12a_AB-Test_Between-Subjects-Experiments.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "## A/B Tests or Between Subjects Experiements\n",
    " # will review statistical modeling, power analysis, effect size, measurement, etc.\n",
    "\n",
    "# Company is rebranding, executives have selected three logos that they like.\n",
    " # These were tested on sample of 100 customers, each completing a survey about a radomly selected logo.\n",
    " # Participants rated their impression of the logo on several deminsions \"friendly\", \"inviting\", \"interesting\", \n",
    " #    \"positive\", \"plesant\" on a scale from 1-10 (1= does not describe logo; 10= describes logo perfectly).\n",
    "  # Will combine al positive adjectives into single 'positive sentiment' scale & will compare logos on that.\n",
    "\n",
    "# Import/load packages to be used\n",
    "\n",
    "import pandas as pd\n",
    "import numpy as np\n",
    "import scipy.stats as ss\n",
    "import statsmodels.stats.weightstats as ws\n",
    "from statsmodels.stats.power import tt_ind_solve_power\n",
    "from statsmodels.stats.multicomp import pairwise_tukeyhsd\n",
    "import matplotlib.pyplot as plt\n",
    "import seaborn as sns\n",
    "\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Index(['id', 'friendly', 'inviting', 'interesting', 'positive', 'pleasant',\n",
       "       'sex', 'logo'],\n",
       "      dtype='object')"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Import dataset to be used as Pandas data frame\n",
    "\n",
    "data = pd.read_csv(\"datasets/logos.csv\")\n",
    "\n",
    "# Explore the names\n",
    "data.columns"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Index(['id', 'friendly', 'inviting', 'interesting', 'positive', 'pleasant',\n",
       "       'sex', 'logo'],\n",
       "      dtype='object')"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Import dataset to be used as Pandas data frame\n",
    "\n",
    "data = pd.read_csv(\"datasets/logos.csv\")\n",
    "\n",
    "# Explore the names\n",
    "data.columns"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>id</th>\n",
       "      <th>friendly</th>\n",
       "      <th>inviting</th>\n",
       "      <th>interesting</th>\n",
       "      <th>positive</th>\n",
       "      <th>pleasant</th>\n",
       "      <th>sex</th>\n",
       "      <th>logo</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>3</td>\n",
       "      <td>9</td>\n",
       "      <td>8</td>\n",
       "      <td>9</td>\n",
       "      <td>10</td>\n",
       "      <td>9</td>\n",
       "      <td>f</td>\n",
       "      <td>Logo A</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>98</td>\n",
       "      <td>7</td>\n",
       "      <td>6</td>\n",
       "      <td>8</td>\n",
       "      <td>7</td>\n",
       "      <td>7</td>\n",
       "      <td>f</td>\n",
       "      <td>Logo C</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>73</td>\n",
       "      <td>5</td>\n",
       "      <td>3</td>\n",
       "      <td>6</td>\n",
       "      <td>6</td>\n",
       "      <td>6</td>\n",
       "      <td>m</td>\n",
       "      <td>Logo C</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>89</td>\n",
       "      <td>4</td>\n",
       "      <td>5</td>\n",
       "      <td>2</td>\n",
       "      <td>3</td>\n",
       "      <td>4</td>\n",
       "      <td>f</td>\n",
       "      <td>Logo C</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>13</td>\n",
       "      <td>8</td>\n",
       "      <td>7</td>\n",
       "      <td>9</td>\n",
       "      <td>8</td>\n",
       "      <td>6</td>\n",
       "      <td>f</td>\n",
       "      <td>Logo A</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   id  friendly  inviting  interesting  positive  pleasant sex    logo\n",
       "0   3         9         8            9        10         9   f  Logo A\n",
       "1  98         7         6            8         7         7   f  Logo C\n",
       "2  73         5         3            6         6         6   m  Logo C\n",
       "3  89         4         5            2         3         4   f  Logo C\n",
       "4  13         8         7            9         8         6   f  Logo A"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Above- Looks like this is not the whole dataset, as there would have been more variables.\n",
    " # 1) ID variable representing individual participants\n",
    " # 2) Have variables representing different adjectives on which people rated the logo\n",
    " # 3) Have participant sex\n",
    " # 4) Have the logo that was rated\n",
    "\n",
    "\n",
    "# Briefly check structure of dataset\n",
    "data.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "id              int64\n",
       "friendly        int64\n",
       "inviting        int64\n",
       "interesting     int64\n",
       "positive        int64\n",
       "pleasant        int64\n",
       "sex            object\n",
       "logo           object\n",
       "dtype: object"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Above- Adjectives scored as numeric variables & logo variable scored as categorical varaible.\n",
    "\n",
    "data.dtypes"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>id</th>\n",
       "      <th>friendly</th>\n",
       "      <th>inviting</th>\n",
       "      <th>interesting</th>\n",
       "      <th>positive</th>\n",
       "      <th>pleasant</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>count</th>\n",
       "      <td>100.000000</td>\n",
       "      <td>100.000000</td>\n",
       "      <td>100.000000</td>\n",
       "      <td>100.000000</td>\n",
       "      <td>100.000000</td>\n",
       "      <td>100.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>mean</th>\n",
       "      <td>50.500000</td>\n",
       "      <td>8.050000</td>\n",
       "      <td>7.990000</td>\n",
       "      <td>7.930000</td>\n",
