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% Document Info
\author{sasha2411 (sasha2411)}
\pdfinfo{
  /Title (hypothesis-testing-with-scipy.pdf)
  /Creator (Cheatography)
  /Author (sasha2411 (sasha2411))
  /Subject (Hypothesis testing with Scipy Cheat Sheet)
}

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\noindent
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    {\parbox{\dimexpr\textwidth-2\fboxsep\relax}{\noindent
        \hspace*{-6pt}\includegraphics[width=5.8cm]{/web/www.cheatography.com/public/images/cheatography_logo.pdf}}
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    \vspace{-2pt}\large{\bf{\textcolor{DarkBackground}{\textrm{Hypothesis testing with Scipy Cheat Sheet}}}} \\
    \normalsize{by \textcolor{DarkBackground}{sasha2411 (sasha2411)} via \textcolor{DarkBackground}{\uline{cheatography.com/65860/cs/16458/}}}
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  \mymulticolumn{2}{p{5.377cm}}{\bf\textcolor{white}{Cheatographer}}  \\
  \vspace{-2pt}sasha2411 (sasha2411) \\
  \uline{cheatography.com/sasha2411} \\
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  \mymulticolumn{1}{p{5.377cm}}{\bf\textcolor{white}{Cheat Sheet}}  \\
   \vspace{-2pt}Published 26th July, 2018.\\
   Updated 26th July, 2018.\\
   Page {\thepage} of \pageref{LastPage}.
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  %\includegraphics[width=48px,height=48px]{dave.jpeg}
  Measure your website readability!\\
  www.readability-score.com
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\begin{document}
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\begin{multicols*}{2}

\begin{tabularx}{8.4cm}{X}
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\mymulticolumn{1}{x{8.4cm}}{\bf\textcolor{white}{1 Sample T-Testing}}  \tn
\SetRowColor{white}
\mymulticolumn{1}{x{8.4cm}}{For {\bf{numerical}} data.  \newline % Row Count 1 (+ 1)
Compares a sample mean to a hypothetical population mean.  \newline % Row Count 3 (+ 2)
{\bf{from scipy.stats import ttest\_1samp}} \newline % Row Count 4 (+ 1)
{\emph{ttest\_1samp}} requires two inputs, a distribution of values and an expected mean. \newline % Row Count 6 (+ 2)
{\bf{tstat, pval = \seqsplit{ttest\_1samp(example\_distribution}, expected\_mean)}}% Row Count 8 (+ 2)
} \tn 
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\end{tabularx}
\par\addvspace{1.3em}

\begin{tabularx}{8.4cm}{X}
\SetRowColor{DarkBackground}
\mymulticolumn{1}{x{8.4cm}}{\bf\textcolor{white}{2 Sample T-Test}}  \tn
\SetRowColor{white}
\mymulticolumn{1}{x{8.4cm}}{For {\bf{numerical}} data. \newline % Row Count 1 (+ 1)
Compares two sets of data, which are both approximately normally distributed. \newline % Row Count 3 (+ 2)
The {\emph{null hypothesis}}, in this case, is that the two distributions have the same mean. \newline % Row Count 5 (+ 2)
{\bf{from scipy.stats import ttest\_ind}} \newline % Row Count 6 (+ 1)
It takes the two distributions as inputs and returns the t-statistic and a p-value. \newline % Row Count 8 (+ 2)
{\bf{t, pval = ttest\_ind(dataset1, dataset2)}}% Row Count 9 (+ 1)
} \tn 
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\par\addvspace{1.3em}

