hotellingsTest {celltrackR}

Test Unbiasedness of Motion

Description

Test the null hypothesis that a given set of tracks originates from an uncorrelated and unbiased type of motion (e.g., a random walk without drift). This is done by testing whether the mean step vector is equal to the null vector.

Usage

hotellingsTest(
  tracks,
  dim = c("x", "y"),
  step.spacing = 0,
  plot = FALSE,
  add = FALSE,
  ellipse.col = "blue",
  ellipse.border = "black",
  conf.level = 0.95,
  ...
)

Arguments

tracks

the tracks whose biasedness is to be determined.

dim

vector with the names of the track's dimensions that are to be considered. By default c("x", "y").

step.spacing

How many positions are to be left out between the steps that are considered for the test. For persistent motion, subsequent steps will be correlated, which leads to too low p-values because Hotelling's test assumes that the input data is independent. To avoid this, the resulting p-value should either be corrected for this dependence (e.g. by adjusting the degrees of freedom accordingly), or 'step.spacing' should be set to a value high enough to ensure that the considered steps are approximately independent.

plot

logical indicating whether the scatter of the step's directions, origin of ordinates (green circle) and the mean of the data points (green cross) are to be plotted. (In one dimension also the bounds of the condfidence interval are given.) Plot works only in one or two dimensions.

add

whether to add the plot to the current plot (TRUE) or create a

ellipse.col

color with which to draw the confidence ellipse of the mean (for 1D, this corresponds to the confidence interval of the mean). Use NA to omit the confidence ellipse.

ellipse.border

color of the confidence ellipse border. Use NA to omit the border.

conf.level

the desired confidence level for the confidence ellipse.

...

further arguments passed on to plot.

Details

Computes the displacement vectors of all segments in the tracks given in tracks, and performs Hotelling's T-square Test on that vector.

Value

A list with class htest.

References

Johannes Textor, Antonio Peixoto, Sarah E. Henrickson, Mathieu Sinn, Ulrich H. von Andrian and Juergen Westermann (2011), Defining the Quantitative Limits of Intravital Two-Photon Lymphocyte Tracking. PNAS 108(30):12401–12406. doi:10.1073/pnas.1102288108

Examples

## Test H_0: T-cells migrate by uncorrelated random walk on x and y coordinates,
## and report the p-value.
hotellingsTest( TCells )$p.value