Lower values means it’s less likely that the means are equal.

For the Tukey HSD, which calculates the difference of means and creates a confidence interval around that difference, look for whether the 95% confidence interval (‘lwr ’and ‘upr’) contains 0 in the range.

If it does, then the means are not significantly different because 0 —indicating no difference — is a plausible value.

Otherwise, the differences are significant.

If ‘diff’ is negative, the first neighborhood is cheaper than the second, and vice versa for positive.

I’m more of a visual person, so let’s look at the Tukey HSD in a graph:But what does it mean?Beacon Hill looked more expensive than downtown.

Now, we can say it is.

The 95% confidence interval does not contain 0 and the difference is statistically significant.

We now know with confidence that, in 2018, the assessed values on a per-square-foot level were highest in Beacon Hill, followed by Downtown then Back Bay.

In fact, the only pair that is not statistically significant among our sample neighborhoods is Kenmore and the North End; we cannot conclude that the mean values of these two neighborhoods is different on a per-square-foot level.

Business Implications and ConclusionThe use of ANOVA and related statistics in business is wide-reaching.

For example, if we’re looking at performance of various companies in a market, the first question we want to ask is:Is there opportunity to differentiate in the market?If all mean values are statistically the same, then the company has to look beyond performance to actually move the needle on customer wins (service, breadth of offering, etc.

).

In other words, if product performance is a baseline criteria to win a contract, where should the next level of investment capital go to actually differentiate?Once we’ve established where the opportunity to differentiate is, we want to know:Where is the company differentiated?That’s when we can proceed with the pairwise comparison or Tukey HSD to determine differences between companies.

Is the score of 5.

95 for Group A in the chart at the beginning of the article actually different than 5.

83 for Group C?The result is understanding within a given market of:Where is there opportunity to differentiate?Where is the company differentiated today?How should the company allocate capital (M&A, R&D, etc.

) to double down on differentiating criteria or accelerate improvement on underperformance?I’m a firm believer in the practical application of learning and, while fun to run an analysis on the neighborhoods that I know and experience every day, the implications for business and what these can do is much more significant and interesting to explore.

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