{smcl} {* *! version 10.1 22jul2010} {cmd: help mstat , mtest} {hline} {title:Title} {phang} {bf:M statistics} {hline 2} 2 samples M statistics for spatial distribution analysis {title:Syntax} 2 samples M statistics {cmd:mstat} {cmd:,} x({it:varname}) y({it:varname}) g({it:varname}) [{it:options} {help mstat##graph_opt:{it:graphic_options}}] 2 samples M statistics and Monte Carlo test {cmd:mtest} {cmd:,} x({it:varname}) y({it:varname}) g({it:varname}) [{it:options} {help mstat##graph_opt:{it:graphic_options}}] {title:Options for {cmd:mstat}} {synoptset 20 tabbed}{...} {synopthdr} {synoptline} {syntab:Main} {synopt: * {cmdab:x(}{help varname:{it:varname}}{cmd:)}}x-coordinates{p_end} {synopt: * {cmdab:y(}{help varname:{it:varname}}{cmd:)}}y-coordinates{p_end} {synopt: * {cmdab:g(}{help varname:{it:varname}}{cmd:)}}group dummy variable{p_end} {synopt:{opt bins(#)}}choose the number of bins to be used{p_end} {synopt:{opt chi2}}returns the upper tail pvalue of the asymptotic chi2 distribution{p_end} {synopt:{opt sc:atter}}plot the spatial distribution of two groups{p_end} {synopt:{opt den:sity}}plot the Kernel density for the interpoint distances{p_end} {synopt:{help mstat##graph_opt:{it:graphic_options}}}manipulate graphic output{p_end} {synoptline} {p 4 6 2}* Required option{p_end} {title:Options for {cmd:mtest}} {synoptset 20 tabbed}{...} {synopthdr} {synoptline} {syntab:Main} {synopt: * {cmdab:x(}{help varname:{it:varname}}{cmd:)}}x-coordinates{p_end} {synopt: * {cmdab:y(}{help varname:{it:varname}}{cmd:)}}y-coordinates{p_end} {synopt: * {cmdab:g(}{help varname:{it:varname}}{cmd:)}}group dummy variable{p_end} {synopt:{opt bins(#)}}choose the number of bins to be used{p_end} {synopt:{opt iter(#)}}choose the number of Monte Carlo permutation in the test{p_end} {synopt:{opt level(#)}}choose the level for the p-value confidence interval to be reported{p_end} {synopt:{opt sc:atter}}plot the spatial distribution of two groups{p_end} {synopt:{opt den:sity}}plot the Kernel density for the interpoint distances{p_end} {synopt:{help mstat##graph_opt:{it:graphic_options}}}manipulate graphic output{p_end} {synoptline} {p 4 6 2}* Required option{p_end} {title:Description} {pstd} The dataset is required to have the following structure: {center: x-coord y-coord group} {center:{hline 50}} {center: 23.4 45.8 0} {center: 26.4 41.3 1} {center: 71.3 39.2 1} {center: 55.0 42.8 0} {center: ... ... ...} {center:{hline 50}} {title:{cmd:mstat}} Computes the two samples observed M statistic using {it:k} bins (via option {opt bins(k)}). {title:{cmd:mtest}} Computes the two samples observed M statistic using {it:k} bins (via option {opt bins(k)}) and executes a Monte Carlo test permuting the group variable (option {opt g(varname)}) n times (via option {opt iter(n)}. It returns the upper tail p-value=#(M>=M0)/n and a corresponding l% confidence interval (via option {opt level(l)}). {title:Required options for {cmd:mstat} and {cmd:mtest}} {cmdab:x(}{help varname:{it:x-coord}}{cmd:)} variable containing the x-coordinate of the location {cmdab:y(}{help varname:{it:y-coord}}{cmd:)} variable containing the y-coordinate of the location {cmdab:g(}{help varname:{it:group}}{cmd:)} binary variable (0-1) indicating the group {title:Options for {cmd:mstat}} {cmdab:bins(}{it:#}{cmd:)} selects the number of bins. The number must be a positive integer, not larger than the number of distances in the dataset, that is (number of observations choose 2). The default is {opt bins(20)}. For the theoretical implications refer to {it:Forsberg, L., Bonetti, M. and Pagano, M. 2009}. {cmdab:chi2} displays and returns the pvalue for the asymptotic chi2 test (upper tail). {cmdab:scatter} generates scatter plot of the two groups. {cmdab:density} generates Kernel density of the interpoint distance distribution for the two groups. {title:Options for {cmd:mtest}} {cmdab:bins(}{it:#}{cmd:)} selects the number of bins. The number must be a positive integer, not larger than the number of distances in the dataset, that is (number of observations choose 2). The default is {opt bins(20)}. For the theoretical implications refer to {it:White, F. L., Bonetti, M. and Pagano, M. 2009}. {cmdab:iter(}{it:#}{cmd:)} set the number of random permutations of the group variable (option {opt g(varname)} to be performed for the Monte Carlo test. The default value is {opt iter(100)}. {cmdab:level(}{it:#}{cmd:)} set the confidence level for the p-value's confidence interval. The default is {opt level(95)}. {cmdab:scatter} generates a scatter plot of