Std Dev Lower and Upper 95% from oneway analysis details of calculation

[#1]

Hello,

I am in JMP17.2.0 Pro

could you please explain me how is computed Std Dev Lower and Upper 95% in the example below ?

Especially why the interval is not symmetric around the StdDev value ?

Thank you very much.

dt = Open( "$SAMPLE_DATA/Big Class.jmp" );
platoneway = Oneway(
	Y( :weight ),
	X( :age ),
	Each Pair( 1 ),
	All Pairs( 1 ),
	Comparison Circles( 0 ),
	Means and Std Dev( 1 ),
	Box Plots( 1 ),
	Mean Diamonds( 1 ),
	Mean Error Bars( 1 ),
	Std Dev Lines( 1 ),
	Comparison Circles( 0 ),
	Grand Mean( 0 ),
	SendToReport(
		Dispatch(
			{"Means and Std Deviations"},
			"Std Dev Lower 95%",
			NumberColBox,
			{Visibility( "Visible" )}
		),
		Dispatch(
			{"Means and Std Deviations"},
			"Std Dev Upper 95%",
			NumberColBox,
			{Visibility( "Visible" )}
		),
		Dispatch(
			{"Means and Std Deviations"},
			"~Std Dev",
			PlotColBox,
			{Visibility( "Visible" )}
		),
		Dispatch( {}, "Means Comparisons", OutlineBox, {Close( 1 )} )
	)
);

[#2 · Accepted solution]

Hi @carole : Yes, it is not symmetric.  It is calculated as shown in the link below.

https://www.statology.org/confidence-interval-standard-deviation/

Why not symmetric? The answer has to with the distribution of the sample SD; it is based on a skewed distribution (the Chi-Squared distribution).  

[#3]

Thanks a lot for the link very interesting, and your answer.

Best regards,

Carole