Metrics Used to Compare Histograms

[#1]

I have two data sets with +/- same average & variance however the shape/histogram is diferent. What is an appropriate metric in JMP to compare two Histograms and assess difference in shape/distribution?

[#2]

Hi @frankderuyck,

There may be several options in the "Distribution" platform :

• You can customize "Summary statistics" (by clicking on the red triangle) to show skewness (asymetry of the distribution) and kurtosis (heaviness of the distribution tails) for example. You can look at the complete distribution metrics available here : The Summary Statistics Report (jmp.com)

• You can also try to Fit Continuous distributions (in the red triangle of your response distribution, "Continuous Fit" and then "Fit All"), in order to compare the type of distribution and the value of its parameters. Here with a Weibull distribution, I can look at the scale and shape estimates for example :

• You can also plot the distributions with the Graph Builder, use Box Plots and show the 5-numbers summary : max, min, med, Q1 and Q3 :

This is clearly not an exhaustive list of options, and other users may also have other ideas to better compare distributions metrics.

I hope these few ideas may help you,

[#3]

Hi Victor, thanks for input, I am familiar with the options you propose and yes these are good indicators.

However, what I would like to know is how to assess that there is a statistically signficant difference between distribution profile in two histograms; I think the nonparametric median test may be an appropriate tool ? Are there other methods?

[#4]

I know of no test "...to assess that there is a statistically significant difference between distribution profile in two histograms." What can be evaluated by classic hypothesis testing methods are various parameter estimates of two populations. Or alternatively bootstrapping methods could be employed within a JMP framework. Many pathways in JMP to accomplish this.

[#5 · Accepted solution]

Hi @frankderuyck,

You're right, in the platform "Fit Y by X", you can find non-parametric test in order to assess if there is a statistically significant difference between distributions.
You might be interested in tests like Wilcoxon or Steel-Dwass : Nonparametric Multiple Comparisons Reports (jmp.com)

There was already a topic dealing about this distribution comparison : Solved: Re: Nonparametric Tests: Kolmogorov Smirnov test for variance testing - JMP User Community

Even if this is not statistical testing, you can also visualize your distributions by looking at "densities" and CDF plots in the Fit Y by X platform :

I hope this answer will help you,

[#6]

Great, thanks Victor!