20220409_understanding_clt_and_ttest_part6.ipynb

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    "def plot_histograms_sample_mean_diff(m, n_min, n_max, \n",
    "                                     n_step, df, variable):\n",
    "    \"\"\"\n",
    "    Plot \"(n_max-n_min)/n_step\" histograms for the \n",
    "    difference between the means of 2 random samples of\n",
    "    different sizes. On top of histogram will also \n",
    "    plot the corresponding distribution curve.\n",
    "    \n",
    "    Parameters\n",
    "    ----------\n",
    "    m: int\n",
    "        Number of samples to take.\n",
    "    m_min: int\n",
    "        Minimun sample 1 size\n",
    "    n_max: int\n",
    "        Maximum sample 1 size\n",
    "    n_step: int\n",
    "        Difference between sample sizes\n",
    "    df: pandas dataframe\n",
    "        Dataframe where each column is a dataset\n",
    "    variable: str\n",
    "         Pandas dataframe column (in our example can be one \n",
    "         of following: 'normal', 'uniform', 'binomial')\n",
    "    \"\"\"\n",
    "    \n",
    "    diff_mean_dict = {}\n",
    "    std_sample1_dict = {}\n",
    "    std_sample2_dict = {}\n",
    "    \n",
    "    params_dict =  {\n",
    "        \"mean\": df[variable].mean(),\n",
    "        \"std\": df[variable].std(),\n",
    "        \"median\": df[variable].median(),\n",
    "    }\n",
    "\n",
    "    for n in range(n_min, n_max, n_step):\n",
    "        for x in range(m):\n",
    "            #We are going to generate the difference between the \n",
    "            #mean of 2 samples. First sample with size = n, \n",
    "            #second sample with size round(n/4)\n",
    "            \n",
    "            n1 = n\n",
    "            n2 = round(n/4)\n",
    "            df_sample_1 = df.sample(n=n1)[variable]\n",
    "            df_sample_2 = df.sample(n=n2)[variable]\n",
    "            if (n in diff_mean_dict.keys()):\n",
    "                diff_mean_dict[n].append(df_sample_1.mean()-df_sample_2.mean())\n",
    "                std_sample1_dict[n].append(df_sample_1.std())\n",
    "                std_sample2_dict[n].append(df_sample_2.std())\n",
    "            else:\n",
    "                diff_mean_dict[n] = [df_sample_1.mean() - df_sample_2.mean()]\n",
    "                std_sample1_dict[n] = [df_sample_1.std()]\n",
    "                std_sample2_dict[n] = [df_sample_2.std()]\n",
    "\n",
    "        df_diff_means = pd.DataFrame.from_dict(diff_mean_dict)\n",
    "        df_sample1_std = pd.DataFrame.from_dict(std_sample1_dict)\n",
    "        df_sample2_std = pd.DataFrame.from_dict(std_sample2_dict)\n",
    "\n",
    "    fig, ax = plt.subplots(1, \n",
    "                           int(np.ceil((n_max-n_min)/n_step)), \n",
    "                           sharex='col', \n",
    "                           sharey='row', \n",
    "                           figsize=(20, 3))\n",
    "    \n",
    "    fig.suptitle(f\"\"\"Histograms for {m} (difference between 2 samples) mean:\n",
    "                sample_1 size between {n_min} and {n_max}\n",
    "                sample_2 size between {round(n_min/4)} and {round(n_max/4)}\n",
    "                for variable with {variable} distribution\"\"\", \n",
    "                 fontsize=16, \n",
    "                 y = 1.45)\n",
    "\n",
    "    for i in range(len(df_diff_means.columns)):\n",
    "        df_diff_means.hist(column=df_diff_means.columns[i], \n",
    "                           ax=ax[i], \n",
    "                           alpha=0.5, \n",
    "                           color='red', \n",
    "                           bins = 30)\n",
    "        ax[i].set_xlim((-1.5*params_dict['std'],\n",
    "                        1.5*params_dict['std']))\n",
    "        ax[i].tick_params(axis='both', which='major', labelsize=12)\n",
    "        ax[i].set_title(f\"n1 = {df_diff_means.columns[i]} \\n n2 = {round(df_diff_means.columns[i]/4)}\",\n",
    "                       fontsize=16)\n",
    "        \n",
    "        #Here we compute the standard error for this kind of test\n",
    "        n1 = df_sample1_std.columns[i]\n",
    "        n2 = round(n1/4)\n",
    "        s1 = df_sample1_std[df_sample1_std.columns[i]].mean()   \n",
    "        s2 = df_sample2_std[df_sample2_std.columns[i]].mean()\n",
    "        sp = np.sqrt(((n1-1)*s1**2 + (n2-1)*s2**2)/(n1+n2-2))\n",
    "        std_error = sp*np.sqrt((1/n1) + (1/n2))\n",
    "        \n",
    "        #Here we plot the distribution curve\n",
    "        x = np.linspace(-6*params_dict['std'], \n",
    "                        6*params_dict['std'], \n",
    "                        1000)\n",
    "        y_normcurve_2 = norm.pdf(x, 0, std_error)\n",
    "        ax[i].plot(x, y_normcurve_2, 'b--', linewidth=2)\n",
    "\n",
    "#Here we exetute the following example:\n",
    "plot_histograms_sample_mean_diff(300, 10, 100, 20, df, 'normal')"
   ]
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