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Making ANOVA & Tukey HSD testing clearer with Compact Letter Display PowerPoint Presentation

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Making ANOVA & Tukey HSD testing clearer with Compact Letter Display Presentation Transcript

Slide 1 - Making ANOVA & Tukey HSD testing clearer with Compact Letter Display Gaetan Lion, September 3, 2022 1
Slide 2 - Introduction ANOVA is an incomplete test because it only tells you if several variables, or factors, have different Means. But, it does not tell you which specific ones are truly different. Maybe out of 5 variables (A, B, C, D, E) only E is truly different. And, this sole variable causes the ANOVA F test to be statistically significant. The other 4 variables could have similar Means. The Tukey Highly Significant Difference test (Tukey HSD) remedies the above situation. This is a post-ANOVA test that tests whether each variable is different from any of the other ones. And, Tukey HSD is conducted on a one-on-one matched variable basis just like an unpaired t test. So, Tukey HSD tests the difference in Means for A vs. B, A vs. C, A vs. D, etc. While the Tukey HSD test provides an abundance of supplementary information to ANOVA, its output is overwhelming for non-statisticians. Compact Letter Display (CLD) dramatically improves the clarity of the ANOVA & Tukey HSD test output. 2
Slide 3 - CLD basics 1. CLD identifies where the statistical significant differences are. Each variable that shares a Mean that is not statistically different from another one will share the same letter. For examples: ”a” “ab” “b” The above indicates that the first variable “a” has a Mean that is statistically different from the third one “b”. But, the second variable “ab” has a Mean that is not statistically different from either the first or third variable. ”a” “ab” “bc” “c” The above indicates that the first variable “a” has a Mean that is statistically different from the third variable “bc” and the fourth one “c”. But, this first variable “a” is not statistically different from the second one “ab”. 2. CLD also ranks the variables in descending Mean order. So, the variable with the highest Mean will be named “a” (if it is statistically different from all the others). And, the variable with the lowest Mean will have the highest letter. 3
Slide 4 - Working through an Example We are going to test if the average rainfall in 5 West Coast cities is statistically different. These cities are: Eugene (OR) Portland (OR) San Francisco (CA) Seattle (WA) Spokane (WA) The data is annual rainfall (1951 – 2021). The data source is NOAA. 4
Slide 5 - The basic data summary 5
Slide 6 - ANOVA F test. So, we know that the Cities have statistically different Average Rainfall But, as shown this ANOVA F test really does not tell you much if anything. 6
Slide 7 - Tukey HSD test identifies the difference between specific matched cities Tukey HSD test output We can observe that two pairs of matched cities have non-statistically difference in Means. These are: Portland - Seattle. p-value 0.54 San Francisco - Spokane. p-value 0.08 San Francisco – Spokane is not quite statistically significant, when using an alpha level of 0.05. 7
Slide 8 - Using a Box Plot to visualize this data 8 Top whisker = ~ 99.7th percentile Top of box = 75th percentile Line near middle of box = Median or 50th percentile Bottom of box = 25th percentile Bottom whisker = ~ 0.3d percentile Box Plot explanation This box plot has a lot of information. But, it is a bit challenging to readily identify the cities’ rainfall levels that are different from each other vs. the ones that are similar. There is more info on Box Plot visual interpretation on the last slide in the Appendix section.
Slide 9 - Putting an information package together Tukey HSD test output All the info is there. But, it is rather challenging to interpret. 9
Slide 10 - Rearranging the basic data with CLD The original data set just sorted in alphabetical order is not that informative. The revised data set using CLD is a lot more informative. The cities are ranked by Mean rainfall descending order. And, the CLD identifies readily which cities have statistically significant Mean differences, and which do not. Eugene has a statistically significant higher Mean rainfall than all the other cities. So, it is “a”. Seattle and Portland have similar Mean rainfall (not statistically different). So, they both come in as “b”. San Francisco and Spokane have less rainfall than the other cities. And, their respective rainfall levels are similar. So, they come in as “c”. 10
Slide 11 - Rearranging the Box Plots using CLD Within this Box Plot, it is challenging to differentiate cities’ rainfall relative levels and to figure out which ones are similar vs. dissimilar. This Box Plot using CLD is more informative. The cities’ rainfall levels are sorted in descending order. The color intensity is tiered with more dense texture reflecting higher rainfall levels. And, the CLD letters identify which cities have similar rainfall levels and which do not. 11
Slide 12 - 12 Upgraded information package with CLD Using CLD, you can readily identify the cities with similar vs. dissimilar rainfall levels.
Slide 13 - Appendix: Box Plot explanation 13