#!/usr/bin/env python
# coding: utf-8

# In[1]:


import numpy as np 

from pycircstat2 import Circular, load_data


# # Hypothesis Testing
# 
# ### Table of Contents
# 
# - [rayleigh_test](#the-rayleigh-test)
# - [V_test](#the-v-test)
# - [omnibus_test](#the-hodges-ajne-test)
# - [batschelet_test](#the-batschelet-test)
# - [chisquare_test](#chi-square-test)
# - [kuiper_test](#kuipers-test)
# - [watson_test](#watsons-one-sample-u2-test)
# - [raospacing_test](#raos-spacing-test)
# - [symmetry_test](#symmetry-test-around-the-median)
# - [one_sample_test](#one-sample-test)
# - [watson_williams_test](#watson-williams-test-for-two-multisample)
# - [watson_u2_test](#watsons-u2-test-for-two-multisample-with-or-without-ties)
# - [wheeler_watson_test](#wheeler-and-watson-two-sample-test)
# - [wallraff_test](#wallraffs-two-sample-test-for-angular-dispersion)
# 
# ### See also
# 
# Chapter 27 of Zar (2010) contains many examples and step-by-step guide of how to compute most of circular hypothesis testing. We replicated all those examples and figures in notebook [`B2-Zar-2010`](https://nbviewer.org/github/circstat/pycircstat2/blob/main/examples/B2-Zar-2010.ipynb) with `pycircstats2`.

# ## Testing for Uniformity

# ### The Rayleigh Test 
# 
# `rayleigh_test(alpha)` tests $H_{0}: \rho=0$ vs. $H_{A}: \rho \neq 0$, where $\rho$ is the population mean vector length. If the Rayleigh Test rejects $H_0$ ($p<0.05$), then the population is not a uniform circular distribution, or there is a mean population direction.
# 
# **NOTE**: The Rayleigh Test assumes the data is <mark>unimodal</mark>.

# In[2]:


from pycircstat2.hypothesis import rayleigh_test

d1 = load_data('D1', source='zar')['θ'].values
c1 = Circular(data=d1)

z, pval = rayleigh_test(c1.alpha, verbose=True)


# ### The V Test
# 
# `V_test(angle, alpha)` is a modified Rayleigh test that tests $H_{0}: \rho=0$ vs. $H_{A}: \rho \neq 0$ and has a mean angle ($\mu$).

# In[3]:


from pycircstat2.hypothesis import V_test

d7 = load_data('D7', source='zar')['θ'].values
c7 = Circular(data=d7)

V, u, pval = V_test(angle=np.deg2rad(90), alpha=c7.alpha, verbose=True)


# ### The Hodges-Ajne Test
# 
# 
# `omnibus_test(alpha)` tests $H_0$: uniform vs. $H_A$: not unifrom. Also called Ajne's A Test, or "omnibus test" because it works well for unimodal, bimodal, and multimoodal distributions.

# In[4]:


from pycircstat2.hypothesis import omnibus_test

d8 = load_data('D8', source='zar')['θ'].values
c8 = Circular(data=d8)

A, pval = omnibus_test(c8.alpha, verbose=True)


# ### The Batschelet Test
# 
# `batschelet_test(alpha)` is a modified Hodges-Ajne Test that tests $H_0$: uniform vs. $H_A$: not unifrom but concentrated around an angle θ.

# In[5]:


from pycircstat2.hypothesis import batschelet_test

C, pval = batschelet_test(angle=np.deg2rad(45), alpha=c8.alpha, verbose=True)


# ### Goodness-of-Fit Tests for Uniformity
# 
# #### Chi-Square Test
# 
# `chisquare_test(alpha)` tests the goodness of fit of a theoretical circular frequency distribution to an observed one. Here it is used to test whether the data in the population are distributed unifromly around the circle. This method is for <mark>grouped</mark> data.

# In[6]:


from pycircstat2.hypothesis import chisquare_test


d2 = load_data("D2", source="zar")
c2 = Circular(data=d2["θ"].values, w=d2["w"].values)

chi2, pval = chisquare_test(c2.w, verbose=True)


# `kuiper_test(alpha)`, `watson_test(alpha)`, and `raospacing_test(alpha)` are Goodness-of-fit tests for ungrouped data. P-values for these tests are computed through simulation.

# In[7]:


from pycircstat2.hypothesis import kuiper_test, watson_test, rao_spacing_test

pigeon = np.array([20, 135, 145, 165, 170, 200, 300, 325, 335, 350, 350, 350, 355])
c_pigeon = Circular(data=pigeon)


# #### Kuiper's Test

# In[8]:


V, pval = kuiper_test(c_pigeon.alpha, n_simulation=9999, verbose=True)


# #### Watson's one-sample U2 Test

# In[9]:


U2, pval = watson_test(c_pigeon.alpha, n_simulation=9999, verbose=True)


# #### Rao's Spacing Test

# In[10]:


U, pval = rao_spacing_test(c_pigeon.alpha, n_simulation=9999, verbose=True)


# ## Testing for Symmetry

# ### Symmetry Test (around the median)
# 
# `symmetry_test(alpha)` tests $H_0$: symmetrical around $\theta$ vs. $H_A$: not symmetrical around $\theta$, where $\theta$ is the median of the population.