the two groups. {cmdab:density} generates a Kernel density of the interpoint distance distribution for the two groups. {marker graph_opt}{title:Graphic Options} The graphic options are designed to manipulate the graphic output of the commands. The options are active only if the corresponding option ({cmdab:scatter} or {cmdab:density}) is specified. Options when option {cmdab:scatter} is specified {cmdab:scolor0(}{help colorstyle:{it:colorstyle}}{cmd:)} set the color for the marker of group 0. {cmdab:scolor1(}{help colorstyle:{it:colorstyle}}{cmd:)} set the color for the marker of group 1. {cmdab:smarker0(}{help symbolstyle:{it:marker symbol}}{cmd:)} set the symbol for the marker of group 0. {cmdab:smarker1(}{help symbolstyle:{it:marker symbol}}{cmd:)} set the symbol for the marker of group 1. {cmdab:ssize0(}{help markersizestyle:{it:marker size}}{cmd:)} set the size for the marker of group 0. {cmdab:ssize1(}{help markersizestyle:{it:marker size}}{cmd:)} set the size for the marker of group 1. {cmdab:slabel0(}{it:string}{cmd:)} input the label for group 0 in the legend, default: "Group 0". {cmdab:slabel1(}{it:string}{cmd:)} input the label for group 1 in the legend, default: "Group 1". {cmdab:stitle(}{it:string}{cmd:)} specifies the title for the scatter, default: "Spatial Distribution of the two groups". {cmdab:sytitle(}{it:string}{cmd:)} specifies the title for the y axis, default is the name of the variable in option {cmdab:y(}{help varname:{it:y-coord}}{cmd:)}. {cmdab:sxtitle(}{it:string}{cmd:)} specifies the title for the x axis, default is the name of the variable in option {cmdab:x(}{help varname:{it:x-coord}}{cmd:)}. Options when option {cmdab:density} is specified {cmdab:dcolor0(}{help colorstyle:{it:colorstyle}}{cmd:)} set the color for the line of the density of group 0. {cmdab:dcolor1(}{help colorstyle:{it:colorstyle}}{cmd:)} set the color for the line of the density of group 1. {cmdab:dpattern0(}{help linepatternstyle:{it:line pattern style}}{cmd:)} set the pattern style for the line of the density of group 0. {cmdab:dpattern1(}{help linepatternstyle:{it:line pattern style}}{cmd:)} set the pattern style for the line of the density of group 1. {cmdab:dwidth0(}{help linewidthstyle:{it:line width style}}{cmd:)} set the width for the line of the density of group 0. {cmdab:dwidth1(}{help linewidthstyle:{it:line width style}}{cmd:)} set the width for the line of the density of group 1. {cmdab:dlabel0(}{it:string}{cmd:)} input the label for group 0 in the legend, default: "Group 0". {cmdab:dlabel1(}{it:string}{cmd:)} input the label for group 1 in the legend, default: "Group 1". {cmdab:dtitle(}{it:string}{cmd:)} specifies the title for the Kernel density, default: "IDD Kernel Densities". {title:Saved results} {cmd:mstat} saves the following in {cmdab:r()} Scalars {cmdab:r(M)} observed M statistic {cmdab:r(p)} chi-squared p-value (if option {opt chi2} is specified) Matrices {cmdab:r(difF)} difference between the ECDFs in the two groups {cmdab:r(Sinv)} generalized inverse of the covariance matrix of {cmdab:r(difF)} {cmdab:r(d)} cutoffs of the equiprobable bins {cmd:mtest} saves the following in {cmdab:r()} Scalars {cmdab:r(N)} sample size Matrices {cmdab:r(M)} observed M statistic {cmdab:r(c)} count when M>=M(obs) is true {cmdab:r(p)} observed empirical p-value {cmdab:r(se)} standard error of empirical p-value {cmdab:r(ci)} exact binomial confidence interval of observed p-value {cmdab:r(reps)} number of nonmissing results {cmdab:r(d)} cutoffs of the equiprobable bins {cmdab:r(Sinv)} generalized inverse of the covariance matrix {title:Author} {p 4} Pietro Tebaldi {p_end} {p 4} Department of Biostatistics , Harvard School of Public Health {p_end} {p 4} Bocconi University , Milan - Italy {p_end} {p 4} {browse "mailto:pietro.tebaldi@studbocconi.it":pietro.tebaldi@studbocconi.it} {title:References} {p 4 8 2}Bonetti, M., and Pagano, M. The interpoint distance distribution as a descriptor of point patterns, with an application to spatial disease clustering. {it:Stat Med} 2005; 24(5):753-773. {p 4 8 2}Forsberg, L., Bonetti, M. and Pagano, M. 2009. The choice of the number of bins for the M statistic. {it:CSDA} 2009; 53(10):3640-3649. {p 4 8 2}Manjourides, J., and Pagano, M. 2010. An interpoint distance based test for the difference between two spatial distribution. {it:Submitted}. {p 4 8 2}Ozonoff, A. , Jeffery, C. , Manjourides, J. , White, L.F., and Pagano, M. 2007. Effect of spatial resolution on cluster detection: a simulation study. {it:Int J Health Geogr} 2007; 52(6).