What statistical method is utilized when you have only one variable at three or more levels?

The correct method for analyzing one variable that has three or more levels is One-way Analysis of Variance (ANOVA). This statistical technique is specifically designed to compare the means of different groups within a single independent variable.

In cases where there is only one independent variable with multiple categories, such as different groups or treatment levels, One-way ANOVA tests whether there are statistically significant differences in the means among those groups. This allows researchers to determine if at least one group mean differs from the others without conducting multiple t-tests, which would increase the risk of Type I error.

Using this method is appropriate when the assumptions of normality and homogeneity of variances are met, making it an effective way to analyze data with a single factor at multiple levels.