Way ANOVA, you need to have multiple samples or groups with corresponding data. In your case, you have the following data:
Scores: 1, 2, 3, 2, 3, 4, 4, 5, 6
Group: 1, 1, 1, 2, 2, 2, 3, 3, 3
To perform a One-Way ANOVA using this data, you need to calculate the mean and variance for each group, and then perform the ANOVA test.
Step 1: Calculate the mean for each group:
Group 1: (1 + 2 + 3) / 3 = 2
Group 2: (2 + 3 + 4) / 3 = 3
Group 3: (4 + 5 + 6) / 3 = 5
Step 2: Calculate the variance for each group:
Group 1: ((1 - 2)^2 + (2 - 2)^2 + (3 - 2)^2) / 3 = (1+0+1) / 3 = 0.67
Group 2: ((2 - 3)^2 + (3 - 3)^2 + (4 - 3)^2) / 3 = (1+0+1) / 3 = 0.67
Group 3: ((4 - 5)^2 + (5 - 5)^2 + (6 - 5)^2) / 3 = (1+0+1) / 3 = 0.67
Step 3: Calculate the total variance:
Total variance = (0.67 + 0.67 + 0.67) / 3 = 0.67
Step 4: Calculate the between-group variance:
Between-group variance = (3 * ((2 - 3)^2 + (3 - 3)^2 + (5 - 3)^2)) / (3 - 1) = 4
Step 5: Calculate the within-group variance:
Within-group variance = (9 * 0.67) / (9 - 3) = 1.12
Step 6: Calculate the F-statistic:
F-statistic = between-group variance / within-group variance = 4 / 1.12 = 3.57
Step 7: Determine the critical F-value for your desired level of significance and the degrees of freedom for the between-group and within-group variance. The critical F-value will help you determine if the observed F-statistic is statistically significant or not.
Once you have the critical F-value, compare it to the calculated F-statistic. If the calculated F-statistic is larger than the critical F-value, you can conclude that there is a significant difference between the groups' means.
Note: This is a simplified explanation of the steps involved in performing a One-Way ANOVA. In practice, statistical software or calculators can automate these calculations for you and provide more accurate results.