\begin{tabularx}{8.4cm}{X}
\SetRowColor{DarkBackground}
\mymulticolumn{1}{x{8.4cm}}{\bf\textcolor{white}{ANOVA}}  \tn
\SetRowColor{white}
\mymulticolumn{1}{x{8.4cm}}{For {\bf{numerical}} data. \newline % Row Count 1 (+ 1)
Compares more than two numerical datasets.  \newline % Row Count 2 (+ 1)
ANOVA (Analysis of Variance) tests the null hypothesis that all of the datasets have the same mean. \newline % Row Count 4 (+ 2)
{\bf{from scipy.stats import f\_oneway}} \newline % Row Count 5 (+ 1)
It takes in each dataset as a different input and returns the t-statistic and the p-value. \newline % Row Count 7 (+ 2)
{\bf{t, pval = f\_oneway(a, b, c)}}% Row Count 8 (+ 1)
} \tn 
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\begin{tabularx}{8.4cm}{X}
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\mymulticolumn{1}{x{8.4cm}}{\bf\textcolor{white}{Tukey's Range Test}}  \tn
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\mymulticolumn{1}{x{8.4cm}}{For {\bf{numerical}} data. \newline % Row Count 1 (+ 1)
We can perform a {\bf{Tukey's Range Test}} to determine the difference between datasets. \newline % Row Count 3 (+ 2)
{\bf{from \seqsplit{statsmodels.stats.multicomp} import pairwise\_tukeyhsd}} \newline % Row Count 5 (+ 2)
We have to provide the function with one {\emph{list of all of the data}} and a {\emph{list of labels}} that tell the function which elements of the list are from which set. We also provide the {\emph{significance level}} we want, which is usually 0.05. \newline % Row Count 10 (+ 5)
{\bf{values = np.concatenate({[}a, b, c{]})}} \newline % Row Count 11 (+ 1)
{\bf{labels = {[}'a'{]} * len(a) + {[}'b'{]} * len(b) + {[}'c'{]} * len(c)}} \newline % Row Count 13 (+ 2)
{\bf{tukey\_results = \seqsplit{pairwise\_tukeyhsd(values}, labels, 0.05)}}% Row Count 15 (+ 2)
} \tn 
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\end{tabularx}
\par\addvspace{1.3em}

\begin{tabularx}{8.4cm}{X}
\SetRowColor{DarkBackground}
\mymulticolumn{1}{x{8.4cm}}{\bf\textcolor{white}{Binomial Test}}  \tn
\SetRowColor{white}
\mymulticolumn{1}{x{8.4cm}}{For {\bf{categorical}} data. \newline % Row Count 1 (+ 1)
To analyze a dataset with two different possibilities for entries. \newline % Row Count 3 (+ 2)
The {\bf{null hypothesis}}, in this case, would be that there is no difference between the observed behavior and the expected behavior.  \newline % Row Count 6 (+ 3)
{\bf{from scipy.stats import binom\_test}} \newline % Row Count 7 (+ 1)
{\emph{binom\_test}} requires three inputs, the number of observed successes, the number of total trials, and an expected probability of success.  \newline % Row Count 10 (+ 3)
{\bf{pval = binom\_test(525, n=1000, p=0.5)}}% Row Count 11 (+ 1)
} \tn 
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\begin{tabularx}{8.4cm}{X}
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\mymulticolumn{1}{x{8.4cm}}{\bf\textcolor{white}{Chi Square Test}}  \tn
\SetRowColor{white}
\mymulticolumn{1}{x{8.4cm}}{For {\bf{categorical}} data. \newline % Row Count 1 (+ 1)
To compare two or more categorical datasets. \newline % Row Count 2 (+ 1)
{\bf{from scipy.stats import chi2\_contingency}} \newline % Row Count 3 (+ 1)
The input to chi2\_contingency is a {\bf{contingency table}} where: \newline % Row Count 5 (+ 2)
 - {\bf{The columns}} represent different outcomes, like "Survey Response A" vs. "Survey Response B" or "Clicked a Link" vs. "Didn't Click" \newline % Row Count 8 (+ 3)
- {\bf{The rows}} are each a different condition, such as men vs. women or Interface A vs. Interface B \newline % Row Count 10 (+ 2)
X = {[}{[}30, 10{]}, \newline % Row Count 11 (+ 1)
     {[}35, 5{]}, \newline % Row Count 12 (+ 1)
     {[}28, 12{]}, \newline % Row Count 13 (+ 1)
     {[}20, 20{]}{]} \newline % Row Count 14 (+ 1)
{\bf{\_, pval, \_, \_ = chi2\_contingency(X)}}% Row Count 15 (+ 1)
} \tn 
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\par\addvspace{1.3em}


% That's all folks
\end{multicols*}

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