Final answer:
To compare the means of three groups' data, the one-way ANOVA is the best statistical method, which assesses whether group means are significantly different from one another.
Step-by-step explanation:
If you want to compare the means of three groups' data, the best statistical method to use is the one-way ANOVA. This method tests the hypothesis that all group means are equal and is appropriate if the populations are normally distributed, have equal standard deviations, and the samples are randomly and independently selected. The F statistic from the ANOVA will tell you if there are any significant differences between the group means.
Calculating the mean of each group is essential in analyzing the data because it provides a summary statistic that represents the central tendency of each dataset. It also enables the ANOVA to compare the variance among the groups (MSbetween) to the variance within each of the groups (MSwithin). If the calculated p-value from the ANOVA is small (typically less than 0.05), it suggests that at least one group mean is different from the others.
For example, consider the group means from a hypothetical study: Terry's mean is 3.7, Davis's mean is 2.7, and Maris's mean is 4.6. The one-way ANOVA would compare these means to determine if these differences are statistically significant or if they could have occurred by chance.