stats.ipynb

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   "source": [
    "This notebook is part of my [Python data science curriculum](http://www.terran.us/articles/python_curriculum.html)"
   ]
  },
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   "source": [
    "import numpy as np\n",
    "import pandas as pd\n",
    "import scipy.stats as stats\n",
    "\n",
    "import statsmodels.api as sm\n",
    "import statsmodels.formula.api as smf\n",
    "import statsmodels.stats.power as power\n",
    "import statsmodels.stats.proportion as proportion\n",
    "\n",
    "import altair as alt\n",
    "alt.renderers.enable('notebook')\n",
    "\n",
    "tips=pd.read_csv('/usr/lib/python3/dist-packages/pandas/tests/data/tips.csv')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Distributions\n",
    "\n",
    "https://docs.scipy.org/doc/scipy/reference/tutorial/stats.html"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "All the distributions are of the form `stats.{name}`\n",
    "\n",
    "Common parameters are:\n",
    "- `loc` (mean) \n",
    "- `scale` (sd)\n",
    "\n",
    "Common functions are:\n",
    "- `stats`, `mean`, `var`: distributional properties\n",
    "- `rvs`: Random values (R's r*)\n",
    "- `pdf`: Probability distribution function (R's d*) for continuous distributions\n",
    "- `pmf`: Probability mass function (R's m*) for discrete distributions\n",
    "- `cdf`: Cumulative distribution function (R's p*)\n",
    "- `ppf`: Percent Point Function (R's q*), inverse of the cdf  Note: _not actually a percent_, goes from 0 to 1.\n",
    "- `sf`: Survival Function, 1-cdf, (R's lower.tail=F)\n",
    "- `isf`: Inverse Survival Function (cdf:ppf :: sf:isf)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Descriptive Statistics"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(array(0.), array(1.02564103), array(0.), array(0.07894737))"
      ]
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     "execution_count": 2,
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   ],
   "source": [
    "# Mean, Variance, Skew, Kurtosis (which you can see is excess kurtosis)\n",
    "stats.t.stats(df=80,moments='mvsk')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "AttributeError(\"'norm_gen' object has no attribute 'skew'\",)\n"
     ]
    }
   ],
   "source": [
    "# There's also mean() and var(), but you can't get skew() with a separate function of that name\n",
    "[stats.norm.mean(), stats.norm.var()]\n",
    "try:\n",
    "    stats.norm.skew()\n",
    "except Exception as ex:\n",
    "    print(repr(ex))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Random Draws"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 1.28677558, -0.0720748 , -1.04294764,  0.87754612, -0.00220538,\n",
       "       -1.1727566 ,  1.03985863, -0.16205662,  1.41696977, -0.95579242])"
      ]
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     "execution_count": 4,
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   ],
   "source": [
    "stats.norm.rvs(size=10)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Density"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
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"
     },
     "metadata": {
      "jupyter-vega": "#149ffc5d-0616-42c7-bebf-344ad9cb29ea"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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"
     },
     "metadata": {
      "jupyter-vega": "#149ffc5d-0616-42c7-bebf-344ad9cb29ea"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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"
     },
     "metadata": {
      "jupyter-vega": "#149ffc5d-0616-42c7-bebf-344ad9cb29ea"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "x=np.arange(-3,3,.1)\n",
    "y=stats.norm.pdf(x)\n",
    "\n",
    "y2=stats.t.pdf(x,df=3)\n",
    "alt.Chart(pd.DataFrame({'x':x,'y':y,'dist':'normal'})).mark_line().encode(x='x',y='y',color='dist') + \\\n",
    "  alt.Chart(pd.DataFrame({'x':x,'y':y2, 'dist':'t'})).mark_line().encode(x='x',y='y',color='dist')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "If you want a noncentral t distribution, note that it's a separate distribution in Python, `nct`;\n",
    "it's _not_ a parameter to the t distribution like in R."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "'df, nc'"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# You can see what parameters are available with .shapes:\n",
    "stats.nct.shapes"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Cumulative Distributions"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0.0249979, 0.9750021])"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "stats.norm.cdf([-1.96,1.96])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([-1.95996398,  1.95996398])"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# The inverse of the cdf is the Percent Point Function (actually 0 to 1, not a percent)\n",
    "stats.norm.ppf([0.025,0.975])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/javascript": [
