def test_variance_of_weighted_mean(self):
"""variance_of_weighted_mean calculates the variance of a weighted mean"""
#Just a hand calculated example using the formula from here:
#http://en.wikipedia.org/wiki/Weighted_mean
#TODO: test if this works for arrays of variances
#If all weights and standard deviations are equal, then
#variance = stdev/sqrt(n)
weights = array([0.5,0.5])
sample_stdevs = array([4.0,4.0])
variances = sample_stdevs**2
exp = 4.0/sqrt(2.0)
obs = variance_of_weighted_mean(weights,variances)
self.assertFloatEqual(obs,exp)
#If standard deviations are equal, but weights are not, the result
#is equal to stdev*sqrt(sum(squared_weights))
weights = array([0.1,0.9])
sample_stdevs = array([4.0,4.0])
variances = sample_stdevs**2
exp_unbalanced = 4.0*sqrt(sum(weights**2))
obs = variance_of_weighted_mean(weights,variances)
self.assertEqual(obs,exp_unbalanced)
#If all standard deviations are equal:
#The minimal value for the variance is when all weights are equal
#the maximal value is when one weight is 1.0 and another is 0.0
sample_variances = array([3.0,3.0,3.0,3.0])
balanced_weights = array([0.25,0.25,0.25,0.25])
two_weights = array([0.0,0.50,0.50,0.0])
unbalanced_weights = array([0.0,1.0,0.0,0.0])
balanced_variance = variance_of_weighted_mean(balanced_weights,sample_variances)
two_weight_variance = variance_of_weighted_mean(two_weights,sample_variances)
unbalanced_variance = variance_of_weighted_mean(unbalanced_weights,sample_variances)
#We expect balanced_variance < two-weight_variance < unbalanced_variance
self.assertTrue(balanced_variance < two_weight_variance)
self.assertTrue(balanced_variance < unbalanced_variance)
self.assertTrue(two_weight_variance < unbalanced_variance)
#Check that doing this for two 1D arrays is equal to using a single 2d array
weights1 = array([0.1,0.9])
weights2 = array([0.5,0.5])
vars1 = array([4.0,4.0])
vars2 = array([1000.0,1000.0])
obs1 = variance_of_weighted_mean(weights1,vars1)
obs2 = variance_of_weighted_mean(weights2,vars2)
#Expect that calculating the result as a single 2D array
#gives identical results to calculating as two 1D arrays
exp = array([obs1,obs2])
combined_weights = array([[0.1,0.9],[0.5,0.5]])
combined_vars = array([[4.0,4.0],[1000.0,1000.0]])
combined_obs = variance_of_weighted_mean(combined_weights,combined_vars)
self.assertFloatEqual(combined_obs,exp)
def test_variance_of_weighted_mean(self):
"""variance_of_weighted_mean calculates the variance of a weighted mean"""
#Just a hand calculated example using the formula from here:
#http://en.wikipedia.org/wiki/Weighted_mean
#TODO: test if this works for arrays of variances
#If all weights and standard deviations are equal, then
#variance = stdev/sqrt(n)
weights = array([0.5,0.5])
sample_stdevs = array([4.0,4.0])
variances = sample_stdevs**2
exp = 4.0/sqrt(2.0)
obs = variance_of_weighted_mean(weights,variances)
self.assertFloatEqual(obs,exp)
#If standard deviations are equal, but weights are not, the result
#is equal to stdev*sqrt(sum(squared_weights))
weights = array([0.1,0.9])
sample_stdevs = array([4.0,4.0])
variances = sample_stdevs**2
exp_unbalanced = 4.0*sqrt(sum(weights**2))
obs = variance_of_weighted_mean(weights,variances)
self.assertEqual(obs,exp_unbalanced)
#If all standard deviations are equal:
#The minimal value for the variance is when all weights are equal
#the maximal value is when one weight is 1.0 and another is 0.0
sample_variances = array([3.0,3.0,3.0,3.0])
balanced_weights = array([0.25,0.25,0.25,0.25])
two_weights = array([0.0,0.50,0.50,0.0])
unbalanced_weights = array([0.0,1.0,0.0,0.0])
balanced_variance = variance_of_weighted_mean(balanced_weights,sample_variances)
two_weight_variance = variance_of_weighted_mean(two_weights,sample_variances)
unbalanced_variance = variance_of_weighted_mean(unbalanced_weights,sample_variances)
#We expect balanced_variance < two-weight_variance < unbalanced_variance
self.assertTrue(balanced_variance < two_weight_variance)
self.assertTrue(balanced_variance < unbalanced_variance)
self.assertTrue(two_weight_variance < unbalanced_variance)
#Check that doing this for two 1D arrays is equal to using a single 2d array
weights1 = array([0.1,0.9])
weights2 = array([0.5,0.5])
vars1 = array([4.0,4.0])
vars2 = array([1000.0,1000.0])
obs1 = variance_of_weighted_mean(weights1,vars1)
obs2 = variance_of_weighted_mean(weights2,vars2)
#Expect that calculating the result as a single 2D array
#gives identical results to calculating as two 1D arrays
exp = array([obs1,obs2])
combined_weights = array([[0.1,0.9],[0.5,0.5]])
combined_vars = array([[4.0,4.0],[1000.0,1000.0]])
combined_obs = variance_of_weighted_mean(combined_weights,combined_vars)
self.assertFloatEqual(combined_obs,exp)