t_test.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import pandas as pd\n",
    "from matplotlib import pyplot as plt\n",
    "import seaborn as sns"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Problem Statement: \n",
    "\n",
    "For an orange juice company,\n",
    "the marketing team claimed that their new marketing strategy resulted in an increase of sales. \n",
    "\n",
    "Determine if this is actually true.\n",
    "\n",
    "Data:\n",
    "\n",
    "January:\n",
    "\n",
    "Average Daily Sales = \\$10,000, sample size = 31, variance = 10,000,000\n",
    "\n",
    "February:\n",
    "\n",
    "Average Daily Sales = \\$12,000, sample size = 28, variance = 20,000,000\n",
    "\n",
    "How do we know that the increase in daily orange juice sales was not due to random variation in data?"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Null and Alternative Hypothesis"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The amount of sales per day is not consistent throughout the month. \n",
    "\n",
    "The January data has a variance of 10,000,000 and a standard deviation of ~3162. \n",
    "\n",
    "\n",
    "\n",
    "On bad days, we would sell \\$8,000, of orange juice. On good days, we would sell $14,000 of orange juice. \n",
    "\n",
    "We have to prove that the increase in average daily sales in February did not occur purely by chance."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "H0: Null Hypothesis: No change in sales\n",
    "    \n",
    "H1: Alternate Hypothesis: Jan < Feb : Sales Increased\n",
    "\n",
    "Possible Alternate Hypothesis:\n",
    "    \n",
    "1. Jan < Feb : Sales Increased\n",
    "\n",
    "2. Jan > Feb : Sales Decreased\n",
    "\n",
    "3. Jan Sales not equal to Feb Sales : Sales Changed \n",
    "\n",
    "\n",
    "In our case, the marketing department claimed that the sales has increased. So we would use the first alternative hypothesis."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "NO ERROR: Null Hypothesis is Correct, Retain H0\n",
    "    \n",
    "Type II error, false negative: Alt Hypothesis(Sales Increased) is Correct, but Retain H0\n",
    "    \n",
    "Type I error, false positive: Null Hypothesis is Correct, but Retain H1\n",
    "\n",
    "NO ERROR: Alt Hypothesis is Correct, Retain H1\n",
    "\n",
    "\n",
    "Hypothesis testing uses the logic, The null hypothesis is True unless proved otherwise using data.\n",
    "\n",
    "We use data as evidence to determine if the claims made against the null hypothesis is true.\n",
    "\n",
    "--\n",
    "\n",
    "\n",
    "p-value or Significance Level:\n",
    "\n",
    "In order to come to a decision, we need to know if the February data is statistically significant.\n",
    "\n",
    "We would have to calculate the probability of finding the observed, or more extreme data assuming that the null hypothesis, $H_0$ is true. This probability is known as the p-value.\n",
    "\n",
    "If this probability is high, we would retain the null hypothesis. If this probability is low, we would reject the null hypothesis. \n",
    "\n",
    "This probability threshold known as the significance level, or $\\alpha$. Many statisticians typically use $\\alpha$ = 0.05."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Lets perform t test for facebook posts dataset"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "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></th>\n",
       "      <th>Page total likes</th>\n",
       "      <th>Type</th>\n",
       "      <th>Category</th>\n",
       "      <th>Post Month</th>\n",
       "      <th>Post Weekday</th>\n",
       "      <th>Post Hour</th>\n",
       "      <th>Paid</th>\n",
       "      <th>Lifetime Post Total Reach</th>\n",
       "      <th>Lifetime Post Total Impressions</th>\n",
       "      <th>Lifetime Engaged Users</th>\n",
       "      <th>Lifetime Post Consumers</th>\n",
       "      <th>Lifetime Post Consumptions</th>\n",
       "      <th>Lifetime Post Impressions by people who have liked your Page</th>\n",
       "      <th>Lifetime Post reach by people who like your Page</th>\n",
       "      <th>Lifetime People who have liked your Page and engaged with your post</th>\n",
       "      <th>comment</th>\n",
       "      <th>like</th>\n",
       "      <th>share</th>\n",
       "      <th>Total Interactions</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>139441</td>\n",
       "      <td>Photo</td>\n",
       "      <td>2</td>\n",
       "      <td>12</td>\n",
       "      <td>4</td>\n",
       "      <td>3</td>\n",
       "      <td>0.0</td>\n",
       "      <td>2752</td>\n",
       "      <td>5091</td>\n",
       "      <td>178</td>\n",
       "      <td>109</td>\n",
       "      <td>159</td>\n",
       "      <td>3078</td>\n",
       "      <td>1640</td>\n",
       "      <td>119</td>\n",
       "      <td>4</td>\n",
       "      <td>79.0</td>\n",
       "      <td>17.0</td>\n",
       "      <td>100</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>139441</td>\n",
