Holm–Bonferroni method
Imagine you and your friends are trying to decide which game to play at your party. You have a lot of choices, like hide and seek, tag, and capture the flag. Each game has its own rules, and some may be more fun than others.
Now imagine you also want to figure out which game is the most popular among all the kids in your neighborhood. You could ask everyone to vote, but that might take too long. Instead, you and your friends select a random sample of kids and ask them to choose their favorite game.
However, when you look at the results, you notice that some games got a lot more votes than others. You want to be sure that you can confidently say which game is the most popular overall, and not just among the sample you selected.
This is where the Holm-Bonferroni method comes in. It helps you adjust the significance level of your statistical analysis so that you can account for the fact that you're looking at multiple comparisons.
In our game example, you and your friends would use the Holm-Bonferroni method by starting with a significance level, let's say α=0.05, which means that there's a 5% chance that any differences in the results are due to chance.
Next, you rank the games by the number of votes they received, and compare each game to the others in the list. For example, you might compare the most popular game to the second most popular game, then to the third most popular, and so on.
However, instead of using the original α value for each comparison, you adjust it using the Holm-Bonferroni formula. This formula takes into account the number of comparisons you're making, and adjusts the α value accordingly.
So, if you're comparing three games, your adjusted α value would be 0.05/3, or 0.017. This means that any difference you find between two games must be significant at this new, lower α value in order to be considered statistically significant. The more comparisons you make, the lower the α value becomes.
By using the Holm-Bonferroni method, you can be more confident in your analysis, because it helps you avoid false positives (i.e., finding a difference between two games that isn't really there).
In summary, the Holm-Bonferroni method helps you adjust the significance level of your statistical analysis to account for the fact that you're making multiple comparisons. This helps you avoid false positives and be more confident in your results.
Now imagine you also want to figure out which game is the most popular among all the kids in your neighborhood. You could ask everyone to vote, but that might take too long. Instead, you and your friends select a random sample of kids and ask them to choose their favorite game.
However, when you look at the results, you notice that some games got a lot more votes than others. You want to be sure that you can confidently say which game is the most popular overall, and not just among the sample you selected.
This is where the Holm-Bonferroni method comes in. It helps you adjust the significance level of your statistical analysis so that you can account for the fact that you're looking at multiple comparisons.
In our game example, you and your friends would use the Holm-Bonferroni method by starting with a significance level, let's say α=0.05, which means that there's a 5% chance that any differences in the results are due to chance.
Next, you rank the games by the number of votes they received, and compare each game to the others in the list. For example, you might compare the most popular game to the second most popular game, then to the third most popular, and so on.
However, instead of using the original α value for each comparison, you adjust it using the Holm-Bonferroni formula. This formula takes into account the number of comparisons you're making, and adjusts the α value accordingly.
So, if you're comparing three games, your adjusted α value would be 0.05/3, or 0.017. This means that any difference you find between two games must be significant at this new, lower α value in order to be considered statistically significant. The more comparisons you make, the lower the α value becomes.
By using the Holm-Bonferroni method, you can be more confident in your analysis, because it helps you avoid false positives (i.e., finding a difference between two games that isn't really there).
In summary, the Holm-Bonferroni method helps you adjust the significance level of your statistical analysis to account for the fact that you're making multiple comparisons. This helps you avoid false positives and be more confident in your results.