Class: Perfer::Statistics

Inherits:
Object
  • Object
show all
Includes:
Math
Defined in:
lib/perfer/statistics.rb

Constant Summary collapse

CONFIDENCE_LEVEL = 
0.95
ALPHA =

significance level

1.0 - CONFIDENCE_LEVEL
T_QUANTILES =

Student’s t quantiles is used as n is small (= number of measurements) Indexed by: probability, degrees of freedom

{
  0.975 => [
    nil,
    12.71, 4.303, 3.182, 2.776, 2.571, 2.447, 2.365, 2.306, 2.262, 2.228, #  1-10
    2.201, 2.179, 2.160, 2.145, 2.131, 2.120, 2.110, 2.101, 2.093, 2.086, # 11-20
    2.080, 2.074, 2.069, 2.064, 2.060, 2.056, 2.052, 2.048, 2.045, 2.042, # 21-30
    2.040, 2.037, 2.035, 2.032, 2.030, 2.028, 2.026, 2.024, 2.023, 2.021  # 31-40
  ]
}

Class Method Summary collapse

Instance Method Summary collapse

Constructor Details

#initialize(sample) ⇒ Statistics

Returns a new instance of Statistics.



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# File 'lib/perfer/statistics.rb', line 33

def initialize(sample)
  @sample = sample
end

Class Method Details

.t_quantile(p, degrees_of_freedom) ⇒ Object 



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# File 'lib/perfer/statistics.rb', line 23

def self.t_quantile(p, degrees_of_freedom)
  if degrees_of_freedom <= 40
    T_QUANTILES[p][degrees_of_freedom]
  elsif degrees_of_freedom <= 100
    T_QUANTILES[p][degrees_of_freedom.round(-1)]
  else
    1.960
  end
end

Instance Method Details

#coefficient_of_variation ⇒ Object 



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# File 'lib/perfer/statistics.rb', line 68

def coefficient_of_variation
  standard_deviation / mean
end

#margin_of_error ⇒ Object

Assumes a standard normal distribution This is half the width of the confidence interval for the mean



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# File 'lib/perfer/statistics.rb', line 86

def margin_of_error
  Statistics.t_quantile(1.0 - ALPHA/2, size-1) * standard_error
end

#maximum_absolute_deviation ⇒ Object 



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# File 'lib/perfer/statistics.rb', line 90

def maximum_absolute_deviation
  @sample.map { |v| (v - mean).abs }.max
end

#mean ⇒ Object 



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# File 'lib/perfer/statistics.rb', line 41

def mean
  @mean ||= @sample.inject(0.0) { |sum, i| sum + i } / size
end

#mean_absolute_deviation ⇒ Object 



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# File 'lib/perfer/statistics.rb', line 76

def mean_absolute_deviation
  @sample.inject(0.0) { |dev, i| dev + (i - mean).abs } / size
end

#median ⇒ Object 



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# File 'lib/perfer/statistics.rb', line 45

def median
  @median ||= begin
    sorted = @sample.sort
    if size.odd?
      sorted[size/2]
    else
      (sorted[size/2-1] + sorted[size/2]) / 2.0
    end
  end
end

#median_absolute_deviation ⇒ Object 



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# File 'lib/perfer/statistics.rb', line 80

def median_absolute_deviation
  Statistics.new(@sample.map { |i| (i - median).abs }).median
end

#size ⇒ Object 



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# File 'lib/perfer/statistics.rb', line 37

def size
  @sample.size
end

#standard_deviation ⇒ Object 



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# File 'lib/perfer/statistics.rb', line 64

def standard_deviation
  sqrt(variance)
end

#standard_error ⇒ Object 



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# File 'lib/perfer/statistics.rb', line 72

def standard_error
  standard_deviation / sqrt(size)
end

#variance ⇒ Object 



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# File 'lib/perfer/statistics.rb', line 56

def variance
  mean = mean()
  @sample.inject(0.0) { |var, i|
    d = i - mean
    var + d*d
  } / (size - 1) # unbiased sample variance
end