       "      <td>8.000000</td>\n",
       "      <td>7.890000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>std</th>\n",
       "      <td>29.011492</td>\n",
       "      <td>1.520068</td>\n",
       "      <td>1.690705</td>\n",
       "      <td>1.810491</td>\n",
       "      <td>1.797866</td>\n",
       "      <td>1.740167</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>min</th>\n",
       "      <td>1.000000</td>\n",
       "      <td>4.000000</td>\n",
       "      <td>3.000000</td>\n",
       "      <td>2.000000</td>\n",
       "      <td>3.000000</td>\n",
       "      <td>3.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>25%</th>\n",
       "      <td>25.750000</td>\n",
       "      <td>7.000000</td>\n",
       "      <td>7.000000</td>\n",
       "      <td>7.000000</td>\n",
       "      <td>7.000000</td>\n",
       "      <td>7.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>50%</th>\n",
       "      <td>50.500000</td>\n",
       "      <td>8.000000</td>\n",
       "      <td>8.000000</td>\n",
       "      <td>8.000000</td>\n",
       "      <td>8.000000</td>\n",
       "      <td>8.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>75%</th>\n",
       "      <td>75.250000</td>\n",
       "      <td>9.000000</td>\n",
       "      <td>9.000000</td>\n",
       "      <td>10.000000</td>\n",
       "      <td>10.000000</td>\n",
       "      <td>9.250000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>max</th>\n",
       "      <td>100.000000</td>\n",
       "      <td>10.000000</td>\n",
       "      <td>10.000000</td>\n",
       "      <td>10.000000</td>\n",
       "      <td>10.000000</td>\n",
       "      <td>10.000000</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "               id    friendly    inviting  interesting    positive    pleasant\n",
       "count  100.000000  100.000000  100.000000   100.000000  100.000000  100.000000\n",
       "mean    50.500000    8.050000    7.990000     7.930000    8.000000    7.890000\n",
       "std     29.011492    1.520068    1.690705     1.810491    1.797866    1.740167\n",
       "min      1.000000    4.000000    3.000000     2.000000    3.000000    3.000000\n",
       "25%     25.750000    7.000000    7.000000     7.000000    7.000000    7.000000\n",
       "50%     50.500000    8.000000    8.000000     8.000000    8.000000    8.000000\n",
       "75%     75.250000    9.000000    9.000000    10.000000   10.000000    9.250000\n",
       "max    100.000000   10.000000   10.000000    10.000000   10.000000   10.000000"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Inspect variables in dataset\n",
    "\n",
    "data.describe()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Above- All ranges are w/in 1-10\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Count</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>logo</th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>Logo A</th>\n",
       "      <td>33</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Logo B</th>\n",
       "      <td>32</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Logo C</th>\n",
       "      <td>34</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "        Count\n",
       "logo         \n",
       "Logo A     33\n",
       "Logo B     32\n",
       "Logo C     34"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#Below- Determine # of unique categorgies & # of cases for each category, for label=logo\n",
    "\n",
    "data['Count'] = 1\n",
    "data[['logo','Count']].groupby('logo').count()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "For column sex\n",
      "f    67\n",
      "m    33\n",
      "Name: sex, dtype: int64\n",
      "\n",
      "For column logo\n",
      "Logo C    34\n",
      "Logo A    33\n",
      "Logo B    32\n",
      "Name: logo, dtype: int64\n"
     ]
    }
   ],
   "source": [
    "# Above- Logo was randomly assigned to parcipants, so this is approximately evenly distributed (no class imbalance).\n",
    "    \n",
    "# Below- Compute & display frequency table for categorical variables w/pandas value_counts\n",
    "\n",
    "def count_unique(data, cols):\n",
    "    for col in cols:\n",
    "        print('\\n' + 'For column ' + col)\n",
    "        print(data[col].value_counts())\n",
    "        \n",
    "cat_cols = ['sex', 'logo']\n",
    "count_unique(data, cat_cols)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Above- Sex weight towards females, which we assume is representative of data source.\n",
    "\n",
    "# Visually looking at raw data, a missing value is shown for logo variable."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
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       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>friendly</th>\n",
       "      <th>inviting</th>\n",
       "      <th>interesting</th>\n",
       "      <th>positive</th>\n",
       "      <th>pleasant</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>friendly</th>\n",
       "      <td>1.000</td>\n",
       "      <td>0.857</td>\n",
       "      <td>0.867</td>\n",
       "      <td>0.824</td>\n",
       "      <td>0.854</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>inviting</th>\n",
       "      <td>0.857</td>\n",
       "      <td>1.000</td>\n",
       "      <td>0.663</td>\n",
       "      <td>0.698</td>\n",
       "      <td>0.758</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>interesting</th>\n",
       "      <td>0.867</td>\n",
       "      <td>0.663</td>\n",
       "      <td>1.000</td>\n",
       "      <td>0.770</td>\n",
       "      <td>0.725</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>positive</th>\n",
       "      <td>0.824</td>\n",
       "      <td>0.698</td>\n",
       "      <td>0.770</td>\n",
       "      <td>1.000</td>\n",
       "      <td>0.688</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>pleasant</th>\n",
       "      <td>0.854</td>\n",