       "      <td>Status</td>\n",
       "      <td>2</td>\n",
       "      <td>12</td>\n",
       "      <td>3</td>\n",
       "      <td>10</td>\n",
       "      <td>0.0</td>\n",
       "      <td>10460</td>\n",
       "      <td>19057</td>\n",
       "      <td>1457</td>\n",
       "      <td>1361</td>\n",
       "      <td>1674</td>\n",
       "      <td>11710</td>\n",
       "      <td>6112</td>\n",
       "      <td>1108</td>\n",
       "      <td>5</td>\n",
       "      <td>130.0</td>\n",
       "      <td>29.0</td>\n",
       "      <td>164</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>139441</td>\n",
       "      <td>Photo</td>\n",
       "      <td>3</td>\n",
       "      <td>12</td>\n",
       "      <td>3</td>\n",
       "      <td>3</td>\n",
       "      <td>0.0</td>\n",
       "      <td>2413</td>\n",
       "      <td>4373</td>\n",
       "      <td>177</td>\n",
       "      <td>113</td>\n",
       "      <td>154</td>\n",
       "      <td>2812</td>\n",
       "      <td>1503</td>\n",
       "      <td>132</td>\n",
       "      <td>0</td>\n",
       "      <td>66.0</td>\n",
       "      <td>14.0</td>\n",
       "      <td>80</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>139441</td>\n",
       "      <td>Photo</td>\n",
       "      <td>2</td>\n",
       "      <td>12</td>\n",
       "      <td>2</td>\n",
       "      <td>10</td>\n",
       "      <td>1.0</td>\n",
       "      <td>50128</td>\n",
       "      <td>87991</td>\n",
       "      <td>2211</td>\n",
       "      <td>790</td>\n",
       "      <td>1119</td>\n",
       "      <td>61027</td>\n",
       "      <td>32048</td>\n",
       "      <td>1386</td>\n",
       "      <td>58</td>\n",
       "      <td>1572.0</td>\n",
       "      <td>147.0</td>\n",
       "      <td>1777</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>139441</td>\n",
       "      <td>Photo</td>\n",
       "      <td>2</td>\n",
       "      <td>12</td>\n",
       "      <td>2</td>\n",
       "      <td>3</td>\n",
       "      <td>0.0</td>\n",
       "      <td>7244</td>\n",
       "      <td>13594</td>\n",
       "      <td>671</td>\n",
       "      <td>410</td>\n",
       "      <td>580</td>\n",
       "      <td>6228</td>\n",
       "      <td>3200</td>\n",
       "      <td>396</td>\n",
       "      <td>19</td>\n",
       "      <td>325.0</td>\n",
       "      <td>49.0</td>\n",
       "      <td>393</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   Page total likes    Type  Category  Post Month  Post Weekday  Post Hour  \\\n",
       "0            139441   Photo         2          12             4          3   \n",
       "1            139441  Status         2          12             3         10   \n",
       "2            139441   Photo         3          12             3          3   \n",
       "3            139441   Photo         2          12             2         10   \n",
       "4            139441   Photo         2          12             2          3   \n",
       "\n",
       "   Paid  Lifetime Post Total Reach  Lifetime Post Total Impressions  \\\n",
       "0   0.0                       2752                             5091   \n",
       "1   0.0                      10460                            19057   \n",
       "2   0.0                       2413                             4373   \n",
       "3   1.0                      50128                            87991   \n",
       "4   0.0                       7244                            13594   \n",
       "\n",
       "   Lifetime Engaged Users  Lifetime Post Consumers  \\\n",
       "0                     178                      109   \n",
       "1                    1457                     1361   \n",
       "2                     177                      113   \n",
       "3                    2211                      790   \n",
       "4                     671                      410   \n",
       "\n",
       "   Lifetime Post Consumptions  \\\n",
       "0                         159   \n",
       "1                        1674   \n",
       "2                         154   \n",
       "3                        1119   \n",
       "4                         580   \n",
       "\n",
       "   Lifetime Post Impressions by people who have liked your Page  \\\n",
       "0                                               3078              \n",
       "1                                              11710              \n",
       "2                                               2812              \n",
       "3                                              61027              \n",
       "4                                               6228              \n",
       "\n",
       "   Lifetime Post reach by people who like your Page  \\\n",
       "0                                              1640   \n",
       "1                                              6112   \n",
       "2                                              1503   \n",
       "3                                             32048   \n",
