Which statistical method is used to analyze the differences among group means in a dataset?

The statistical method used to analyze the differences among group means in a dataset is called Analysis of Variance, or ANOVA. Here are the steps to perform an ANOVA:

1. Formulate the Hypothesis: The null hypothesis (H0) for ANOVA is that there are no differences among the group means. The alternative hypothesis (H1) is that at least one group mean is different.

2. Calculate the Between-group Variability: This measures how much the means of each group differ from the overall mean of the data.

3. Calculate the Within-group Variability: This measures how much the numbers in each group vary around their group mean.

4. Calculate the F statistic: The F statistic is the ratio of the between-group variability to the within-group variability.

5. Determine the P-value: The P-value is the probability of getting a result as extreme as the one observed if the null hypothesis were true. If the P-value is less than the chosen significance level (usually 0.05), we reject the null hypothesis.

6. Interpret the Results: If the P-value is less than 0.05, we can conclude that there is a significant difference among the group means. If the P-value is greater than 0.05, we cannot conclude that there is a significant difference.

Remember, ANOVA only tells us if there is a significant difference among the group means, but it does not tell us which specific groups are significantly different from each other. To determine this, we would need to perform a post hoc test, such as Tukey's HSD (Honestly Significant Difference) test.