class Statsample::Test::T::TwoSamplesIndependent

Two Sample t-test.

Usage¶ ↑

a=1000.times.map {rand(100)}.to_scale
b=1000.times.map {rand(100)}.to_scale
t_2=Statsample::Test::T::TwoSamplesIndependent.new(a,b)
t_2.summary

Output¶ ↑

= Two Sample T Test
Mean and standard deviation
+----------+---------+---------+------+
| Variable |    m    |   sd    |  n   |
+----------+---------+---------+------+
| 1        | 49.3310 | 29.3042 | 1000 |
| 2        | 47.8180 | 28.8640 | 1000 |
+----------+---------+---------+------+

== Levene Test
 Levene Test
 F: 0.3596
 p: 0.5488
 T statistics
 +--------------------+--------+-----------+----------------+
 |        Type        |   t    |    df     | p (both tails) |
 +--------------------+--------+-----------+----------------+
 | Equal variance     | 1.1632 | 1998      | 0.2449         |
 | Non equal variance | 1.1632 | 1997.5424 | 0.1362         |
 +--------------------+--------+-----------+----------------+

Two Sample t-test.

Usage¶ ↑

a=1000.times.map {rand(100)}.to_scale
b=1000.times.map {rand(100)}.to_scale
t_2=Statsample::Test::T::TwoSamplesIndependent.new(a,b)
t_2.summary

Output¶ ↑

= Two Sample T Test
Mean and standard deviation
+----------+---------+---------+------+
| Variable |    m    |   sd    |  n   |
+----------+---------+---------+------+
| 1        | 49.3310 | 29.3042 | 1000 |
| 2        | 47.8180 | 28.8640 | 1000 |
+----------+---------+---------+------+

== Levene Test
 Levene Test
 F: 0.3596
 p: 0.5488
 T statistics
 +--------------------+--------+-----------+----------------+
 |        Type        |   t    |    df     | p (both tails) |
 +--------------------+--------+-----------+----------------+
 | Equal variance     | 1.1632 | 1998      | 0.2449         |
 | Non equal variance | 1.1632 | 1997.5424 | 0.1362         |
 +--------------------+--------+-----------+----------------+

Attributes

df_equal_variance[R]

Degress of freedom (equal variance)

df_not_equal_variance[R]

Degress of freedom (not equal variance)

name[RW]

Name of test

opts[RW]

Options

probability_equal_variance[R]

Probability(equal variance)

probability_not_equal_variance[R]

Probability(unequal variance)

t_equal_variance[R]

Value of t for equal_variance

t_not_equal_variance[R]

Value of t for non-equal_variance

tails[RW]

Tails for probability (:both, :left or :right)

Public Class Methods

new(v1, v2, opts=Hash.new) click to toggle source

Create a Two Independent T Test Options:

:name = Name of the analysis
:tails = Tail for probability. Could be :both, :left, :right

# File lib/statsample/test/t.rb, line 258
def initialize(v1, v2, opts=Hash.new)
  @v1=v1
  @v2=v2
  default={:u=>0, :name=>"Two Sample T Test",  :tails=>:both}
  @opts=default.merge(opts)
  @name=@opts[:name]
  @tails=@opts[:tails]          
end

Public Instance Methods

compute() click to toggle source

Set t and probability for given u

# File lib/statsample/test/t.rb, line 268
def compute
  @t_equal_variance= T.two_sample_independent(@v1.mean, @v2.mean, @v1.sd, @v2.sd, @v1.n_valid, @v2.n_valid,true)
  
  @t_not_equal_variance= T.two_sample_independent(@v1.mean, @v2.mean, @v1.sd, @v2.sd, @v1.n_valid, @v2.n_valid, false)

  @df_equal_variance=T.df_equal_variance(@v1.n_valid, @v2.n_valid)
  @df_not_equal_variance=T.df_not_equal_variance(@v1.sd, @v2.sd, @v1.n_valid, @v2.n_valid)
  
  @probability_equal_variance = p_using_cdf(Distribution::T.cdf(@t_equal_variance, @df_equal_variance), tails)
  
  @probability_not_equal_variance = p_using_cdf(Distribution::T.cdf(@t_not_equal_variance, @df_not_equal_variance), tails)

end

d() click to toggle source

Cohen's d is a measure of effect size. Its defined as the difference between two means divided by a standard deviation for the data

# File lib/statsample/test/t.rb, line 282
def d
  n1=@v1.n_valid
  n2=@v2.n_valid
  num=@v1.mean-@v2.mean
  den=Math::sqrt( ((n1-1)*@v1.sd+(n2-1)*@v2.sd).quo(n1+n2))
  num.quo(den)
end