estebanz01 / ruby-statistics Goto Github PK

We need to do this urgent, because the descriptive_statistics gem is using a formula to calculate variance not for samples but for populations, which is not accurate for statistical tests and distribution calculations.

It's causing #13

This is the simplest example that seems to trigger the hanging behaviour. If the BigDecimal is cast to a float then it works as expected:

require 'statistics'

expected = [BigDecimal(0.2, 1)]
observed = [3.3]

chi_squared = Statistics::StatisticalTest::ChiSquaredTest
stats = chi_squared.goodness_of_fit(0.05, expected, observed)
# Observe that the process hangs at this point.

due to rush, I was only able to add two discrete distribution. The idea is to have more common discrete elements like the negative binomial or the geometric distribution.

Excuse me but I would like to know if there is a function for the Standard Deviation. I was looking into the wiki and did not find it.

Thank you in advance.

The idea is to implement the KS test where we pass a sample and a distribution object, to validate if it belongs or not.

Something like this:

distribution = Distribution::StandardNormal.new
samples = distribution.random(elements: 1_000, seed: 100)
# This should return null hypothesis as true,
# so we assume that the sample belongs to the specified distribution.
StatisticalTest::KSTest.one_group(samples: samples, distribution: distribution)

Implement a way to generate a random sampling using any written distribution.

Implement the spearman's rank correlation test and the Kolmogorov–Smirnov test to complete a proper list of non-parametric test.

This is a task extracted from #7.

ChiSquaredTest#goodness_of_fit gives an error with some distributions. The shortest code I could reproduce the error is as follows:

irb(main):001:0> require 'statistics'
=> true
irb(main):002:0> StatisticalTest::ChiSquaredTest.goodness_of_fit(0.01, 477, [481, 483, 482, 488, 478, 471, 477, 479, 475, 462])
        9: from /usr/bin/irb:23:in `<main>'
        8: from /usr/bin/irb:23:in `load'
        7: from /usr/lib/ruby/gems/2.7.0/gems/irb-1.2.1/exe/irb:11:in `<top (required)>'
        6: from (irb):2
        5: from /var/lib/gems/2.7.0/gems/ruby-statistics-3.0.0/lib/statistics/statistical_test/chi_squared_test.rb:28:in `goodness_of_fit'
        4: from /var/lib/gems/2.7.0/gems/ruby-statistics-3.0.0/lib/statistics/distribution/chi_squared.rb:14:in `cumulative_function'
        3: from /var/lib/gems/2.7.0/gems/ruby-statistics-3.0.0/lib/math.rb:49:in `lower_incomplete_gamma_function'
        2: from /var/lib/gems/2.7.0/gems/ruby-statistics-3.0.0/lib/math.rb:27:in `simpson_rule'
        1: from /var/lib/gems/2.7.0/gems/ruby-statistics-3.0.0/lib/math.rb:27:in `/'
ZeroDivisionError (divided by 0)

Perhaps a problem lies in lib/math.rb:49. It looks to cause a zero division if x < 0.5.

Thank you in advance.

Some two sided tests are reporting wrong p-values, hence wrong hypotesis evaluation results. According to https://support.minitab.com/en-us/minitab/18/help-and-how-to/statistics/basic-statistics/supporting-topics/basics/manually-calculate-a-p-value/ we should calculate the p-value with the following rules:

1. if test is assuming a lower tail, p-value = CDF(t_score). We show this calculation as probability.
2. if test is assuming a greater tail, p-value = 1 - CDF(t_score). We show this calculation as p_value for one_tail tests.
3. if test is assuming a two sided test, p-value = 2 * ( 1 - CDF( |t_score| ). We dont calculate the CDF of the absolute value of the t_score. We use the normal t_score. This is yielding weird results reported in the p_value field.

