shotGroups (version 0.1)

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)

Arguments

DF

a data frame containing (at least) these variables: Distance, Aim.X, Aim.Y defining point of aim, Point.X, and Point.Y defining the bullet holes.

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.

Value

• A list with the results from the numerical analyses and statistical tests.
• Outliers
  a vector of row indices for observations identified as outliers.
• ShapiroX
  Shapiro-Wilk-Test result for normality of x-coordinates.
• ShapiroY
  Shapiro-Wilk-Test result for normality of y-coordinates.
• multNorm
  E-statistic-Test result for multivariate normality of (x,y)-coordinates.
• sdXY
  standard deviations of x- and y coordinates in original measurement units and MOA.
• sdXYrob
  robust standard deviations of x- and y-coordinates in original measurement units and MOA (MCD algorithm).
• covXY
  covariance matrix of (x,y)-coordinates.
• covXYrob
  robust estimate of covariance matrix of (x,y)-coordinates (MCD algorithm).
• corXY
  correlation matrix of (x,y)-coordinates.
• corXYrob
  robust estimate of correlation matrix of (x,y)-coordinates (MCD algorithm).
• meanDistToCtr
  average distance from points to their center in original measurement units and MOA.
• maxPairDist
  maximum pairwise distance between points in original measurement units and MOA.
• groupWidth
  width of minimum bounding box in original measurement units and MOA.
• groupHeight
  height of minimum bounding box in original measurement units and MOA.
• minCircleRad
  radius for the minimum enclosing circle in original measurement units and MOA.
• ctr
  (x,y)-offset of group center relative to point of aim.
• ctrRob
  robust estimate of group center offset relative to point of aim (MCD algorithm).
• distPOA
  distance from group center to point of aim in original measurement units and MOA.
• distPOArob
  distance from robust estimate of group center to point of aim in original measurement units and MOA.
• Hotelling
  Hotelling's T^2-Test result from testing if group center equals point of aim.
• CItX
  95% t-confidence interval for x-coordinates.
• CItY
  95% t-confidence interval for y-coordinates.
• CIbootX
  95% bootstrap-confidence intervals for x-coordinates (percentile and BCa, 1499 replicates).
• CIbootY
  95% bootstrap-confidence intervals for y-coordinates (percentile and BCa, 1499 replicates).

Details

This function is a wrapper for groupShape, groupLocation, and groupSpread. 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, 95\%-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 plot for eyeballing multivariate normality as produced bychisq.plot, including a reference line through the first and third quantile
• a heatmap of a 2D-kernel density estimate for the (x,y)-coordinates together with group center and characteristic 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 nonparametric kernel density estimate

See Also

groupShape, groupLocation, groupSpread, compareGroups, combineData, getDistToCtr, getMaxPairDist, getMinBBox, getMinCircle, getMOA, smoothScatter, aq.plot, chisq.plot, qqnorm, hist, kernel, shapiro.test, mvnorm.etest, anova.mlm, boot, boot.ci, covMcd

Examples

data(DFinch)

# select combined data from only first 4 series
DF  <- subset(DFinch, Series %in% c(1:4))
res <- analyzeGroup(DF, conversion='yd2in')
names(res)
res$multNorm
res$corXY
res$ctrRob
res$CIbootX
res$CIbootY