sphstat.twosample module
Functions for inferential statistics on two or more samples
Functions for inferential statistics on two or more samples
iscommonmedian()tests the null hypothesis that two samples have a common medianpooledmedian()calculates the pooled medianiscommonmean()tests the null hypothesis that two samples have a common population meanpooledmean()calculates the pooled meanisfishercommonmean()tests the null hypothesis that two Fisherian samples have a common population meanfishercommonmean()calculates the common population mean for two Fisherian samplesisfishercommonkappa()tests the null hypothesis that two Fisherian samples have the same population concentration parameterfishercommonkappa()calculates the common population concentration parameter for two Fisherian samples
Utility functions
a20(),a21(),a23(),bilinearinterp(),linearinterp()are used to read and interpolate critical valueserrors()calculates the non-negative angular error between two vectors
- sphstat.twosample.a20(N=12, alpha: float = 0.05, Rbar: float = 0.7)[source]
Utility function used by isfishercommonmean() to extract tabulated critical values
- sphstat.twosample.a21(gamma=2, N=20, alpha=0.05, Rbar=0.1)[source]
Utility function used by isfishercommonmean() to extract tabulated critical values
- sphstat.twosample.a23(nu=2, r=2)[source]
Utility function used by isfishercommonkappa() to extract tabulated critical values
- sphstat.twosample.bilinearinterp(z00: float, z01: float, z10: float, z11: float, alpha: float, beta: float)[source]
Bilinear interpolation between 4 values
- Parameters
z00 (float) – Value 1
z01 (float) – Value 2
z10 (float) – Value 3
z11 (float) – Value 4
alpha (float) – Interpolation coefficient along axis 1 (0<=alpha<=1)
beta (float) – Interpolation coefficient along axis 2 (0<=beta<=1)
- Returns
Interpolated value
- Return type
float
- sphstat.twosample.errors(samplecart: dict, srcpos: tuple) list[source]
Calculate angular error from a given direction
- Parameters
samplecart (dict) – Sample in cart format
srcpos – Direction (th, ph) with respect to which the error will be calculated
- Returns
Errors in radians
- Return type
list
- sphstat.twosample.fishercommonkappa(samplecartlist, alpha=0.05)[source]
Estimation of the common concentration parameter of two or more Fisher distributions
- Parameters
samplecartlist (list[dict]) – List containing individual samples top be tested in ‘cart’ format
alpha (float) – Semi-vertical angle for (1-alpha)% confidence cone is calculated
- Returns
kappahat: Pooled concentration parameter [float]
ku, kl: Upper and lower critical values for the (1-alpha)% CI
- Return type
tuple
- sphstat.twosample.fishercommonmean(samplecartlist: list, alpha: float = 0.05) tuple[source]
Estimation of the common mean direction of two or more Fisher distributions 1, 2
- Parameters
samplecartlist (list[dict]) – List containing individual samples top be tested in ‘cart’ format
alpha (float) – Semi-vertical angle for (1-alpha)% confidence cone is calculated
- Returns
mdir: Tuple containing the common mean direction [th, ph]
qw: Semi-vertical angle [float]
- Return type
tuple
- 1
Fisher, N. I. & Lewis, T. (1983). Estimating the common mean direction of several circular or spherical distributions with differing dispersions. Biometrika 70, 333-341.
- 2
Watson, G. S. (1983). Statistics on Spheres. University of Arkansas Lecture Notes in the Mathematical Sciences, Volume 6. New York: John Wiley.
- sphstat.twosample.iscommonmean(samplecartlist: list, alpha: float = 0.05) dict[source]
Test of whether two or more axisymmetric distributions have a common mean 3
- Parameters
samplecartlist (list[dict]) – List containing individual samples top be tested in ‘cart’ format
alpha (float) – Type-I error level
- Returns
Dictionary containing: - Gr: Test statistic [float] - cval: Critical value to test against [float] - testresult: Test result [bool]
- 3
Watson, G. S. (1983a). Statistics on Spheres. University of Arkansas Lecture Notes in the Mathematical Sciences, Volume 6. New York: John Wiley.