       "4                                              3200   \n",
       "\n",
       "   Lifetime People who have liked your Page and engaged with your post  \\\n",
       "0                                                119                     \n",
       "1                                               1108                     \n",
       "2                                                132                     \n",
       "3                                               1386                     \n",
       "4                                                396                     \n",
       "\n",
       "   comment    like  share  Total Interactions  \n",
       "0        4    79.0   17.0                 100  \n",
       "1        5   130.0   29.0                 164  \n",
       "2        0    66.0   14.0                  80  \n",
       "3       58  1572.0  147.0                1777  \n",
       "4       19   325.0   49.0                 393  "
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import pandas as pd\n",
    "data = pd.read_csv('facebook_dataset.csv', delimiter=';')\n",
    "data.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x216 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "sample_size: 359\n",
      "sample_mean: 155.84679665738162\n",
      "sample_variance: 48403.23623970993\n"
     ]
    }
   ],
   "source": [
    "unpaid_likes = data[data['Paid']==0]['like']\n",
    "unpaid_likes = unpaid_likes.dropna()\n",
    "sns.set(font_scale=1.65)\n",
    "fig = plt.figure(figsize=(10,3))\n",
    "ax=unpaid_likes.hist(range=(0, 1500),bins=30)\n",
    "ax.set_xlim(0,1500)\n",
    "\n",
    "plt.xlabel('Likes (Paid)')\n",
    "plt.ylabel('Frequency')\n",
    "plt.show()\n",
    "\n",
    "print('sample_size: {}'.format(unpaid_likes.shape[0]))\n",
    "print('sample_mean: {}'.format(unpaid_likes.mean()))\n",
    "print('sample_variance: {}'.format(unpaid_likes.var()))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x216 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "sample_size: 139\n",
      "sample_mean: 235.6474820143885\n",
      "sample_variance: 247175.07048274425\n"
     ]
    }
   ],
   "source": [
    "paid_likes = data[data['Paid']==1]['like']\n",
    "\n",
    "fig = plt.figure(figsize=(10,3))\n",
    "ax=paid_likes.hist(range=(0, 1500),bins=30)\n",
    "ax.set_xlim(0,1500)\n",
    "\n",
    "plt.xlabel('Likes (Unpaid)')\n",
    "plt.ylabel('Frequency')\n",
    "plt.show()\n",
    "\n",
    "print('sample_size: {}'.format(paid_likes.shape[0]))\n",
    "print('sample_mean: {}'.format(paid_likes.mean()))\n",
    "print('sample_variance: {}'.format(paid_likes.var()))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x216 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Calculate confidence interval\n",
    "paid_err = 1.96 * (paid_likes.std() / np.sqrt(paid_likes.shape[0]))\n",
    "unpaid_err = 1.96 * (unpaid_likes.std() / np.sqrt(unpaid_likes.shape[0]))\n",
    "\n",
    "x = ['Paid Posts', 'Unpaid Posts']\n",
    "y = [paid_likes.mean(), unpaid_likes.mean()]\n",
    "fig = plt.figure(figsize=(6, 3))\n",
    "ax = sns.barplot(x=x, y=y, yerr=[paid_err, unpaid_err])\n",
    "ax.set_ylim(0, 400)\n",
    "plt.ylabel('Likes')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "t-value: 1.824490721115131\n"
     ]
    }
   ],
   "source": [
    "paid_var_ratio = paid_likes.var()/paid_likes.shape[0]\n",
    "unpaid_var_ratio = unpaid_likes.var()/unpaid_likes.shape[0]\n",
    "\n",
    "s_welch = np.sqrt(paid_var_ratio + unpaid_var_ratio)\n",
    "\n",
    "t = (paid_likes.mean() - unpaid_likes.mean())/s_welch\n",
    "\n",
    "print('t-value: {}'.format(t))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "degrees of freedom: 159.3668015083367\n"
     ]
    }
   ],
   "source": [
    "df_num = (paid_var_ratio + unpaid_var_ratio)**2\n",
    "df_dem = paid_var_ratio**2/(paid_likes.shape[0]-1) + unpaid_var_ratio**2/(unpaid_likes.shape[0]-1)\n",
    "dof = df_num/df_dem\n",
    "print('degrees of freedom: {}'.format(dof))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Ttest_indResult(statistic=1.824490721115131, pvalue=0.06995072279510872)"
      ]
     },
     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from scipy import stats\n",
    "\n",
    "t_score = stats.ttest_ind_from_stats(paid_likes.mean(), paid_likes.std(), paid_likes.shape[0], \\\n",
    "                               unpaid_likes.mean(), unpaid_likes.std(), unpaid_likes.shape[0], \\\n",
    "                               equal_var=False)\n",
    "t_score"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "From the Welch's t-test we ended up with a two-tailed p-value of ~0.07, or ~0.035 for a one-tail test. We will reject the null hypothesis, and accept that Facebook advertisements does have a positive effect on the number \"likes\" on a post."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "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",
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