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Chapter17_Parametric_non_tests.html
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Chapter17_Parametric_non_tests.html
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<!DOCTYPE html>
<html>
<head><meta charset="utf-8" />
<title>Chapter17_Parametric_non_tests</title>
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<p>Setting up a fancy stylesheet</p>
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<div class=" highlight hl-ipython3"><pre><span class="kn">from</span> <span class="nn">IPython.core.display</span> <span class="k">import</span> <span class="n">HTML</span>
<span class="n">css_file</span> <span class="o">=</span> <span class="s">'style.css'</span>
<span class="n">HTML</span><span class="p">(</span><span class="nb">open</span><span class="p">(</span><span class="n">css_file</span><span class="p">,</span> <span class="s">'r'</span><span class="p">)</span><span class="o">.</span><span class="n">read</span><span class="p">())</span>
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<p>Setting up the required python ™ environment</p>
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<div class=" highlight hl-ipython3"><pre><span class="kn">import</span> <span class="nn">numpy</span> <span class="k">as</span> <span class="nn">np</span>
<span class="c">#import pandas as pd</span>
<span class="kn">from</span> <span class="nn">scipy</span> <span class="k">import</span> <span class="n">stats</span>
<span class="c">#from scipy.stats import bayes_mvs</span>
<span class="c">#from math import factorial</span>
<span class="c">#import scikits.bootstrap as bs</span>
<span class="kn">import</span> <span class="nn">matplotlib.pyplot</span> <span class="k">as</span> <span class="nn">plt</span>
<span class="kn">import</span> <span class="nn">seaborn</span> <span class="k">as</span> <span class="nn">sns</span>
<span class="kn">from</span> <span class="nn">warnings</span> <span class="k">import</span> <span class="n">filterwarnings</span>
<span class="o">%</span><span class="k">matplotlib</span> inline
<span class="n">sns</span><span class="o">.</span><span class="n">set_style</span><span class="p">(</span><span class="s">'dark'</span><span class="p">)</span>
<span class="n">sns</span><span class="o">.</span><span class="n">set_context</span><span class="p">(</span><span class="s">'paper'</span><span class="p">,</span> <span class="n">font_scale</span> <span class="o">=</span> <span class="mf">2.0</span><span class="p">,</span> <span class="n">rc</span> <span class="o">=</span> <span class="p">{</span><span class="s">'lines.linewidth'</span><span class="p">:</span> <span class="mf">1.5</span><span class="p">,</span> <span class="s">'figure.figsize'</span> <span class="p">:</span> <span class="p">(</span><span class="mi">10</span><span class="p">,</span> <span class="mi">8</span><span class="p">)})</span>
<span class="n">filterwarnings</span><span class="p">(</span><span class="s">'ignore'</span><span class="p">)</span>
<span class="n">np</span><span class="o">.</span><span class="n">random</span><span class="o">.</span><span class="n">seed</span><span class="p">(</span><span class="mi">123</span><span class="p">)</span>
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<h1 id="Parametric-vs-non-parametric-statistical-tests">Parametric vs non-parametric statistical tests<a class="anchor-link" href="#Parametric-vs-non-parametric-statistical-tests">¶</a></h1>
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<h2 id="Introduction">Introduction<a class="anchor-link" href="#Introduction">¶</a></h2>
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<p>Before, I mentioned that a histogram of the mean of all possible means will be normally distributed. Actually things are a bit more complicated than that. No surprise! In the grander scheme of things, there are two types of statistical tests, called parametric and non-parametric tests. These two groups exist, because using the appropriate type of test for an appropriate setting allows for more accurate anlaysis and a more proper representation of what we are trying to achieve (infering statistics on population parameters).</p>
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<h2 id="The-QQ-plot">The QQ plot<a class="anchor-link" href="#The-QQ-plot">¶</a></h2>
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<p>A parametric test is used when the sample data is taken from a normal distribution and a non-parametric test if it is not. Wow! We only have our sample data. How can we know this? Well, there's the probability plot from the *scipy.stats* library. It is more commonly known as the QQ-plot. It plots every data point against its quartile on a Cartesian plane. It then gives you a visual representation of how correlated these are. If they are not, the data is not from a normal distribution and you have to use a non-parametric test.</p>
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<p>First, I'll generate 40 random values from the normal distribution, and constrain it to a mean of 100 and a standand deviation of 20.</p>
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<div class=" highlight hl-ipython3"><pre><span class="n">rv1_values</span> <span class="o">=</span> <span class="n">stats</span><span class="o">.</span><span class="n">norm</span><span class="o">.</span><span class="n">rvs</span><span class="p">(</span><span class="n">loc</span> <span class="o">=</span> <span class="mi">100</span><span class="p">,</span> <span class="n">scale</span> <span class="o">=</span> <span class="mi">20</span><span class="p">,</span> <span class="n">size</span> <span class="o">=</span> <span class="mi">40</span><span class="p">)</span>
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<p>Now let's do the QQ plot</p>
<p>The *stats.probplot()* function takes three arguments. The first is the acutal data values, the second teels the software to compare our values to normal distribution. If I wanted to see if my valuyes fit some other distribution I could have used something other than 'norm' and lastly we plot.</p>
<p>The plot will state a R<sup>2</sup> value. A value of 1.0 means an absolute fit and 0.0 means no fit (i.e. realy, really not from a normal distribution.</p>
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<div class=" highlight hl-ipython3"><pre><span class="n">plt</span><span class="o">.</span><span class="n">figure</span><span class="p">(</span><span class="n">figsize</span> <span class="o">=</span> <span class="p">(</span><span class="mi">10</span><span class="p">,</span><span class="mi">8</span><span class="p">))</span>
<span class="n">stats</span><span class="o">.</span><span class="n">probplot</span><span class="p">(</span><span class="n">rv1_values</span><span class="p">,</span> <span class="n">dist</span><span class="o">=</span><span class="s">"norm"</span><span class="p">,</span> <span class="n">plot</span><span class="o">=</span><span class="n">plt</span><span class="p">)</span> <span class="c"># </span>
<span class="n">plt</span><span class="o">.</span><span class="n">show</span><span class="p">();</span>
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<p>Now I'll generate 40 values from anotehr type of continuous random distribution called the exponential distribution and see how it compares.</p>
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<div class=" highlight hl-ipython3"><pre><span class="n">rv2_values</span> <span class="o">=</span> <span class="n">stats</span><span class="o">.</span><span class="n">expon</span><span class="o">.</span><span class="n">rvs</span><span class="p">(</span><span class="n">size</span> <span class="o">=</span> <span class="mi">40</span><span class="p">)</span>
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<div class=" highlight hl-ipython3"><pre><span class="n">stats</span><span class="o">.</span><span class="n">probplot</span><span class="p">(</span><span class="n">rv2_values</span><span class="p">,</span> <span class="n">dist</span><span class="o">=</span><span class="s">"norm"</span><span class="p">,</span> <span class="n">plot</span><span class="o">=</span><span class="n">plt</span><span class="p">);</span>
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