ANOVA - One Factor

ANOVA - One Factor

Example

We consider a dadta set with one factor and several levels, as in the following table.

^{click here to download the data}

To use the tool ANOVA the user must follow these steps: 

1. Access the menu:

Action ANOVA ANOVA

2. The following screen will be shown.

3. With the cursor in the field Data Set select the columns that contain the data; 

4. The titles of the columns can also be selected. If only the data ared selected, disable the option Columns with Name. Then, click the button Read;

REMARK: The names of the columns can not contain simbols, space or tab.

5. Select the Response Variable, in the appropriate item;

 6. Create the Formula: use a double click in the process variable to add it in the box Formula.

7. In the field Options you can select Residuals Analysis and Lack of Fit Test. In this example we will use Residuals Analysis.

8. In the field Charts you can select Effects and Interactions. In this example we will use Effects.

 9. In Show Results, choose one of the options. We suggest the option New Sheet, because Action does not have the undo command;

Results and Interpretation

Once the process is finished, the following results will be shown:

In this example we have that the Sum of Squares of the Factor (475.76) is greater than the Sum of Squares of the Error (161.20) what is already evidence that the means are not equal.

• If the p-value is lower or equal to the significance level , then the means are different. Otherwise, they are equal. In this case, as it is lower than 0.05, we reject the null hypothesis of equality of these means, that is, we can say that the meas of the levels are different.  

• In the first chart we plotted an histogram of the residuals to have an idea of how they are distributed. Then a Residuals versus Fitted values chart.
• In the second chart we verify the adherence to the normal distribution. In our case, we will use the Anderson Darling test, where the null hypothesis is that of normality and, for the chart we do not reject (we accept) the null hypothesis and verify the normality of the residuals.
• In the third chart we plotted a Residuals versus order of collection chart. With this chart we verify if the residuals are independent. the criterion for the analysis is that if the points of the chart are distributed in a random way, it is an indication of independence, otherwise, if they present a pattern, it is an indication of dependence of the residuals. In this example, we verity the independence of the residuals.
  
• In the fourth chart we verify the homoscedasticity of the data where our initial hypothesis to construct the model is that the errors are homoskedastic. The criterion to the analysis is that the more random the points, the greater the evidence of homoscedasticity. On the other hand, if the chart shows a trend, generally cone-shapped, we have an indication of heteroscedasticity. In this example, we have an indication of homoscedasticity.