Anova- One way & Two Way

Anova- One way & Two Way

Dhiresh Patil

One-way ANOVA (Analysis of Variance) is a statistical method used to compare the means of three or more independent groups. It is used to determine whether there is a significant difference in the means of the groups.

In a one-way ANOVA, there is only one independent variable, and it has multiple levels or categories. The dependent variable is continuous. The goal is to determine whether there is a significant difference in the mean values of the dependent variable across the different levels of the independent variable.

For example, consider a study that wants to determine if there is a significant difference in the average weight loss of people who follow three different diets (low-carb, low-fat, and high-protein). The independent variable is the type of diet (with three levels: low-carb, low-fat, and high-protein) and the dependent variable is the weight loss (measured in pounds).

Two-way ANOVA is a statistical method that is used to compare the means of two or more independent variables. It is used to determine whether there is a significant interaction between the two independent variables and a significant effect on the dependent variable.

In a two-way ANOVA, there are two independent variables, and each variable has multiple levels or categories. The dependent variable is continuous. The goal is to determine whether there is a significant interaction between the two independent variables and a significant effect on the dependent variable.

For example, consider a study that wants to determine if there is a significant difference in the average test scores of students who receive two different teaching methods (lecture and hands-on) and who have two different learning styles (visual and auditory). The two independent variables are teaching method (with two levels: lecture and hands-on) and learning style (with two levels: visual and auditory), and the dependent variable is test score (measured as a percentage).

In summary, the difference between one-way ANOVA and two-way ANOVA is that one-way ANOVA compares the means of three or more groups based on one independent variable, while two-way ANOVA compares the means of two or more groups based on two independent variables and examines the interaction between these variables.

Let’s take a practical example to understand further

One-way ANOVA Example:

Suppose we want to determine if there is a significant difference in the average height of tomato plants grown in three different types of soil (sand, clay, and loam). We measure the height of 10 plants for each soil type and the results are as follows:

Sand: 12.2, 12.7, 11.9, 12.1, 11.8, 11.7, 12.0, 11.9, 12.3, 12.2

Clay: 13.5, 13.2, 13.4, 13.3, 13.1, 13.4, 13.5, 13.3, 13.2, 13.4

Loam: 14.0, 14.1, 14.2, 14.2, 14.1, 14.0, 14.2, 14.0, 14.2, 14.1

We perform a one-way ANOVA to determine if there is a significant difference in the average height of the tomato plants grown in the three different types of soil.

Two-way ANOVA Example:

Now suppose we want to determine if there is a significant difference in the average height of tomato plants grown in three different types of soil (sand, clay, and loam) and under two different levels of sunlight (high and low). We measure the height of 10 plants for each combination of soil type and sunlight level and the results are as follows:

Sand (High Sunlight): 12.2, 12.7, 11.9, 12.1, 11.8, 11.7, 12.0, 11.9, 12.3, 12.2

Sand (Low Sunlight): 11.7, 11.8, 11.9, 11.8, 11.7, 11.9, 11.7, 11.8, 11.7, 11.9

Clay (High Sunlight): 13.5, 13.2, 13.4, 13.3, 13.1, 13.4, 13.5, 13.3, 13.2, 13.4

Clay (Low Sunlight): 12.8, 12.9, 12.7, 12.8, 12.6, 12.9, 12.7, 12.8, 12.7, 12.9

Loam (High Sunlight): 14.0, 14.1, 14.2, 14.2, 14.1, 14.0, 14.2, 14.0, 14.2, 14.1

Loam (Low Sunlight): 13.5, 13.6, 13.7, 13.6, 13.5, 13.6, 13.7, 13.5, 13.6, 13.7

We perform a two-way ANOVA to determine if there is a significant difference in the average height of the tomato plants grown in the three different types of soil and under two different levels of sunlight. We will also examine the interaction between the soil type and sunlight level to determine if their effects on the average height of the plants are independent or dependent.