Module: Statsample::Test::T

Extended by:
Math
Defined in:
lib/statsample/test/t.rb

Defined Under Namespace

Classes: OneSample, TwoSamplesIndependent

Class Method Summary collapse

Class Method Details

.df_equal_variance(n1, n2) ⇒ Object

Degrees of freedom for equal variance



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# File 'lib/statsample/test/t.rb', line 35

def df_equal_variance(n1,n2)
  n1+n2-2
end

.df_not_equal_variance(s1, s2, n1, n2) ⇒ Object

Degrees of freedom for unequal variance

  • s1: sample 1 standard deviation

  • s2: sample 2 standard deviation

  • n1: sample 1 size

  • n2: sample 2 size

Reference



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# File 'lib/statsample/test/t.rb', line 45

def df_not_equal_variance(s1,s2,n1,n2)
  s2_1=s1**2
  s2_2=s2**2
  num=(s2_1.quo(n1)+s2_2.quo(n2))**2
  den=(s2_1.quo(n1)**2).quo(n1-1) + (s2_2.quo(n2)**2).quo(n2-1)
  num.quo(den)
end

.one_sample(x, u, s, n) ⇒ Object

Test the null hypothesis that the population mean is equal to a specified value u, one uses the statistic. Is the same formula used on t-test for paired sample.

  • x: sample/differences mean

  • u: population mean

  • s: sample/differences standard deviation

  • n: sample size



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# File 'lib/statsample/test/t.rb', line 12

def one_sample(x,u,s,n)
  (x-u).quo(s.quo(Math::sqrt(n)))
end

.two_sample_independent(x1, x2, s1, s2, n1, n2, equal_variance = false) ⇒ Object

Test if means of two samples are different.

  • x1: sample 1 mean

  • x2: sample 2 mean

  • s1: sample 1 standard deviation

  • s2: sample 2 standard deviation

  • n1: sample 1 size

  • n2: sample 2 size

  • equal_variance: true if equal_variance assumed



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# File 'lib/statsample/test/t.rb', line 24

def two_sample_independent(x1, x2, s1, s2, n1, n2, equal_variance = false)
  num=x1-x2
  if equal_variance
    sx1x2 = sqrt(((n1-1)*s1**2 + (n2-1)*s2**2).quo(n1+n2-2))
    den   = sx1x2*sqrt(1.quo(n1)+1.quo(n2))
  else
    den=sqrt((s1**2).quo(n1) + (s2**2).quo(n2))
  end
  num.quo(den)
end