- sphstat.twosample.iscommonmedian(samplecartlist: list, similarflag: bool = True, alpha: float = 0.05) dict[source]
Test for a common median direction of two or more distributions 4
- Parameters
samplecartlist (list[dict]) – List containing individual samples top be tested in ‘cart’ format
similarflag (bool) – Flag indicating similar distributions for all samples
alpha (float) – Type-I error level
- Returns
Dictionary containing… - Z2: Test statistic [float] - cval: Critical value to test against [float] - result: Test result [bool]
- 4
Fisher, N. I. (1985). Spherical medians. J.R. Statist. Soc. B47, 342-348.
- sphstat.twosample.isfishercommonkappa(samplecartlist: list) dict[source]
Test of whether two or more Fisher distributions (with unknown means) have a common concentration parameter at 0.05 level 5, 6
- Parameters
samplecartlist (list[dict]) – List containing individual samples top be tested in ‘cart’ format
- Returns
Dictionary containing test results… - Z: Test statistics [float] - cval: Critical value [float] - df: Degrees of freedom [int, tuple(int, int)] - testresult: Test result [bool]
- Return type
dict
- 5
Watson, G. S. & Irving, E. (1957). Statistical methods in rock magnetism. Mon. Not. R. astr. Soc. geophys. Suppl. 7, 289-300. (66, 136, 224)
- 6
Watson, G. S. & Williams, E. J. (1956). On the construction of significance tests on the circle and the sphere. Biometrika 43, 344-352. (14, 133, 211, 224)
- sphstat.twosample.isfishercommonmean(samplecartlist: list, alpha: float = 0.05) dict[source]
Test of whether two or more Fisher distributions have a common mean direction 7, 8, 9
- Parameters
samplecartlist (list[dict]) – List containing individual samples top be tested in ‘cart’ format
alpha (float) – Type-I error level
- Returns
Dictionary with the fields… - gr: Test statistic [float] - cval: Critical value to test against [float] - testresult: Test result [bool]
- Return type
dict
- 7
Watson, G. S. (1956). Analysis of dispersion on a sphere. Mon. Not. R. Astr. Soc. Geophys. Suppl. 7, 153-159.
- 8
Watson, G. S. & Williams, E. J. (1956). On the construction of significance tests on the circle and the sphere. Biometrika 43, 344-352.
- 9
Watson, G. S. (1983). Large sample theory of the Langevin distributions. Journal of Statistical Planning and Inference 8, 245-256.
- sphstat.twosample.linearinterp(z00: float, z01: float, alpha: float) float[source]
Linear interpolation between 4 values
- Parameters
z00 (float) – Value 1
z01 (float) – Value 2
alpha (float) – Interpolation coefficient (0<=alpha<=1)
- Returns
Interpolated value
- Return type
float
- sphstat.twosample.pooledmean(samplecartlist: list, alpha: float = 0.05) tuple[source]
Estimation of the common mean direction of two or more rotationally symmetric distributions
- Parameters
samplecartlist (list[dict]) – List containing individual samples top be tested in ‘cart’ format
alpha (float) – (1-alpha)% confidence cone is calculated
- Returns
mdirpooled: Estimated pooled mean direction in radians [np.array]
sigmaw: Spherical standard error [float]
qw: Semi-vertical angle in radians [float]
- sphstat.twosample.pooledmedian(samplecartlist: list, similarflag: bool = False) tuple[source]
Estimation of the common median direction of two or more unimodal distributions
- Parameters
samplecartlist (list[dict]) – List containing individual samples top be tested in ‘cart’ format
similarflag (bool) – Flag indicating similar distributions for all samples
- Returns
pooledmedi: Pooled median in polar coordinates [th, ph]
V: Matrix to be used for calculating the confidence cone [np.array]
- Return type
tuple