# In[11]:


from pycircstat2.hypothesis import symmetry_test

d9 = load_data('D9', source='zar')['θ'].values
c9 = Circular(data=d9)

statistics, pval = symmetry_test(alpha=c9.alpha, verbose=True)


# ## Testing for the Mean Angle

# ### One-Sample Test
# 
# `one_sample_test(alpha)` tests $H_{0}: \mu_a=\mu_0$ vs. $H_{A}: \mu_a \neq \mu_0$ ,where $\mu_{a}$ is the population mean angle and $\mu_{0}$ is a specified angle. This test is simply observing whether  $\mu_{0}$ lies within the confidence interval for $\mu_{a}$.

# In[12]:


from pycircstat2.hypothesis import one_sample_test

reject_or_not = one_sample_test(angle=np.deg2rad(90), alpha=c7.alpha, verbose=True)


# ## Two-Sample or Multisample Test

# ### Watson-Williams Test for Two-/Multisample
# 
# `watson_williams_test(circs)` tests $H_0$: $\mu_1 = \mu_2 = ... = \mu_n$ vs. $H_A$: $\mu_1 \neq \mu_2 \neq ... \neq \mu_n$ 

# In[13]:


from pycircstat2.hypothesis import watson_williams_test

data = load_data("D11", source="zar")
s1 = Circular(data=data[data["sample"] == 1]["θ"].values)
s2 = Circular(data=data[data["sample"] == 2]["θ"].values)
s3 = Circular(data=data[data["sample"] == 3]["θ"].values)

F, pval = watson_williams_test(circs=[s1, s2, s3], verbose=True)


# ### Watson's U2 Test for Two-/multisample with or without Ties
# 
# `watson_U2_test(circs)` tests $H_0$: $\mu_1 = \mu_2 = ... = \mu_n$ vs. $H_A$: $\mu_1 \neq \mu_2 \neq ... \neq \mu_n$ for data with or without ties

# In[14]:


from pycircstat2.hypothesis import watson_u2_test


# In[15]:


# without ties
d = load_data("D12", source="zar")
c0 = Circular(data=d[d["sample"] == 1]["θ"].values)
c1 = Circular(data=d[d["sample"] == 2]["θ"].values)
U2, pval = watson_u2_test(circs=[c0, c1], verbose=True)


# In[16]:


# with ties
d = load_data("D13", source="zar")
c0 = Circular(data=d[d["sample"] == 1]["θ"].values, w=d[d["sample"] == 1]["w"].values)
c1 = Circular(data=d[d["sample"] == 2]["θ"].values, w=d[d["sample"] == 2]["w"].values)
U2, pval = watson_u2_test(circs=[c0, c1], verbose=True)


# ### Wheeler and Watson Two-sample Test
# 
# `wheeler_watson_test(circs)` tests $H_0$: $\mu_1 = \mu_2 = ... = \mu_n$ vs. $H_A$: $\mu_1 \neq \mu_2 \neq ... \neq \mu_n$.

# In[17]:


from pycircstat2.hypothesis import wheeler_watson_test

d = load_data("D12", source="zar")
c0 = Circular(data=d[d["sample"] == 1]["θ"].values)
c1 = Circular(data=d[d["sample"] == 2]["θ"].values)

W, pval = wheeler_watson_test(circs=[c0, c1], verbose=True)


# ### Wallraff's Two-sample Test for Angular Dispersion

# In[18]:


from pycircstat2.hypothesis import wallraff_test

d = load_data("D14", source="zar")
c0 = Circular(data=d[d["sex"] == "male"]["θ"].values)
c1 = Circular(data=d[d["sex"] == "female"]["θ"].values)
U, pval = wallraff_test(angle=np.deg2rad(135), circs=[c0, c1], verbose=True)


# In[19]:


from pycircstat2.utils import time2float

d = load_data("D15", source="zar")
c0 = Circular(data=time2float(d[d["sex"] == "male"]["time"].values))
c1 = Circular(data=time2float(d[d["sex"] == "female"]["time"].values))
U, pval = wallraff_test(angle=np.deg2rad(time2float(['7:55', '8:15'])), circs=[c0, c1], verbose=True)


# In[20]:


get_ipython().run_line_magic('load_ext', 'watermark')
get_ipython().run_line_magic('watermark', '--time --date --timezone --updated --python --iversions --watermark -p pycircstat2')