       "var spec = {\"config\": {\"view\": {\"width\": 400, \"height\": 300}}, \"layer\": [{\"data\": {\"name\": \"data-fa2d0018fa2b27324b3ee8f41da708b5\"}, \"mark\": \"line\", \"encoding\": {\"color\": {\"type\": \"nominal\", \"field\": \"func\"}, \"x\": {\"type\": \"quantitative\", \"field\": \"x\"}, \"y\": {\"type\": \"quantitative\", \"field\": \"y\"}}}, {\"data\": {\"name\": \"data-e39a807ada98edd35c2b3e786112ef14\"}, \"mark\": \"line\", \"encoding\": {\"color\": {\"type\": \"nominal\", \"field\": \"func\"}, \"x\": {\"type\": \"quantitative\", \"field\": \"x\"}, \"y\": {\"type\": \"quantitative\", \"field\": \"y\"}}}], \"$schema\": \"https://vega.github.io/schema/vega-lite/v2.6.0.json\", \"datasets\": {\"data-fa2d0018fa2b27324b3ee8f41da708b5\": [{\"x\": -3.0, \"y\": 0.0013498980316300933, \"func\": \"cdf\"}, {\"x\": -2.9, \"y\": 0.0018658133003840375, \"func\": \"cdf\"}, {\"x\": -2.8, \"y\": 0.002555130330427932, \"func\": \"cdf\"}, {\"x\": -2.6999999999999997, \"y\": 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       "var opt = {};\n",
       "var type = \"vega-lite\";\n",
       "var id = \"46f46b83-ad7f-4a65-ac37-3cdf899c1a4b\";\n",
       "\n",
       "var output_area = this;\n",
       "\n",
       "require([\"nbextensions/jupyter-vega/index\"], function(vega) {\n",
       "  var target = document.createElement(\"div\");\n",
       "  target.id = id;\n",
       "  target.className = \"vega-embed\";\n",
       "\n",
       "  var style = document.createElement(\"style\");\n",
       "  style.textContent = [\n",
       "    \".vega-embed .error p {\",\n",
       "    \"  color: firebrick;\",\n",
       "    \"  font-size: 14px;\",\n",
       "    \"}\",\n",
       "  ].join(\"\\\\n\");\n",
       "\n",
       "  // element is a jQuery wrapped DOM element inside the output area\n",
       "  // see http://ipython.readthedocs.io/en/stable/api/generated/\\\n",
       "  // IPython.display.html#IPython.display.Javascript.__init__\n",
       "  element[0].appendChild(target);\n",
       "  element[0].appendChild(style);\n",
       "\n",
       "  vega.render(\"#\" + id, spec, type, opt, output_area);\n",
       "}, function (err) {\n",
       "  if (err.requireType !== \"scripterror\") {\n",
       "    throw(err);\n",
       "  }\n",
       "});\n"
      ],
      "text/plain": [
       "<vega.vegalite.VegaLite at 0x7efed8619f98>"
      ]
     },
     "metadata": {
      "jupyter-vega": "#46f46b83-ad7f-4a65-ac37-3cdf899c1a4b"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": []
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
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"
     },
     "metadata": {
      "jupyter-vega": "#46f46b83-ad7f-4a65-ac37-3cdf899c1a4b"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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"
     },
     "metadata": {
      "jupyter-vega": "#46f46b83-ad7f-4a65-ac37-3cdf899c1a4b"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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"
     },
     "metadata": {
      "jupyter-vega": "#46f46b83-ad7f-4a65-ac37-3cdf899c1a4b"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# The other tail is accessed as a separate function, sf()\n",
    "x=np.arange(-3,3,.1)\n",
    "alt.Chart(pd.DataFrame({'x':x,'y':stats.norm.cdf(x),'func':'cdf'})).mark_line().encode(x='x',y='y',color='func') + \\\n",
    "alt.Chart(pd.DataFrame({'x':x,'y':stats.norm.sf(x),'func':'sf'})).mark_line().encode(x='x',y='y',color='func')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Discrete Distributions\n",
    "\n",
    "In Python, discrete distributions have some differently named functions (pmf instead of pdf), but the cumulative functions are the same."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "'n, p'"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "stats.binom.shapes"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0.0625, 0.25  , 0.375 , 0.25  , 0.0625])"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "stats.binom.pmf(np.arange(0,5), 4,.5)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0.0625, 0.3125, 0.6875, 0.9375, 1.    ])"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "stats.binom.cdf(np.arange(0,5), 4,.5)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0., 1., 2., 3., 4.])"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "stats.binom.ppf([0.0625,0.3125,0.6875,0.9375,1], 4, .5)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([1., 1., 2.])"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "stats.binom.ppf([0.3124,0.3125,0.3126], 4, .5)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([3., 2., 2.])"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# the other tail of the ppf is called the isf (inverse survival function)\n",
    "stats.binom.isf([0.3124,0.3125,0.3126], 4, .5)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Continuous Variable Tests\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Single Sample T-Test\n",
    "\n",
    "The primary function here is `stats.ttest_1samp`.  Only a two-sided test is available; there is no one-sided option (you're expected to check the side and divide the p-value by 2 manually).\n",
    "\n",
