The above thermal comfort limits were derived from a linear regression model attached to this text.

As outlined by Box’s approach to hypothesis testing. Here’s the step-by-step:

Fidel Vallejo , hows does that address the situation in the question at all ?

I don't see any reasonable way to do a hypothesis test here. I think your main plot is great. I would just describe the obvious difference among some of the standards.

Sal Mangiafico Thank you for your question. The approach I outlined, following Box’s methodology, directly addresses the question by providing a structured way to test for significant differences between the existing and proposed comfort limits. The F-test first compares the variances of the two groups to determine which t-test (equal variances or Welch’s) should be applied. Then, the t-test assesses whether the means of the comfort limits differ significantly. This two-step process ensures we can statistically determine if the proposed limits are significantly different from the existing ones, as asked in the question.

I hope this clarifies the relevance of the approach. Let me know if you’d like further details!

I agree that with Fidel Vallejo that Step 1 should be computation of variance ratios to determine whether the data justify parametric comparisons of means. If so, insofar as the pairs of means as ordered are comparable, one could do MANOVA followed by ANOVAS 0r t-tests for individual pairs of means. (Here each F would equal the square of the corresponding t.)

If variance ratios didn't support the assumption of homogeneity, one could conduct nonparametic comparisons. One could use the Kruskal-Wallis test in place of MANOVA and either the Mann-Whitney U test or the Wilcoxon signed-rank test for the individual comparisons.

Fidel Vallejo , Paul Max Kohn , variance ratios of what data ?

t-test, anova, manova on what data ?

I imagine that the comfort limits in the figure are just a range. Like, literally, someone just said, "If you work in an office, the thermostat should be set between 19 and 28 degrees." These aren't a set of observations.

To answer @Sal Manfafiaco's question the numerical data appearing are range lower limits, range upper limits and range differences. @Abdul Mohsin Ali can take his pick(s) among these, depending on what he finds meaninful.

To answer @Sal Manfafiaco's question the numerical data appearing are range lower limits, range upper limits and range differences. @Abdul Mohsin Ali can take his pick(s) among these, depending on what he finds meaningful. (One spelling correction.)