analyzeGroup: Analysis for a single group of bullet holes

Description

Performs a comprehensive numerical and graphical analysis of a single group of bullet holes.

Usage

analyzeGroup(DF, xyTopLeft = TRUE, conversion = 'm2cm', bandW = 0.5,
             CEPtype = c('Rayleigh', 'Grubbs', 'RAND'))

Arguments

a data frame containing (at least) either the variables Point.X, Point.Y or X, Y defining the bullet holes. Variables Distance (distance to target), Aim.X, Aim.Y (p

xyTopLeft

a logical value indicating whether the origin of the absolute coordinate system is in the top-left corner. This is the default for data exported by OnTarget PC/TDS.

conversion

how to convert the measurement unit for distance to target to that of the (x,y)-coordinates in MOA calculation. See getMOA.

bandW

for argument bandwith of smoothScatter.

CEPtype

string vector indicating which CEP estimate to report in getCEP.

Value

A list with the results from the numerical analyses and statistical tests.
corXYcorrelation matrix of (x,y)-coordinates.
corXYrobrobust estimate of correlation matrix of (x,y)-coordinates.
Outliersa vector of row indices for observations identified as outliers.
ShapiroXShapiro-Wilk-Test result for normality of x-coordinates.
ShapiroYShapiro-Wilk-Test result for normality of y-coordinates.
multNormE-statistic-Test result for multivariate normality of (x,y)-coordinates.
sdXYstandard deviations of x- and y coordinates (in original measurement units and MOA).
sdXciparametric and bootstrap confidence intervals for the standard deviation of x-coordinates (1499 replicates, in original measurement units and MOA).
sdYciparametric and bootstrap confidence intervals for the standard deviation of y-coordinates (1499 replicates, in original measurement units and MOA).
sdXYrobrobust standard deviations of x- and y-coordinates (in original measurement units and MOA).
covXYcovariance matrix of (x,y)-coordinates.
covXYrobrobust estimate of covariance matrix of (x,y)-coordinates.
distToCtrmean and median distance from points to their center as well as estimated Rayleigh parameters sigma (precision), radial standard deviation RSD, and mean radius MR (in original measurement units and MOA).
sigmaCIparametric and bootstrap confidence intervals for sigma (1499 replicates, in original measurement units and MOA).
RSDciparametric and bootstrap confidence intervals for radial standard deviation RSD (1499 replicates, in original measurement units and MOA).
MRciparametric and bootstrap confidence intervals for mean radius MR (1499 replicates, in original measurement units and MOA).
maxPairDistmaximum pairwise distance between points (center-to-center, a.k.a. maximum spread, in original measurement units and MOA).
groupRectwidth and height of bounding box with diagonal and figure of merit FoM (average side length, in original measurement units and MOA).
groupRectMinwidth and height of minimum-area bounding box with diagonal and figure of merit FoM (average side length, in original measurement units and MOA).
minCircleRadradius for the minimum enclosing circle (in original measurement units and MOA).
confElllength of semi-major and semi-minor axis of the confidence ellipse (in original measurement units and MOA).
confEllRoblength of semi-major and semi-minor axis of the confidence ellipse based on a robust estimate for the covariance matrix (in original measurement units and MOA).
confEllShapeaspect ratio and flattening of the confidence ellipse.
confEllShapeRobaspect ratio and flattening of the confidence ellipse based on a robust estimate for the covariance matrix.
CEPestimate(s) for the circular error probable (CEP, in original measurement units and MOA).
ctr(x,y)-offset of group center relative to point of aim.
ctrXciparametric and bootstrap confidence intervals for center x-coordinate (1499 replicates).
ctrYciparametric and bootstrap confidence intervals for center y-coordinate (1499 replicates).
ctrRobrobust estimate of group center offset relative to point of aim (MCD algorithm).
distPOAdistance from group center to point of aim (in original measurement units and MOA).
distPOArobdistance from robust estimate of group center to point of aim (in original measurement units and MOA).
HotellingHotelling's T^2-Test result from testing if group center equals point of aim.

Details

Robust estimates for the group center and the covariance matrix of (x,y)-coordinates are from covMcd using the MCD algorithm. This function is a wrapper for groupShape, groupLocation, and groupSpread. If the data is missing information about the point of aim, (0,0) is assumed. If distance to target is missing, 100 is assumed. In addition to the numerical results listed below, this function produces the following diagrams:

a combined plot for multivariate outlier identification as produced byaq.plot
a scatterplot of the (x,y)-coordinates together with group center, circle with average distance to center, 50\%-confidence ellipse - the latter also based on a robust estimate for the covariance matrix
a scatterplot of the (x,y)-coordinates together with the minimum bounding box, minimum enclosing circle, and maximum group spread
a chi-square Q-Q-plot for eyeballing multivariate normality as produced bychisq.plot, including a reference line with intercept 0 and slope 1
a heatmap of a 2D-kernel density estimate for the (x,y)-coordinates as produced bysmoothScattertogether with group center and error ellipse based on a robust estimate for the covariance matrix
a Q-Q-plot for x-coordinates for eyeballing normality
a Q-Q-plot for y-coordinates for eyeballing normality
a histogram for x-coordinates including a fitted normal distribution as well as a nonparametric kernel density estimate
a histogram for y-coordinates including a fitted normal distribution as well as a nonparametric kernel density estimate
a histogram for distances to group center including a fitted Rayleigh distribution as well as a nonparametric kernel density estimate

Examples

Run this code

data(DFinch)

# select combined data from only first 2 series
DF  <- subset(DFinch, Series %in% 1:2)
res <- analyzeGroup(DF, conversion='yd2in')
names(res)
res$multNorm
res$corXY
res$ctrRob
res$ctrXci
res$ctrYci

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