    "https://docs.scipy.org/doc/scipy/reference/tutorial/stats.html#t-test-and-ks-test"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Ttest_1sampResult(statistic=-0.37559294451919506, pvalue=0.7075471935626723)"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Is the average bill statistically different from $20?\n",
    "stats.ttest_1samp(tips.total_bill, popmean=20)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Two-Sample T-Test\n",
    "\n",
    "`stats.ttest_ind` (the \"ind\" is for \"independent\").  The only significant parameter is `equal_var` - if true, use pooled variance.  Unlike R, the default is _True_.\n",
    "\n",
    "https://docs.scipy.org/doc/scipy/reference/tutorial/stats.html#comparing-two-samples"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Ttest_indResult(statistic=-1.1432770167349968, pvalue=0.2542456188927583)"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Do men and women tip differently?\n",
    "tips2 = tips.assign(tip_pct=tips.tip/tips.total_bill)\n",
    "stats.ttest_ind(tips2[tips2.sex=='Male'].tip_pct,\n",
    "                tips2[tips2.sex=='Female'].tip_pct, equal_var=False)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Continuous Power Tests\n",
    "\n",
    "http://www.statsmodels.org/stable/stats.html#power-and-sample-size-calculations\n",
    "\n",
    "Parameters to `tt_ind_solve_power` are:\n",
    "- effect_size\n",
    "- nobs1\n",
    "- alpha (significance level)\n",
    "- power\n",
    "- ratio (nobs2/nobs1), default 1\n",
    "\n",
    "You must specify None for exactly one of the parameters, and it solves for that one.\n",
    "\n",
    "This is very similar to R, except that instead of giving a delta and sd, you need to divide delta by sd and get the effect size yourself.  More conveniently than in R, you can have different values for n, and specify the _ratio_ between them, which is exactly what you want most of the time."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "26.98920499749065"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "power.tt_ind_solve_power(effect_size=1, nobs1=None, ratio=1, alpha=0.05, power=0.95)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.5620066386966457"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "power.tt_ind_solve_power(effect_size=1, nobs1=10, ratio=1, alpha=0.05, power=None)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "There is also an analogous `zt_ind_solve_power`, using the z instead of t distribution."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## ANOVA"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "ANOVA requires a fitted linear regression object, so it will be covered with statsmodels instead of here."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Discrete Variable Tests"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Single Sample Proportion Tests \n",
    "\n",
    "The Python implementation `proportions_ztest` offers a Z-test instead of R's $X^2$.  There is little or no practical difference in most situations.  The return values are:\n",
    "- z statistic\n",
    "- p value\n",
    "\n",
    "https://www.statsmodels.org/dev/generated/statsmodels.stats.proportion.proportions_ztest.html"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(4.6779276972624935, 2.8978868440605785e-06)"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "proportion.proportions_ztest(sum(tips.sex=='Male'), tips.shape[0], value=0.5)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "There is also `binom_test`, which is exactly analogous to R's `binom.test`.  These use the binomial distribution instead of an approximation."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.08240747932752653"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "stats.binom_test(50,120)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Two Sample Proportion Tests"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead tr th {\n",
       "        text-align: left;\n",
       "    }\n",
       "\n",
       "    .dataframe thead tr:last-of-type th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr>\n",
       "      <th></th>\n",
       "      <th colspan=\"2\" halign=\"left\">sex</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th></th>\n",
       "      <th>total</th>\n",
       "      <th>male</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>smoker</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>No</th>\n",
       "      <td>151</td>\n",
       "      <td>97</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Yes</th>\n",
       "      <td>93</td>\n",
       "      <td>60</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "         sex     \n",
       "       total male\n",
       "smoker           \n",
       "No       151   97\n",
       "Yes       93   60"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "t=tips.groupby('smoker').aggregate({'sex':[('total','size'), ('male',lambda x: sum(x=='Male'))]})\n",
    "t"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(-0.04398657223093955, 0.9649151073157316)"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "proportion.proportions_ztest(t.sex.male,t.sex.total)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Chi-squared ($X^2$) tests\n",
