# angleTest: Test whether the direction of two vectors is similar In Morpho: Calculations and Visualisations Related to Geometric Morphometrics

 angleTest R Documentation

## Test whether the direction of two vectors is similar

### Description

Test whether the direction of two vectors is similar

### Usage

```angleTest(x, y)
```

### Arguments

 `x` vector `y` vector

### Details

Under the assumption of all (normalized) n-vectors being represented by an n-dimensional hypersphere, the probability of the angle between two vectors is <= the measured values can be estimated as the area of a cap defined by that angle and divided by the hypersphere's complete surface area.

### Value

a list with

 `angle` angle between vectors `p.value` p-value for the probability that the angle between two random vectors is smaller or equal to the one calculatted from x and y

### References

S. Li , 2011. Concise Formulas for the Area and Volume of a Hyperspherical Cap. Asian Journal of Mathematics & Statistics, 4: 66-70.

### Examples

```x <- c(1,0); y <- c(1,1) # for a circle this should give us p = 0.25 as the angle between vectors
##  is pi/4 and for any vector the segment +-pi/4 covers a quarter of the circle
angleTest(x,y)
```

Morpho documentation built on Feb. 16, 2023, 10:51 p.m.