Is there a way to add skewness and kurtosis parameters to a Weibull number generator?

https://github.com/estebanz01/ruby-statistics/blob/master/lib/statistics/distribution/weibull.rb

I work with the following two test contingency tables (observed1, observed2) with these resulting variables:

observed1 = [[388,51692],[119,45633]]
expected1 = [[269.8969662278191, 51810.10303377218], [237.10303377218088, 45514.89696622782]]
chi_score1 = 111.0839904758887
df1 = 1

observed2 = [[388,51692],[119,45633],[271,40040]]
expected2 = [[293.3065012342283, 51786.69349876577], [257.66818441759625, 45494.3318155824], [227.02531434817544, 40083.974685651825]]
chi_score2 = 114.36002831520479
df2 = 2

When calculated with Python, I get the following results when extracting the pvalue (replace observed with observed1 or observed2):

import scipy.stats as stats
# include above variables here
X2 = stats.chi2_contingency(observed, correction=False)[0]

# observed1 => pvalue = 5.671618200219206e-26
# observed2 => pvalue = 1.469045936431957e-25

When using Distribution::ChiSquared.cumulative_function from the ruby-statistics package, I get the following results (replace dfwith df1or df2, chi_score likewise):

probability = 1.0 - Statistics::Distribution::ChiSquared.new(df).cumulative_function(chi_score)
p_value = 1.0 - probability

# observed1 => p_value = Infinity
# observed2 => p_value = 1.0000333200206515

While I cannot confirm the Python module yields the correct values, it seems more plausible, considering that the p-value should be in the range [0..1]?

It would be easy and better if you can extend this libraries to Crystal programming language to get free performance boost and lower memory consumption.

Add a couple of significance tests, so we can have a pretty robust and interesting statistics gem :)

• Chi-squared goodness fit test.
• Paired-T tests.
• Wilcoxon rank-sum test.
• [ ] Spearman's rank correlation (optional, but desired). (Extracted to #17)

Update wiki with the expected documentation per distribution.

While trying to implement the confidence intervals for the Student's T test, I found out that we are calculating the degrees of freedom for one sample to be wrong: https://github.com/estebanz01/ruby-statistics/blob/master/lib/statistics/statistical_test/t_test.rb#L24.

Per this thread: https://www.reddit.com/r/ruby/comments/76vse9/rubystatistics_a_gem_for_statistical_methods_and/

It's important to have a match between the gem name and the global namespace defined. I tried to move it, but It broke all my specs and the paths didn't load as desired.

I found while building the paired t-test that the p-values (1 - P(x <= X)) calculated using the Student's T distribution are behind of the expected value. A couple of test shows a difference of two decimal values from the expected one:

• In https://www.statsdirect.com/help/parametric_methods/paired_t.htm we have p-value of 0.0006 and 0.0012 but the gem returns p-values of 0.0004 and 0.0008.
• In http://www.unm.edu/~marcusj/Paired2Sample.pdf we have a p-value of 0.026 and I got a p-value of 0.024.

I traced this back to the way how ruby handles the decimal points. The calculated ones by minitab or R are different than the ones calculated by Ruby itself.

I'm logging this as a bug, but it's not related to the code itself (😅). I'm logging it for future references.

• Implement the F-Test for two samples (Implemented as ANOVA F Score).
• Implement the One way ANOVA for more than two samples.

I have a Rails app that I have just upgraded to Ruby 2.7.4 which appears to install ruby-statistics as a dependency. In this application, I have a model/namespace class Distribution. When running bundle exec rails console # or server this gem loads prior to the definition of this class and creates an alias in the main app namespace Distribution here:

This causes the app to fail to load with naming conflicts. Removing this line allows my app to load properly.

sample1 = [1.0, 2.0, 3.0]
sample2 = [2.0, 3.0, 4.0]
StatisticalTest::TTest.paired_test(alpha = 0.05, :one_tail, sample1, sample2)

=> TypeError: nil can't be coerced into Fixnum

sample1 = [1.0, 2.0, 3.0, 4.0]
sample2 = [2.0, 3.0, 4.0, 3.0]
StatisticalTest::TTest.paired_test(alpha = 0.05, :one_tail, sample1, sample2)

=> {:probability=>0.1955011094781139, :p_value=>0.8044988905218862, :alpha=>0.05, :null=>true, :alternative=>false, :confidence_level=>0.95}

It seems like the lowest sample size that can be used is 3. Is this intentional or am I missing something?