       "      <td>0.758</td>\n",
       "      <td>0.725</td>\n",
       "      <td>0.688</td>\n",
       "      <td>1.000</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "             friendly  inviting  interesting  positive  pleasant\n",
       "friendly        1.000     0.857        0.867     0.824     0.854\n",
       "inviting        0.857     1.000        0.663     0.698     0.758\n",
       "interesting     0.867     0.663        1.000     0.770     0.725\n",
       "positive        0.824     0.698        0.770     1.000     0.688\n",
       "pleasant        0.854     0.758        0.725     0.688     1.000"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "## Score the Scale\n",
    " # Goal of creating a \"positive sentiment\" variable for these data.\n",
    " # Can eyeball correlation matrix to ensure measures correlate w/ each other.\n",
    "  # Adjectives represent column 2-6 of data table, so correlations can be shown with that subset.\n",
    "   # Double brackets after data contain list of numeric variable columns\n",
    "   # Added round(3) method to enhance readbility, rounding to two decimals\n",
    "    \n",
    "data[['friendly', 'inviting', 'interesting', 'positive', 'pleasant']].corr().round(3)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
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       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>id</th>\n",
       "      <th>friendly</th>\n",
       "      <th>inviting</th>\n",
       "      <th>interesting</th>\n",
       "      <th>positive</th>\n",
       "      <th>pleasant</th>\n",
       "      <th>sex</th>\n",
       "      <th>logo</th>\n",
       "      <th>Count</th>\n",
       "      <th>sentiment</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>3</td>\n",
       "      <td>9</td>\n",
       "      <td>8</td>\n",
       "      <td>9</td>\n",
       "      <td>10</td>\n",
       "      <td>9</td>\n",
       "      <td>f</td>\n",
       "      <td>Logo A</td>\n",
       "      <td>1</td>\n",
       "      <td>9.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>98</td>\n",
       "      <td>7</td>\n",
       "      <td>6</td>\n",
       "      <td>8</td>\n",
       "      <td>7</td>\n",
       "      <td>7</td>\n",
       "      <td>f</td>\n",
       "      <td>Logo C</td>\n",
       "      <td>1</td>\n",
       "      <td>7.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>73</td>\n",
       "      <td>5</td>\n",
       "      <td>3</td>\n",
       "      <td>6</td>\n",
       "      <td>6</td>\n",
       "      <td>6</td>\n",
       "      <td>m</td>\n",
       "      <td>Logo C</td>\n",
       "      <td>1</td>\n",
       "      <td>5.2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>89</td>\n",
       "      <td>4</td>\n",
       "      <td>5</td>\n",
       "      <td>2</td>\n",
       "      <td>3</td>\n",
       "      <td>4</td>\n",
       "      <td>f</td>\n",
       "      <td>Logo C</td>\n",
       "      <td>1</td>\n",
       "      <td>3.6</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>13</td>\n",
       "      <td>8</td>\n",
       "      <td>7</td>\n",
       "      <td>9</td>\n",
       "      <td>8</td>\n",
       "      <td>6</td>\n",
       "      <td>f</td>\n",
       "      <td>Logo A</td>\n",
       "      <td>1</td>\n",
       "      <td>7.6</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   id  friendly  inviting  interesting  positive  pleasant sex    logo  Count  \\\n",
       "0   3         9         8            9        10         9   f  Logo A      1   \n",
       "1  98         7         6            8         7         7   f  Logo C      1   \n",
       "2  73         5         3            6         6         6   m  Logo C      1   \n",
       "3  89         4         5            2         3         4   f  Logo C      1   \n",
       "4  13         8         7            9         8         6   f  Logo A      1   \n",
       "\n",
       "   sentiment  \n",
       "0        9.0  \n",
       "1        7.0  \n",
       "2        5.2  \n",
       "3        3.6  \n",
       "4        7.6  "
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Above- These ratings are all moderately-strongly correlated.\n",
    " # Assuming here that they all apear to represent \"one underlying factor\".\n",
    "    \n",
    "# Score it as a scale\n",
    " # Use Pandas apply method to apply mean function from numpy package to each row (axis = 1) to numeric columns of data frame to compute sentiment variable\n",
    "    \n",
    "data['sentiment'] = data[['friendly', 'inviting', 'interesting', 'positive', 'pleasant']].apply(np.mean, axis = 1)\n",
    "data.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Mean of Sentiment = 7.972000000000001\n",
      "STD of Sentiment = 1.5357135149499732\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "Text(0.5,0,'Sentiment')"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1abb1327198>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Above- See sentiment variable in data frame.\n",
    "\n",
    "# Check the measure\n",
    "\n",
    "## Print some summary statistics\n",
    "print('Mean of Sentiment = ' + str(np.mean(data.sentiment)))\n",
    "print('STD of Sentiment = ' + str(np.std(data.sentiment)))\n",
    "\n",
    "## Plot a histogram\n",
    "ax = plt.figure(figsize=(8, 6)).gca()   # define axis\n",
    "data.sentiment.plot.hist(ax = ax, alpha = 0.6, bins = 15)\n",
    "plt.title('Histogram of Sentiment')\n",
    "plt.xlabel('Sentiment')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "id has missing values False\n",
      "friendly has missing values False\n",
      "inviting has missing values False\n",
      "interesting has missing values False\n",
      "positive has missing values False\n",
      "pleasant has missing values False\n",
      "sex has missing values False\n",
      "logo has missing values True\n",