    "\n",
    "Remember that with a $X^2$ test, instead of a count of successes and totals, you use a count of successes and failures.\n",
    "\n",
    "The return values from `chi2_contingency` are:\n",
    "- chi^2 statistic\n",
    "- p-value\n",
    "- degrees of freedom\n",
    "- expected values (array)\n",
    "\n",
    "https://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.chi2_contingency.html"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th>smoker</th>\n",
       "      <th>No</th>\n",
       "      <th>Yes</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>sex</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>Female</th>\n",
       "      <td>54</td>\n",
       "      <td>33</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Male</th>\n",
       "      <td>97</td>\n",
       "      <td>60</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "smoker  No  Yes\n",
       "sex            \n",
       "Female  54   33\n",
       "Male    97   60"
      ]
     },
     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "t = tips.groupby(['sex','smoker']).size().unstack()\n",
    "t"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(0.001934818536627623, 0.964915107315732, 1, array([[53.84016393, 33.15983607],\n",
       "        [97.15983607, 59.84016393]]))"
      ]
     },
     "execution_count": 25,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# This is _surprisingly_ close to exactly independent:\n",
    "stats.chi2_contingency(t,correction=False)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Note that the implementation of the correction is not the same in Python as in R, so results will not match with correction."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(10.277251918677742,\n",
       " 0.0013468039268008766,\n",
       " 1,\n",
       " array([[ 62.75409836,  24.24590164],\n",
       "        [113.24590164,  43.75409836]]))"
      ]
     },
     "execution_count": 26,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# This may be more interesting:\n",
    "stats.chi2_contingency(\n",
    "    tips.groupby(['sex','time']).size().unstack(), correction=False)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(13.22200137240661,\n",
       " 0.004180302092822257,\n",
       " 3,\n",
       " array([[ 6.77459016, 31.0204918 , 27.09836066, 22.10655738],\n",
       "        [12.22540984, 55.9795082 , 48.90163934, 39.89344262]]))"
      ]
     },
     "execution_count": 27,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Of course we can also do more than 2x2 this way\n",
    "stats.chi2_contingency(\n",
    "    tips.groupby(['sex','day']).size().unstack(), correction=False)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Discrete Power Tests"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "There are functions available in statsmodels, not in scipy.  You'll need to compute your effect size yourself as a preprocessing step, like in R's pwr() library.\n",
    "\n",
    "http://www.statsmodels.org/stable/generated/statsmodels.stats.proportion.proportion_effectsize.html  \n",
    "http://www.statsmodels.org/stable/generated/statsmodels.stats.power.NormalIndPower.html"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "-0.2837941092083278"
      ]
     },
     "execution_count": 28,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# This is Cohen's standard -2*asin(sqrt(p)) effect size:\n",
    "es=proportion.proportion_effectsize(0.1,0.2)\n",
    "es"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "322.6931930526659"
      ]
     },
     "execution_count": 29,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "power.NormalIndPower().solve_power(es,power=0.95, alpha=0.05)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Don't be fooled by the functions called \"tost\".  That's actually the Two One Sided T-test function, which is a somewhat esoteric tool used for inverting the definition of null hypothesis and _rejecting_ the idea that two samples are _different_.  I just look at confidence intervals for that; I've never used the tost."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Quantile-Quantile Plots\n",
    "\n",
    "There's no convenient qqplot in Altair, so we'll use the one from matplotlib."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 576x576 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "%matplotlib inline\n",
    "plt.rcParams[\"figure.figsize\"] = [8,8]\n",
    "stats.probplot(stats.norm().rvs(25),plot=plt)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.6.5"
  },
  "toc": {
   "base_numbering": 1,
   "nav_menu": {},
   "number_sections": true,
   "sideBar": true,
   "skip_h1_title": false,
   "title_cell": "Table of Contents",
   "title_sidebar": "Contents",
   "toc_cell": false,
   "toc_position": {
    "height": "calc(100% - 180px)",
    "left": "10px",
    "top": "150px",
    "width": "215px"
   },
   "toc_section_display": true,
   "toc_window_display": true
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}