Is there an interactive method in JMP to determine whether the means of two populations differ by at least a certain amount, or more generally to graph a p value or probability by the minimum difference in means?
Example: in the big class data set, show the likelihood that females are shorter than meals by at least X, similar to the table and chart below.
This may or may not be the best way to quantify this, but here is a script to create the above table:
Names default to here(1);
dt = Open("$Sample_data/Big Class.jmp");
// Column to adjust the difference in means between levels
nc = dt << New Column("height differenced", Numeric, "Continuous", Format("Best", 12), Formula(Parameter({b0 = 5}, If(:sex == "F", :height + b0, :height))));
distances = index(-2,7,incr=.5);
pvalless = {};
pvalmore = {};
for(d=1, d<= n items(distances), d++,
dist = distances[d];
Eval( Eval Expr( nc << Set Formula( Parameter({b0 = expr( dist ) }, If(:sex == "F", :height + b0, :height))) ) );
ow = dt << Oneway(
Y( nc ),
X( :sex ),
Means( 1 ),
t Test( 1 ),
Mean Diamonds( 1 ),
SendToReport( Dispatch( {}, "t Test", OutlineBox, {Close( 1 )} ) )
);
//Extract the prob
pvalless[d] = ((ow << XPath("//OutlineBox[text()='Pooled t Test']"))[1][NumberColBox(4)] << get as matrix)[2];
pvalmore[d] = ((ow << XPath("//OutlineBox[text()='Pooled t Test']"))[1][NumberColBox(4)] << get as matrix)[3];
ow << close window;
);
dtSum = New Table( "Results",
Add Rows( n items(distances) ),
New Column( "Distance",
Numeric,
"Continuous",
Format( "Best", 12 ),
Set Values( distances )
),
New Column( "pvalueless",
Numeric,
"Continuous",
Format( "Best", 12 ),
Set Values( pvalless )
),
New Column( "pvaluemore",
Numeric,
"Continuous",
Format( "Best", 12 ),
Set Values( pvalmore )
)
);
gb = dtSum << Graph Builder(
Size( 876, 379 ),
Show Control Panel( 0 ),
Variables( X( :Distance ), Y( :pvalueless ) ),
Elements( Points( X, Y, Legend( 3 ) ), Line( X, Y, Legend( 5 ) ) ),
SendToReport(
Dispatch(
{},
"pvalueless",
ScaleBox,
{Add Ref Line( 0.05, "Solid", "Black", ".05", 1 )}
),
Dispatch(
{},
"400",
ScaleBox,
{Legend Model( 3, Base( -1, 0, 0, Item ID( "pvaluemore", 1 ) ) )}
),
Dispatch(
{},
"graph title",
TextEditBox,
{Set Text(
"Likelihood of average heights of females being shorter than males by different amounts"
)}
),
Dispatch(
{},
"X title",
TextEditBox,
{Set Text( "Minimum Distance Between Average Heights" )}
),
Dispatch( {}, "Y title", TextEditBox, {Set Text( "p value" )} ),
Dispatch(
{},
"Graph Builder",
FrameBox,
{Add Line Annotation(
Line( {233, 222}, {277, 286} ),
Color( "Magenta" ),
Thick( 1 ),
Point to( 1 )
), Add Text Annotation(
Text(
"6% chance that females are not 1 or more inches shorter than males"
),
Fixed Size( 0 ),
Text Box( {43, 175, 332, 237} ),
Filled( 0 ),
Text Color( "Medium Dark Magenta" ),
"Font"("Segoe UI", 12, "Bold")
), Add Text Annotation(
Text(
"34% likelihood that females are not 2.5 or more inches shorter than males"
),
Fixed Size( 0 ),
Text Box( {142, 101, 454, 163} ),
Filled( 0 ),
Text Color( "Medium Dark Magenta" ),
Background Color( "White" ),
"Font"("Segoe UI", 12, "Bold")
), Add Line Annotation(
Line( {353, 149}, {409, 203} ),
Color( "Magenta" ),
Thick( 1 ),
Point to( 1 )
), Add Text Annotation(
Text(
"Highly unlikely that females are
6 or more inches shorter than males"
),
Fixed Size( 0 ),
Text Box( {537, 98, 826, 152} ),
Filled( 0 )
), Add Line Annotation(
Line( {678, 93}, {711, 27} ),
Color( "Magenta" ),
Thick( 1 ),
Point to( 1 )
)}
)
)
);