      "Count has missing values False\n",
      "sentiment has missing values False\n"
     ]
    }
   ],
   "source": [
    "# Above- Sentiment scores are skewe toward positive end of scale.\n",
    " # Are we measuring sentiment & not something else, such as tendency to respond positively on surveys?\n",
    "  # Adjectives seem represemtative of positive sentiment we would want to know about (i.e., content validity) &\n",
    "  #   appear good on their face (i.e., face validity).\n",
    "  # Have no evidence that this sentiment of adjectives tweaks w/ other indicators of sentiment.\n",
    "   # Thus, we are accepting on faith that these are a valid measure of sentiment.\n",
    "    \n",
    "## Dealing w/ Missing Values\n",
    " # in a Pandas data frame missing values can be coded in a number of ways, including as Numpy nan or as none, a null value.\n",
    "    \n",
    "for col in data.columns:\n",
    "    print(col + ' has missing values ' + \n",
    "          str((data[col].isnull().values.any())) or str(data[col].isna().values.any()))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(100, 10)\n",
      "(99, 10)\n",
      "\n",
      "\n",
      "id has missing values False\n",
      "friendly has missing values False\n",
      "inviting has missing values False\n",
      "interesting has missing values False\n",
      "positive has missing values False\n",
      "pleasant has missing values False\n",
      "sex has missing values False\n",
      "logo has missing values False\n",
      "Count has missing values False\n",
      "sentiment has missing values False\n"
     ]
    }
   ],
   "source": [
    "# Remove missing values using Pandas dropna method & test again to ensure all missing values were removed.\n",
    "\n",
    "print(data.shape)\n",
    "data.dropna(subset = ['logo'], inplace = True)\n",
    "print(data.shape)\n",
    "\n",
    "## Check once more\n",
    "print('\\n')\n",
    "for col in data.columns:\n",
    "    print(col + ' has missing values ' + \n",
    "          str((data[col].isnull().values.any())) or str(data[col].isna().values.any()))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.axes._subplots.AxesSubplot at 0x1abb14739b0>"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1abb13525c0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Above- One row was removed from data frame & there are no more missing values.\n",
    "\n",
    "## Visualize Data & Run Descriptives\n",
    " # Visualize relationships in data we want to test & examine descriptive statistics to test our question.\n",
    " # Since randomly assigned particpants to logos, will also be randomly distributed across the three logos.\n",
    "  # Any systematic differences percieved in variables can be attributed to logo, since that was only sytematic sifference between groups.\n",
    "\n",
    "# Compare means across group for b/w subjects design using boxplot method from Seaborn along w/ swarmplot method to see individual data points.\n",
    "\n",
    "ax = plt.figure(figsize=(8,8)).gca() # define axis\n",
    "sns.boxplot(x = 'logo', y = 'sentiment', data = data, ax = ax)\n",
    "sns.swarmplot(x = 'logo', y = 'sentiment', color = 'black', data = data, ax = ax, alpha = 0.4)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      " Mean by logo\n",
      "        sentiment\n",
      "logo             \n",
      "Logo A       8.58\n",
      "Logo B       8.44\n",
      "Logo C       7.00\n",
      "\n",
      " Standard deviation by logo\n",
      "        sentiment\n",
      "logo             \n",
      "Logo A       1.27\n",
      "Logo B       1.51\n",
      "Logo C       1.33\n"
     ]
    }
   ],
   "source": [
    "# Above- In the sample, Logo A & B appear to result in highest positive sentiment, followed by Logo C. Not clear if Logo A or B is better.\n",
    "\n",
    "# Summary statistics using Pandas groupby method to group sentiment values by logo type & compute the mean.\n",
    "\n",
    "logo_grouped = data[['logo','sentiment']].groupby('logo')\n",
    "\n",
    "print(' Mean by logo')\n",
    "print(logo_grouped.mean().round(2))\n",
    "print('\\n Standard deviation by logo')\n",
    "print(logo_grouped.std().round(2))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "DegFreedom    60.546791\n",
       "Difference     0.132008\n",
       "Statistic      0.381916\n",
       "PValue         0.703809\n",
       "Low95CI       -0.561103\n",
       "High95CI       0.825118\n",
       "dtype: float64"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Above- Logo A & B look close together & ahead of Logo C. This is in the sample only & would need inferential tests to infer real difference in the population.\n",
    "\n",
    "## Inferential Test for Two Groups\n",
    " # Conduct an independent samples t-test to compare (means of) two groups.\n",
    "  # Null Hypothesis always states that the effect is absent in the population & that the sample result is an artifact of random chance.\n",
    "   # Meaning the difference b/w the group averages is exactly zero in the population\n",
    "    # H0: muA - muB = 0 where mu is population average.\n",
    "    # Any difference observed in the sample is therefore due to random chance.\n",
    "  # T-test compares size of observed difference (xbar1 - xbar2) against the value in null hypothesis (0), divided by what is typically expected by chance.\n",
    "   # t = (result - null) / (chance)\n",
    "    # Top of fraction is key. The more the data \"disagree\" w/ null, the larger the t-value & hence more evidence for a logo effect.\n",
    "    # A large t-value tells you that the effect is considerably larger than expected by chance, evidence for a real logo effect.\n",
    "    # \"Welch\" version of test is run which does NOT make any assumptions about variances of two groups.\n",
    "     # t' = (((xbar1-xbar2)-0) / (sqrt((sigmahat1^2 / n1) + (sigmahat2^2 / n2))))\n",
    "\n",
