def confidence_interval(data, percentile, number_of_tails):
"""
Computes confidence interval for the
mean of the given data covering the probability given by the
variable percentile.
* data specifies the given data.
* precentile gives the probability that the mean of the data is in
the confidence interval.
* number_of_tails gives the number of tails of the normal distribution
to be considered.
"""
square = math.pow(len(data), 0.5)
mean = statchar.aritmetic_mean(data)
std_dev = statchar.std_dev_corrected(data)
dist = distributions.NormalDistribution(0, 1)
if number_of_tails == 2:
alfa = (1-percentile)/2
c = distributions.find_percentile(1-alfa, dist.cdf)
left = mean - c*std_dev/square
right = mean + c*std_dev/square
return left, right
elif number_of_tails == 1:
alfa = percentile
c = distributions.find_percentile(alfa, dist.cdf)
SEM = statchar.std_error_of_mean(data)
left = mean
right = mean + c*SEM/square
return right
def confidence_interval_theoretical(n, mean, std_dev, percentile,
number_of_tails, SEM=0):
"""
Computes confidence interval for the mean of the implicite data
covering the probability given by the variable percentile.
* n specifies the number of observations in the implicit data.
* mean specifies the mean of the implicit data.
* std_dev specifies the standard deviation of the implicit data.
* precentile gives the probability that the mean of the implicit
data is in the confidence interval
* number_of_tails gives the number of tails of the normal distribution
to be considered.
* SEM gives the estimated standard error of means, it should be used
only if tails == 1.
"""
square = math.pow(n, 0.5)
dist = distributions.NormalDistribution(0, 1)
if number_of_tails == 2:
alfa = (1-percentile)/2
c = distributions.find_percentile(1-alfa, dist.cdf)
left = mean - c*std_dev/square
right = mean + c*std_dev/square
return left, right
elif number_of_tails == 1:
alfa = percentile
c = distributions.find_percentile(alfa, dist.cdf)
right = mean + c*SEM/square
return right
def test_results(self):
normal_dist = distributions.NormalDistribution(0, 1)
t_dist = distributions.t_Distribution(7)
result_norm = distributions.find_percentile(0.95, normal_dist.cdf)
with self.assertRaises(distributions.PercentileError):
distributions.find_percentile(1.2, normal_dist.cdf)
cdf = distributions.NormalDistribution.normal_cdf
result_with_args = distributions.find_percentile(0.8, cdf, (2, 5))
self.assertTrue(1.644 < result_norm and result_norm < 1.645)
def kolmogorov_smirnov_test(data, distribution, percentile):
"""
Computes the Kolmogorov-Smirnov test. This test evaluates
whether the data presented comes from the distribution
given. percentile specifies the desired porbability. The
null hypothesis is that the data is from the given distribution.
-
For more information:
http://en.wikipedia.org/wiki/Kolmogorov%E2%80%93Smirnov_test#
Kolmogorov.E2.80.93Smirnov_statistic
-
"""
if percentile >= 1 or percentile <= 0:
raise PercentileError()
data = sorted(data)
F = distribution.cdf
E = distributions.empirical_cdf
K = distributions.KolmogorovDistribution.kolmogorov_cdf
potential_statistic_list = []
for element in data:
potential_statistic_list.append(abs(E(element, data)-F(element)))
Kolmogorov_Smirnov_statistic = max(potential_statistic_list)
q = math.pow(len(data), 0.5)
critical = distributions.find_percentile(percentile, K)
if math.pow(len(data), 0.5)*Kolmogorov_Smirnov_statistic > critical:
return False
else:
return True
def decision(self, percentile):
critical = distributions.find_percentile(
percentile, distributions.FisherDistribution.f_cdf,
[self.DFtreat, self.DFres])
if self.F > critical:
return "Reject null hypothesis."
else:
return "Accept null hyphothesis."
