One-Way Anova Example Problems And Solutions Pdf
One-Way Anova, also known as Analysis of Variance, is a statistical method used to analyze the variance between multiple groups of data. This method is commonly used in research or experiments to determine whether there is a significant difference between the means of two or more groups. In this article, we will discuss One-Way Anova example problems and solutions in PDF format, which can be helpful for students or researchers who are studying this statistical method.
What is One-Way ANOVA?
One-Way Anova is a statistical method used to compare the means of two or more independent groups of data. In this method, the variation between the groups is compared to the variation within the groups. This method helps to determine whether there is a significant difference between the means of two or more groups.
One-Way Anova Example Problem
Let us consider an example problem to understand One-Way Anova better. Suppose a researcher wants to compare the mean weight of three different breeds of dogs. The researcher collects data from the three breeds and obtains the following results:
| Breed 1 | Breed 2 | Breed 3 |
|---|---|---|
| 10.2 | 9.8 | 12.1 |
| 11.5 | 10.5 | 11.3 |
| 9.8 | 10.2 | 10.9 |
| 10.5 | 11.1 | 12.3 |
| 12.1 | 9.5 | 11.2 |
The null hypothesis for this problem is that there is no significant difference between the mean weight of the three breeds of dogs. The alternative hypothesis is that there is a significant difference between the mean weight of one or more breeds of dogs. We can determine whether the null hypothesis is true or not using One-Way Anova.
One-Way Anova Solution
To solve the One-Way Anova example problem, we first calculate the following values:
- Mean weight of each breed of dogs
- Variance within each breed of dogs
- Overall mean weight of all the breeds of dogs
- Variance between the breeds of dogs
- One-Way Anova test statistic
- P-value
The mean weight of each breed of dogs can be calculated as follows:
- Mean weight of Breed 1 = (10.2 + 11.5 + 9.8 + 10.5 + 12.1) / 5 = 10.42
- Mean weight of Breed 2 = (9.8 + 10.5 + 10.2 + 11.1 + 9.5) / 5 = 10.22
- Mean weight of Breed 3 = (12.1 + 11.3 + 10.9 + 12.3 + 11.2) / 5 = 11.56
The variance within each breed of dogs can be calculated as follows:
- Variance of Breed 1 = [(10.2-10.42)^2 + (11.5-10.42)^2 + (9.8-10.42)^2 + (10.5-10.42)^2 + (12.1-10.42)^2] / 4 = 1.8465
- Variance of Breed 2 = [(9.8-10.22)^2 + (10.5-10.22)^2 + (10.2-10.22)^2 + (11.1-10.22)^2 + (9.5-10.22)^2] / 4 = 0.8235
- Variance of Breed 3 = [(12.1-11.56)^2 + (11.3-11.56)^2 + (10.9-11.56)^2 + (12.3-11.56)^2 + (11.2-11.56)^2] / 4 = 0.5828
The overall mean weight of all the breeds of dogs can be calculated as follows:
- Overall mean weight = (10.42 + 10.22 + 11.56) / 3 = 10.73
The variance between the breeds of dogs can be calculated as follows:
- Variance between the breeds = [(10.42-10.73)^2 + (10.22-10.73)^2 + (11.56-10.73)^2] / 2 = 0.8693
The One-Way Anova test statistic can be calculated as follows:
- One-Way Anova test statistic = Variance between the breeds / Variance within the breeds = 0.8693 / ((1.8465 + 0.8235 + 0.5828) / 12) = 4.2054
The p-value can be obtained from a One-Way Anova table or using statistical software. For this example, the p-value is 0.041. Since the p-value is less than the significance level of 0.05, we reject the null hypothesis and conclude that there is a significant difference between the mean weight of at least one breed of dog.
Conclusion
One-Way Anova is a statistical method used to determine whether there is a significant difference between the means of two or more groups. In this article, we discussed an example problem and its solution using One-Way Anova in PDF format. We hope that this article has been helpful for students or researchers who are studying this statistical method. By understanding One-Way Anova, researchers can make more informed decisions based on the data they collect.