    "# Compute t-test values of Logo A & B using two subsets of the data frame are created using loc method\n",
    "\n",
    "def t_test_two_samp(a, b, alpha, alternative='two-sided'):\n",
    "    \n",
    "    diff = a.mean() - b.mean()\n",
    "\n",
    "    res = ss.ttest_ind(a, b)\n",
    "      \n",
    "    means = ws.CompareMeans(ws.DescrStatsW(a), ws.DescrStatsW(b))\n",
    "    confint = means.tconfint_diff(alpha=alpha, alternative=alternative, usevar='unequal') \n",
    "    degfree = means.dof_satt()\n",
    "\n",
    "    index = ['DegFreedom', 'Difference', 'Statistic', 'PValue', 'Low95CI', 'High95CI']\n",
    "    return pd.Series([degfree, diff, res[0], res[1], confint[0], confint[1]], index = index)   \n",
    "   \n",
    "\n",
    "test = t_test_two_samp(data.loc[data.logo == 'Logo A', 'sentiment'], data.loc[data.logo == 'Logo B', 'sentiment'], 0.05)\n",
    "test"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "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>sentiment</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>logo</th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>Logo A</th>\n",
       "      <td>33</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Logo B</th>\n",
       "      <td>32</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Logo C</th>\n",
       "      <td>34</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "        sentiment\n",
       "logo             \n",
       "Logo A         33\n",
       "Logo B         32\n",
       "Logo C         34"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Above- t-value of 0.38 tells us that the difference is 0.38 times the size of what one would typically expect by chance.\n",
    " # p-value of 0.70, so we could get a result this big in the sample 70% of the time when the null hypothesis says that there is NO difference is true.\n",
    "  # This is not statisitcally significant (p-value must be below 0.05 or 5%)\n",
    "  # Also, confidence interval includes 0.\n",
    " # Must accept the null hypothesis that this could plausibly be due to random chance & don't have enough evidence to declare a real difference b/w Logo A & B.\n",
    "\n",
    "## Variance Assumptions\n",
    " # Another version of t-test, Student's t, which is the same but it uses a form of averaging the two sample variances:\n",
    "  # t= (result - null) / (chance) = ((xbar1 - xbar2) - 0) / (sqrt(sigmahatp^2 *(1/n1 + 1/n2)))\n",
    "  # Sigmahatp^2 is weighted average of two sample variances\n",
    "   # where sigmahatp^2 = (((n1-1)*sigmahat1^2) + ((n2-1)*sigmahat2^2)) / ((n1 - 1) + (n2 - 1))\n",
    "  # Sophisticated form of averaging sigmahat1^2 & sigmahat2^2 so that the one from the larger group has more influence over final answer.\n",
    " # This might not be best test, as it requires variances of two groups to be equal at the population level.\n",
    "  # Since never know anything about population level, can never know if this assumption is met.\n",
    "   # Can test for it, but has own complications.\n",
    "   # Recent advice,(read- Delacre, Lakens, Leys, 2017) indicates Welch's t-test is better under real-world conditions.\n",
    "\n",
    "# Logo A & B are statisically ties, have no evidence for any real difference b/w them at population level.\n",
    " # REMEMBER- When a result is not significant, it means that either:\n",
    " #  1) Null Hypothesis is true (i.e., two groups are exactly equal in population)\n",
    " #  2) Effect is smaller than we have power to detect\n",
    " # Given the sample size, it's possible that there may still be a logo effect and we simply missed it.\n",
    "  # Subject matter expertise to interpret this on a scale of 1-10 satisfaction scale,\n",
    "  #   we are confident that they are within 0.50 to 0.80 points of each other, that's not that big of a difference in my subjective opinion.\n",
    "\n",
    "# Cohen's d Effect Size Statistic\n",
    " # A 1-10 satisfaction scale has somewhat meaningful units\n",
    " # Quantifies size of difference using a standard unit (standard deviations)\n",
    "  # d = (difference) / (SD) = (xbar1 - xbar2) / (sigma) where\n",
    "  #       d Value      Meaning\n",
    "  #   1.  0 - 0.2     Negligible\n",
    "  #   2. 0.2 - 0.5       Small\n",
    "  #   3. 0.5 - 0.8      Medium\n",
    "  #   4. 0.80 +         Large\n",
    "\n",
    "# Find number os samples in each group\n",
    "logo_grouped.count()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.11189360267699688"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Small d value for difference b/w Logo A & Logo B\n",
    "\n",
    "d = (8.58 - 8.44)/(np.std(data.loc[data.logo == 'Logo A', 'sentiment']))\n",
    "d"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.07252871716498652"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Compute Power of t-test\n",
    "\n",
    "tt_ind_solve_power(effect_size=d, nobs1 = 32, alpha=0.05, power=None, ratio=1, alternative='two-sided')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.axes._subplots.AxesSubplot at 