Confidence interval for the Geometric mean from Distribution platform

[#1]

Hello,

Is there any shortcut to get the Confidence interval for the Geometric mean from the distribution platform?

[#2 · Accepted solution]

That result is unavailable from the Distribution platform or any other place in JMP. The computation may be scripted using the guidance in this DO Loop blog post. SAS/IML is similar to JMP JSL, so the conversion is not too bad.

[#3]

Hi Mark,

Thank you very much for the quick feedback.

[#4]

Another way, without JSL but making the same assumptions of a Log-Normal distribution; using the distribution platform, analyze the natural log of the data. The mean and confidence bounds acquired can then be back-transformed via Exp. The resulting interval is a confidence interval on the GM.   

[#5]

I didn't compare details with the guidance that @Mark_Bailey quotes, but you can try the bootstrap too (either interactively or via JSL). For example:

NamesDefaultToHere(1);

// Get some data
dt = Open("$SAMPLE_DATA/Big Class.jmp");

// Use Distribution
dist = dt << Distribution(
					Continuous Distribution(
						Column( :height ),
						Quantiles( 0 ),
						Vertical( 0 ),
						Outlier Box Plot( 0 ),
						Customize Summary Statistics(
							Mean( 0 ),
							Std Dev( 0 ),
							Std Err Mean( 0 ),
							Upper Mean Confidence Interval( 0 ),
							Lower Mean Confidence Interval( 0 ),
							N( 0 ),
							N Missing( 0 ),
							Geometric Mean( 1 )
						)
					)
				);

// Bootstrp the statistic in question (note 'dt2' is a list)
dt2 = Report(dist)[TableBox(1)] << Bootstrap(1000);

// Inspect the bootstrp distribution
dist2 = dt2[2] << runScript("Distribution");

// Get the confidence interval for the statistic by inspection or further JSL . . .

[#6 · Accepted solution]

And if you just care about the interval, you could get it using this kind of approach, which is much quicker since you don't have the overhead of all the platform launches that the generality of Bootstrap requires:

NamesDefaultToHere(1);

// Get some data
dt = Open("$SAMPLE_DATA/Big Class.jmp");

n = NRow(dt);

dataVec = dt[0, "height"];	// Get the requisite data as a vector
nb = 100000;				// Number of bootstrsp samples
gms = J(nb, 1, .);			// Vector to hold the geometric mean of each bootstrap sample

for(s=1, s<=nb, s++,									// Loop over bootstrap samples
	pickMe = J(n, 1, RandomInteger(1, n));				// Indices of elements to compose this bootstrap sample
	bootstrapSampleVec = dataVec[pickMe];				// Values in this bootstrap sample
	gm = exp(Mean(ln(bootstrapSampleVec)));				// Geometric mean of this bootstrap sample
	gms[s] = gm;
);
gm95 = Quantile(0.95, gms);
gm05 = Quantile(0.05, gms);

Print("The Geometric Mean lies betweeen "||Char(Round(gm05, 3))||" and "||Char(Round(gm95, 3))||".");

Probably this code could be parallelised to make it even quicker, but with the loss of some readability.

[#7 · Accepted solution]

Hello Ian,

That's perfect. Thanks a lot for the suggestion.