0x1abb18820b8>"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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IzBokfUISS1x5KjcxIl3yApEdPadCeqx8u7ELyo1fKBtzuawKmVTVMwLzydBYvuz2WKaoVI4Sr1c1L3Hn3D5J/0nS85K+J+lnkvKXbmdmj5nZTjPbOTQ0VOOUqFS0oUUyKxuLNS1UONFYvl1ji6IN5YfOLRJTOJ6sekZgPmlvKj903hALKRm1q2wN3wXywTbn3J865zY75+6TdE7SZefDnXNPOee2OOe2dHR01D4kKhKKxtW8/EaFonEpFFJiUbcS7d1qXn6TwslmSVK0aYGaetapYckqxVrbJTOF4w1qWXGzzPgFCWAubV7aoO7WqExSazKsD69qkhklXq8C+bSDmXU65wbNbLmkRyXdE0QOzI14W5fibV1lY5Fkkxas23LZti0rN9UqFjAvJaIh3b+2OegYqJGgPrL4DTNbJCkn6Z84584HlAMAAG8FUuLOuXuDeFwAAOoJJyQBAPAUJQ4AgKe4jA+Amurr69P4aFhf2NUSdBRgVo6PhtXY1xdoBmbiAAB4ipk4gJrq6elRJn9av7V5JOgowKx8YVeL4j09gWZgJg4AgKcocQAAPEWJAwDgKc6JA4Cnsvmi9vanNZwuaElLVOs6E5Kkg4NpnR7JqTUR1k2LE4pFQjo9nNORMxlFw6YNXQm1JsMBp8dcoMQBwFMvvzuugZGcJKnvQk7ZQmnJ0bf7Skv89imnsxMFbVqS0IuHRqe+7+SFrP76xlbFIhyM9R0lDgAeSueKUwV+0bGz2cu2GxjJKR4uX8Usk3fqH8lr+cJYVTOi+ngbBgAeioRMkUvKORkLKRkrf1mPhE1N8ctf6hOsMV4XKHEA8FAkbLqtJ6mLS4XHIqZbu5O6tTupWKQ0aCbd1pPUjYvLz4GvXBRTZ3M0iNiYYxxOBwBPretMaFlbTCPpghY1RqZm5r+0qU1nx/NqSYSnZuafuKlFZ8YLioWND7XVEUocADx2tUPoXS3lM20zU0cTL/n1hsPpAAB4ihIHAMBTlDgAAJ6ixAEA8BQlDgCApyhxAAA8RYkDAOApShwAAE9R4gAAeIrL92DWnCsqO3xGxXxO8dZ2haJxSVJu/ILyE2OKNrUpkmwKOCUwfwynCuofyak1GdbiFq6RXs8occzayLtvKzd2XpI00f+uWtdsVvbCoCYGjk1t07T8JiUWdAWUEJg/TpzP6pUjY3KTtzd0JbR5WUOgmVA987bE+/r6FJ4YVnL/s0FH8Vo2nZIGTmn6e/3i8BHlx8cUdW5qrHD2oJLdy2ofcB4IT5xVX18+6Bi4TuztT8tNu31gMK2NSxKKRTh7Wo/4V8WsuCuNOSd3yVecu9KWAOZa4dJ9zV15P0V9mLcz8Z6eHvVnIkpt+ETQUbzmnFPx0E9USI2WBkIhNa7erPD5fqXPnJzaLtazVqn2pQGlrG/J/c+qp4dTFSjZ0JnQ68fGp27f0B5XnFl43Zq3JY65YWZqW32b0uf7Sx9sa+tUJNGopoZmRRtblU+NKtq0QLHmhUFHBeaFVe1xNcVDOjWcU1syrBULY0FHQhVR4pg1C0eUvMIsO97WqXhbZwCJgPmtszmqzmY+lT4fcIwFAABPUeIAAHiKEgcAwFOUOAAAnqLEAQDwFCUOAICnKHEAADxFiQMA4ClKHAAAT1HimBPFfFaFzETZmCsWlE+Py7liQKmA+ck5p+FUQbkCS5/UOy67ilmb6D+qicHjknOKNLaq5YZblB8f1mjvXrlCXqFoXC0rNynS0Bx0VKDuDacKeunwqMYzRUXCpq0rGrWc66fXLWbimJV8elwTA8ekyeUP8+PDSg2d0NjJA3KF0hrXxVxGY6cPB5gSmD/eOjmh8Uzp6Fe+4PTj3nEViszI6xUljlkpZtOXjRVSYyrmMuVjlxxqB1Ado5ny01fZvFM2T4nXK0ocsxJtbJWFy1dLii/oUrRpQflYS0ctYwHz1tK28v1xUWNEyRgv9fWKc+KYFQtH1LrqVk0MHlMxn1NiwWLF2zoVbWrTRP/RqfXEG7puCDoqMC/c2p1U2EynRkrrid/anQw6EqqIEsesRRqa1bJyU9lYKBJT09L1ASUC5q9QyHRLT1K39FDe8wHHWAAA8BQlDgCApyhxAAA8RYkDAOApShwAAE9R4gAAeIoSBwDAU5Q4AACeosQBAPAUJQ4AgKe47Crel9TQSaXOnpRZWA1dKxRv61R29Jwm+t+dunZ6w+IbVMimNNZ3SPnUqGJNC9TYvVYWCmn81BFlRoYUiTeqsXuNIsmmoJ8SAHiLEkfFsiNnNX7q0NTt0d69CkVjGjm2RyoWJEkTA8cUisaVPndK+YlRSVLm/IAkUygaU/psnyQpl8tq5NhuLdiwVWZW8+cCAPWAw+moWHbsfPmAc0oN9U0V+EWZkTNTBf7e955TdrT8+4vZNOuMA8AsUOKo2JUOfcfaOqRLZtLRxjaF4uUrKEUSTZd9v4WjCsdYaQkAPigOp6Ni8bYu5cdHlD53SmYhJTtXKNHWKVfIa+L0u3LFvGKtHUq2L1W0sVWjJ/apmEkp0tCspp51slBYxWxaubHzCkXjalq6XhbifSQAfFCUOCpmZmpauk6N3aslM5mVCji5qFuJhYsl52ShsCQp2tiqhRu2qljIKxR+78esdfVtKhbyslCYc+EAMEuUON63i0VdNmYh6QqdPL3ArzUGAHj/OJYJAICnKHEAADxFiQMA4ClKHAAAT1HiAAB4ihIHAMBTlDgAAJ6ixAEA8BQlDgCApwIpcTP7Z2b2jpntMbM/N7NEEDkAoB4dO5vRj46OaW9/SvmCCzoOqqjmJW5mPZJ+XdIW59xGSWFJn651DgCoR/sH0vrR0XEdO5vVT0+m9OrRsaAjoYqCOpwekZQ0s4ikBkmnAsoBAHXlyJlM2e2+Czmlc8WA0qDaal7izrk+Sf9ZUq+k05KGnXPfv3Q7M3vMzHaa2c6hoaFaxwQAL8Uj5SsRhUOmSIgVA+tVEIfTF0j6RUk3SOqW1Ghmf/vS7ZxzTznntjjntnR0dNQ6JgB4aVN3UuFppb2pO6FImBKvV0GsCfmQpKPOuSFJMrO/lPQhSf87gCwAUFe6mqP6xU2tGhzLqzURVmvy8qWDUT+CKPFeSVvNrEFSStKDknYGkAMA6lIiGtLyBbGgY6AGgjgn/oakv5C0S9LuyQxP1ToHAAC+C2ImLufcb0v67SAeGwCAesEV2wAA8BQlDgCApyhxAAA8VVGJm9m2SsYAAEDtVDoTf7LCMQAAUCPX/HS6md2j0oVYOszsn0/7UotKC5cAAICAzPQrZjFJTZPbNU8bH5H0qWqFAgAAM7tmiTvndkjaYWZfds4dr1EmAMAsTGSL6h/JqS0Z1sLGQC4Hghqp9F83bmZPSVo5/Xuccw9UIxQA4IM5PZzTS4dH5Vzp9qbupDZ1J4MNhaqptMS/LumPJf2JpEL14gAAZmP36dRUgUvSO6dT2tCVUJSVzOpSpSWed879UVWTAABmLVdwZbeLTioUHSVepyr9FbNvm9k/NrMlZrbw4v+qmgwA8L6t7YiX3V6+IKZElOt61atKZ+J/d/LPfzFtzElaNbdxAACzsa4zoYZYSKeHc2pNhrW6PT7zN8FbFZW4c+6GagcBAMyNpW0xLW1jPfH5oNLLrjaY2b+e/IS6zGytmf1CdaMBAIBrqfREyf+QlFXp6m2SdFLSf6xKIgAAUJFKS3y1c+73JOUkyTmXksRHHQEACFClJZ41s6RKH2aTma2WlKlaKgAAMKNKP53+25K+J2mZmf2ZpG2S/l61QgEAgJlV+un0581sl6StKh1G/5xz7kxVkwEAgGt6P1cA6FFp+dGYpPvM7NHqRAIAAJWoaCZuZl+SdIukdyQVJ4edpL+sUi4AADCDSs+Jb3XO3VTVJAAA4H2p9HD6a2ZGieOqXLGgYj5bPuaKKmQv/yWGYi4j54qXjQMA3p9KZ+L/U6Ui71fpV8tMknPO3VK1ZPBGauiExvuPSsWCoi2L1LL8JuVSoxrt3SuXyyocb1Dzyo2yUESjx3crPzEqi0TV1LNe8baOoOMDgLcqLfEvSfo7knbrvXPi3gtPnFNy/7NBx/BaPpfT8KleRS8O9EvFwd3Kjo0omhqVJLloUrmB3QqFw7LxsaltM6d+ptaeFbIQKyzNRnjinKSuoGMACEClJd7rnHumqklqbM2aNUFHqAsjIyPqzbWUjTU1JTQWzWswNyZJ6uxoUSQSUSQSUbqhvLDXLluoeJxVlmani59nYJ6qtMT3m9nTkr6taVdqc855++n0xx9/POgIdSGTyejpp59WLpebGrv//vu1b98+ffGLX5Qkbd++XevXr1dDQ4Peeuutqe1aWlq0fft2mXEFXwD4ICot8aRK5f3Xpo3xK2ZQPB7Xww8/rJ07dyqVSmn9+vVat26denp69OUvf1npdFo33nijtm7dqnA4rGKxqGPHjqm1tVVbt26lwAFgFiq9YtuvVjsI/LV48WL9wi+Ur0zb2Nio5cuXS5LuvffeqfG7775bd999d03zAUC9umaJm9lvOud+z8ye1OTiJ9M55369askAAMA1zTQT3zf5585qBwEAAO/PNUvcOfftyb9OOOe+Pv1rZvY3qpYKAADMqNJf0P1XFY4BAIAamemc+MOSPiGpx8y+OO1LLZLy1QwGAACubaZz4qdUOh/+iKSfTBsflfTPqhUKAADMbKZz4j+T9DMze9o5l7vWtgAAoLYqvdjLXWb27yStmPyeiwugrKpWMAAAcG2VlvifqnT4/CeSCtWLAwAAKlVpiQ87556rahIAAPC+VFriL5rZ76t0rfTpC6DsqkoqAAAwo0pL/OLFrrdMG3OSHpjbOAAAoFKVLoDy0WoHAQAA709FV2wzsy4z+1Mze27y9k1m9mvVjQYAAK6l0suuflnS/5XUPXn7oKR/Wo1AAACgMpWWeLtz7v9IKkqScy4vftUMAIBAVVri42a2SJNripvZVknDVUsFAABmVOmn0/+5pGckrTazVyV1SPpU1VIBAIAZVToTXy3pYUkfUunc+CFV/gYAAABUQaUl/m+ccyOSFkh6SNJTkv6oaqkAAMCMKi3xix9i+3lJf+yc+5akWHUiAQCASlRa4n1m9t8l/U1Jz5pZ/H18LwAAqIJKi/hvqnQu/OPOuQuSFkr6F1VLBQAAZlTpZVcnVFr85OLt05JOVysUAACYGYfEAQDwFCUOAICnKHFUhXNO58+f16lTp3Ts2LGg4wDzyqnhrHb2TujQUFrFogs6DqqIC7agKl555RX19fVJkr7//e9r69atuuWWWwJOBdS/Q0NpvXl8Yur24Ghe21Y1BZgI1cRMHHMun8/rwIEDZWN79+4NKA0wvxwczJTd7j2XVTpXDCgNqo0Sx5wLhUIKh8NlY5EIB32AWoiGrey2mRQO2VW2hu8occy5UCikzZs3T902M91xxx0BJgLmj41LErJpnX3T4uRlxY76wfQIVXHrrbdq9erVSqVS2r59u1paWoKOBMwL3a0xPbKxVf2jebUmwmpv4mW+nvGvi6pJJpNKJpMUOFBjjfGwVsfDM28I73E4HQAAT1HiAAB4ihIHAMBTlDgAAJ6ixAEA8BQlDgCApyhxAAA8xe+JA6i53rGwvrCL6wdU08BEaY7W1cB106uldyystQFnoMQB1NSaNWuCjjAvZA8fliTFV/Dfu1rWKvif55qXuJmtl/S1aUOrJP1b59x/rXUWVFc2m1U6nVY6nVYikQg6Dq4Tjz/+eNAR5oXPfe5zkqQnnngi4CSoppqfE3fOHXDO3eacu03SHZImJH2z1jlQXfv27dPBgwfV29urp59+WidPngw6EgDUnaA/2PagpCPOueMB58AcKhaL+vGPfzx1O5/Pl90GAMyNoEv805L+/EpfMLPHzGynme0cGhqqcSzMRrFYVDabLRtLp9MBpQGA+hVYiZtZTNIjkr5+pa87555yzm1xzm3p6OiobTjMSiQS0apVq8rG1q9fH1AaAKhfQc7EH5a0yzk3EGAGVMn999+vrq4utba26r777tMdd9wRdCQAqDtB/orZZ3SVQ+nwXzgc1sUjKBs2bAg4DQDUp0Bm4mbWIOnnJP1lEI8PAEA9CGQm7pybkLQoiMcGAKBeBP3pdAAA8AFR4gAAeIoSBwBqgswrAAANpklEQVTAU5Q4AACeosQBAPAUJQ4AgKcocQAAPEWJo6qKxWLQEQCgblHiqIrBwUEdPHhQe/fu1V/91V9pdHQ06EgAUHcocVTFiy++OLUc6eDgoF599dWAEwFA/aHEMeey2ayGh4fLxlgTHgDmHiWOOReLxdTe3l421tPTE1AaAKhflDiq4qGHHlJTU5PC4bBWr16tbdu2BR0JAOpOkOuJo461tLRo5cqVkqQHH3ww2DAAUKeYiQMA4ClKHAAAT1HiAAB4ihIHAMBTlDgAAJ6ixAEA8BQlDgCApyhxAAA8RYkDAOApShwAAE9R4qiKdDqtU6dO6ciRI3rzzTdVKBSCjgTMC8ViUbt27dKRI0fU19eniYmJoCOhiihxVMUPf/hDnTt3TqlUSm+99ZZef/31oCMB88LOnTu1c+dOpVIpnT9/Xs8//3zQkVBFlDjmXC6X08mTJ8vGjh49GlAaYH65dF8bGBhgNl7HKHHMuUgkooaGhrKxlpaWgNIA88ul+1o8Hlc8Hg8oDaqNEsecMzPde++9CoVKP14NDQ360Ic+FHAqYH7YunWrmpqaJJX2xW3btikcDgecCtXCeuKoihUrVmj9+vXKZrP67Gc/O1XoAKprwYIF+vSnP60dO3YoGo1qzZo1QUdCFVHiqJpwOKxkMkmBAzUWCoWUSCSCjoEa4NUVAABPUeIAAHiKEgcAwFOUOAAAnqLEAQDwFCUOAICnKHEAADxFiQMA4ClKHAAAT1HiqJqRkRENDAzo1KlTQUcB6pJzTu+++6527typgYGBqfGBgQENDAxoeHhYzrkAE6LauOwqquK1115Tb2+vJOk73/mO7r33Xt14440BpwLqy8svv6z9+/dLknbt2qWPfvSjkqQXX3xRQ0NDU9vcd999gWVEdTETx5wrFArau3dv2djbb78dUBqgPmUyGR04cKBsbPfu3dq9e3fZ2IEDB5TJZGoZDTVEiaMqzOyatwHMjpldcT+rZAz1gxLHnAuHw7rlllvKxm6//faA0gD1KRaL6eabb566bWa67bbbdNttt5WV9s0336xYLBZERNQA58RRFVu2bNHKlSuVTqf16KOPqr29PehIQN255557tGzZMp07d05Lly7VwoULJUmf/OQn9dJLLykej+uee+4JOCWqiRJH1TQ1NampqYkCB6po6dKlWrp0adnYwoUL2e/mCQ6nAwDgKUocAABPUeIAAHiKEgcAwFOUOAAAnqLEAQDwFCUOAICnKHEAADxFiQMA4ClKHAAAT1HiAAB4ihIHAMBTlDgAAJ6ixAEA8BQlDgCApyhxAAA8RYkDAOApShwAAE9R4gAAeIoSBwDAU5Q4AACeosQBAPAUJQ4AgKcocQAAPEWJAwDgqUBK3MzazOwvzGy/me0zs3uCyAEAgM8iAT3uE5K+55z7lJnFJDUElAMAvHDw4EG9+eabymazuvHGG3X33XfrzJkzevnll3Xu3DktW7ZMH/nIRyRJO3bs0J49e5RIJDQ0NKT29na98cYb2rdvn2KxmO666y6tXbs24GeEuVDzEjezFkn3Sfp7kuScy0rK1joHAPhiZGREO3bskHNOkvT222+rra1Nb731lkZHRyVJx48f1+uvvz71d0lKp9N64YUXdPvtt+vtt9+WJOVyOb300kvq6upSS0tLAM8GcymIw+mrJA1J+h9m9paZ/YmZNQaQAwC8MDg4OFXgFx0/fnyqwC/q7+9Xf39/2djo6OhUqV/knNPg4GB1wqKmgijxiKTNkv7IOXe7pHFJn790IzN7zMx2mtnOoaGhWmcEgOtGZ2enzKxsbMWKFWpubi4bW7x4sbq6usrGmpubtWLFirIxM1NnZ2d1wqKmgjgnflLSSefcG5O3/0JXKHHn3FOSnpKkLVu2uEu/DgDzRUtLiz7ykY+UnRNfv369Fi1aVHZOfOvWrZKkbLZ0hjKRSOihhx5Se3u7Lly4MHVO/M477+RQep2oeYk75/rN7ISZrXfOHZD0oKS9tc4BAD5Zt26d1q1bVzbW0dGhRx999LJtP/axj+nZZ5+d2kaStm7dOlXyqB9BfTr9cUl/NvnJ9Hcl/WpAOQAA8FYgJe6c+6mkLUE8NgAA9YIrtgEA4ClKHAAAT1HiAAB4ihIHAMBTlDgAAJ6ixAEA8BQlDgCApyhxAAA8FdQV2wAAVeCc0zvvvKNjx44pkUgok8koHo8HHQtVwkwcAOrIW2+9pR/96EcaGxvTmTNn9PzzzwcdCVXETBwAZvDkk0/q8OHDQceoyMGDB5XNZqfWC/+DP/gDPffcc4pErv+X+zVr1ujxxx8POoZXmIkDQB2JRqNTf0ajUYVCIYVCvNTXq+v/rRkABMyn2eHQ0JCee+45pdNphUIhffjDH9aGDRuCjoUqocQBoI50dHTos5/9rIaGhtTW1qZkMhl0JFQRJQ4AdSYSiWjJkiVBx0ANcKIEAABPUeIAAHiKEgcAwFOUOAAAnqLEAQDwFCUOAICnKHEAADxFiQMA4ClKHAAAT1HiAAB4ihIHAMBTlDgAAJ6ixAEA8BQlDgCApyhxAAA8RYkDAOApShwAAE9R4gAAeIoSBwDAU5Q4AACeosQBAPAUJQ4AgKcocQAAPEWJAwDgKUocAABPUeIAAHiKEgcAwFOUOAAAnqLEAQDwFCUOAICnKHEAADxFiQMA4ClKHAAAT1HiAAB4ihIHAMBTlDgAAJ6ixAEA8BQlDgCApyhxAAA8RYkDAOApShwAAE9R4gAAeIoSR1WMjIzo2LFj2rdvn37wgx8ok8kEHQkA6g4ljqp44YUXNDY2pkKhoCNHjujVV18NOhIA1J1I0AFQuSeffFKHDx8OOsaMCoWC9u3bp8HBQUnS1772NYXDYX3rW98KOFll1qxZo8cffzzoGAAwI0occy4cDisWiykajU6NJZPJABMBQH2ixD3i0+xwcHBQL774ooaHh9XZ2akHH3xQzc3NQccCgLpCiaMqOjs7tX37duXzeUUi/JgBQDXwwTZUFQUOANVDiQMA4ClKHAAAT1HiAAB4ihIHAMBTlDgAAJ6ixAEA8BQlDgCApyhxAAA8RYkDAOCpQC6nZWbHJI1KKkjKO+e2BJEDAACfBXlNzI86584E+PgAAHiNw+kAAHgqqBJ3kr5vZj8xs8eutIGZPWZmO81s59DQUI3jAQBw/QuqxLc55zZLeljSPzGz+y7dwDn3lHNui3NuS0dHR+0TAgBwnQukxJ1zpyb/HJT0TUl3BZEDAACf1bzEzazRzJov/l3SX5O0p9Y5AADwXRCfTu+S9E0zu/j4TzvnvhdADgAAvFbzEnfOvSvp1lo/LgAA9cacc0FnmJGZDUk6HnQOfCDtkrgeABAM9j9/rXDOzfipbi9KHP4ys51ckQ8IBvtf/eNiLwAAeIoSBwDAU5Q4qu2poAMA8xj7X53jnDgAAJ5iJg4AgKcocQAAPEWJ45rMbKzGj/fLZubMbEMtHxe4HtVy/zOzgpn91Mx+Zma7zOxDtXpsfHCUOK43n5H0iqRPBx0EmGdSzrnbnHO3SvpXkn4n6ECYGSWO983MVpjZD8zs7ck/l0+Orzaz183sTTP79xdnEVby+2a2x8x2m9n2q9xvk6Rtkn5NlDhwRdXa/y7RIul8NZ8H5gYljg/iDyV9xTl3i6Q/k/TFyfEnJD3hnLtT0qlp2z8q6TaVrpn/kKTfN7MlV7jfX5L0PefcQUnnzGxztZ4A4LFq7X/JycPp+yX9iaT/UK0ngLlDieODuEfS05N//1+SPjxt/OuTf3962vYflvTnzrmCc25A0g5Jd17hfj8j6auTf//q5G0A5aq1/108nL5B0sclfcUml5vE9SuIpUhRf2a62MCMLwRmtkjSA5I2mpmTFJbkzOw3HRczAK5l1vvfZXfo3Gtm1i6pQ9LgB0qFmmAmjg/iR3rvnPXfUumDaJL0uqRPTv59+jnt/ydpu5mFzaxD0n2SfnzJfX5KpUOEK5xzK51zyyQd1XuzDAAl1dj/ykz+dkhY0tm5Co3q4IptuCYzK6r8/Np/kfSXkr6k0jKHQ5J+1TnXa2ZrJf1vld75f1fSY865nslDcr8n6WGVZg3/0Tn3tUse5yVJv+uc+960sV+XdKNz7h9V6/kB17Na7X+Tj1WQtPviTUm/5Zz7bnWeGeYKJY45Y2YNKp1Xc2b2aUmfcc79YtC5gPmA/W9+4pw45tIdkv5w8p3/BUl/P+A8wHzC/jcPMRMHAMBTfLANAABPUeIAAHiKEgcAwFOUODAP1Xp1OgDVQYkDAOApShyYx662wpWZhczsv5nZO2b2HTN71sw+Nfm1B83srcntv2Rm8WCfBTB/UeLA/Ha1Fa4elbRS0iZJ/0ClxTVkZglJX5a03Tm3SaVrTXBFPSAglDgwv11thasPS/q6c67onOuX9OLk9uslHZ1cLlaS/qdK1+IGEABKHJjfrrbC1fsdBxAAShyY3662wtUrkj45eW68S9L9k9vvl7TSzNZM3v47Ks3eAQSAa6cD89s3VTrf/TOVVrj6Tedcv5l9Q9KDkvZIOijpDUnDzrm0mf2qpK+bWUTSm5L+OJjoALh2OoArMrMm59yYmS1SaXa+bfL8OIDrBDNxAFfzHTNrkxST9B8ocOD6w0wcAABP8cE2AAA8RYkDAOApShwAAE9R4gAAeIoSBwDAU/8ftSGPiBHkemAAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1abb1339358>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Above- Difference b/w them in the sample is \"negligible\" by Cohen's d test units w/ 95% CI and leaves rather low power.\n",
    "\n",
    "## Final Report - Summarize Final Conclusions\n",
    " # This would be written differently depending on who audience is (i.e., board members, other data scientists, etc.)\n",
    "    \n",
    "# First begin w/ visualization of data\n",
    "\n",
    "ax = plt.figure(figsize=(8,8)).gca() # define axis\n",
    "temp = data[data.logo != 'Logo C']\n",
    "sns.boxplot(x = 'logo', y = 'sentiment', data = temp, ax = ax)\n",
    "sns.swarmplot(x = 'logo', y = 'sentiment', color = 'black', data = temp, ax = ax, alpha = 0.4)\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.7114799640615099"
      ]
     },
     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# 2nd Present results. State what was observed first, quantifying size of oberserved results/\n",
    " # Try to state something about whether effect is significant, using common language where possible.\n",
    " # Present some measure of uncertainty (e.g., CI) interpreting in plain language as much as possible\n",
    "  # Example - \"The average sentiment for Logo A was slightly higher (M = 8.57, SD = 1.27) than the average sentiment for Logo B (M = 8.44, SD = 1.51). \n",
    "  #            This was a small difference...only 0.13 points on the 1-10 scale. Given our sample size, this was well within what would be expected by \n",
    "  #            random chance (i.e., not statistically significant; t = 0.38, p = 0.70). Thus, they were statistically tied.\"\n",
    "  #\n",
    "  #            \"It is possible that a small sentiment difference may still exist between the two logos. We are 95% confident that the difference is \n",
    "  #             somewhere between 0.80 points higher for Logo A and 0.55 pionts higher for Logo B. So, if they do differ, they are likely very close to one another; \n",
    "  #             however, we woudl need a larger sample to say something more precise than that.\"\n",
    "    \n",
    "\n",
    "## Power Considerations\n",
    " # Power depends on both sample size & effect size.\n",
    "  # Large samples can detect small effects\n",
    "  # Smaller samples cannot detect small effects\n",
    "    \n",
    "# Compute the smallest effect we could reliably detect for our sample size & 80% power\n",
    "\n",
    "tt_ind_solve_power(effect_size=None, nobs1 = 32, alpha=0.05, power=0.8, ratio=1, alternative='two-sided')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "393.4056989990322"
      ]
     },
     "execution_count": 25,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Above - Could ONLY reliably detect effects as small as d = 0.71, a \"moderate-large\" effect. So, this reinforces our conclusion above... we would have detected a \n",
    " # moderate-large difference between Logo A and B, but if there was a smaller difference, we were prone to miss it.\n",
    " # A non-significant result does not mean the effect was exactly zero\n",
    "  # Instead \"there was not a large enough difference b/w Logo A & B\"\n",
    "    \n",
    "# Better to have run this prior to the study to plan sample size\n",
    "\n",
    "tt_ind_solve_power(effect_size=0.2, nobs1 = None, alpha=0.05, power=0.8, ratio=1, alternative='two-sided')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "F-Satatistic = 13.611076880502567\n",
      "p_value = 6.251108050657806e-06\n"
     ]
    }
   ],
   "source": [
    "# Above- Would need nearly 394 people per logo to detect small differences.\n",
    " # Might iteratively explore several sample sizes to find optimal balance b/w sample size (i.e. cost of study) & ability to dtect an effect.\n",
    "    \n",
    "## Inferential Test for Three Groups\n",
    " # When three or more groups are present, switch from a t-test to ANOVA (ANanlysis Of VAriance)\n",
    "  # ANOVA is two stage analysis\n",
    "   # 1) Test whether the logo mattered at all (i.e., null hypothesis says there were no differences: H0: muA = muB = muC).\n",
    "   # 2) If it comes up significant, we can systematically compare the logos.\n",
    " # Compute F-statistic & p-value for two or more groups.\n",
    "    \n",
    "f_statistic, p_value = ss.f_oneway(data.loc[data.logo == 'Logo A', 'sentiment'],\n",
    "                                   data.loc[data.logo == 'Logo B', 'sentiment'],\n",
    "                                   data.loc[data.logo == 'Logo C', 'sentiment'])\n",
    "print('F-Satatistic = ' + str(f_statistic))\n",
    "print('p_value = ' + str(p_value))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Multiple Comparison of Means - Tukey HSD,FWER=0.05\n",
      "=============================================\n",
      "group1 group2 meandiff  lower   upper  reject\n",
      "---------------------------------------------\n",
      "Logo A Logo B  -0.132  -0.9423  0.6783 False \n",
      "Logo A Logo C -1.5758  -2.3739 -0.7776  True \n",
      "Logo B Logo C -1.4438  -2.2482 -0.6393  True \n",
      "---------------------------------------------\n"
     ]
    }
   ],
   "source": [
    "# Above- Remember first step test the null hypothesis that all the group means are equal (logos don't matter at all).\n",
    " # p-value is 6.25e-06, which is p < 0.05, & is highly statistically significant.\n",
    "  # Could only get a logo effect this big 0.0000625% of the time by random chance alone.\n",
    "  # Confident the logo is doing something.\n",
    " # Appreciate ability to conduct a single overall test to tell the logo is doing something, instead of multiple t-test that could provide a false-positive.\n",
    "\n",
    "# Now figure out where difference are using previously made table of results usin the Pandas groupby and mean() methods.\n",
    " # Tukey's HSD takes into account the number of comparisions we want to make.\n",
    "  #  1. A vs. B\n",
    "  #  2. A vs. C\n",
    "  #  3. B vs. C\n",
    " # Tukey's test know how many comparison w want to make.\n",
    "  # It inflates our p-values on each test, making it harder to detect a difference for any one comparision.\n",
    "   # This reduces our likelihood of making a false positive on any one comparision, counteracting the problem of running multiple tests.\n",
    "# Compute three differences using pairwise_tukeyhsd from statsmodels.statsmulticomp package.\n",
    "\n",
    "Tukey_HSD = pairwise_tukeyhsd(data.sentiment, data.logo)\n",
    "print(Tukey_HSD)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1abb18ab400>"
      ]
     },
     "execution_count": 28,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x1abb18ab400>"
      ]
     },
     "metadata": {},
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    }
   ],
   "source": [
    "# Above- Output provided difference score & 95% CIs.\n",
    " #  1. Group A vs. B  = not significant. Logo B was 0.13 points lower than Logo A. We are 95% confident the true difference\n",
    " #     is between -0.94 & 0.68. This includes zero, so we cannot declare a difference b/w Logo B & Logo A.\n",
    " #  2. Group A vs. C = highly significant. Logo C was 1.58 points lower than Logo A. We are 95% confident the true difference \n",
    " #     is between -2.37 and -0.78.\n",
    " #  3. Group B vs. C = highly significant. Logo C was 1.44 points lower than Logo B. We are 95% confident the true difference \n",
    " #     is between -2.25 and -0.64.\n",
    "# As in the t-test example above, we see confidence intervals are helpful. If we wanted more precise CIs, we need a larger sample.\n",
    "\n",
    "#Visually plot Confidence Intervals of means by using plot_simultaneous method\n",
    "\n",
    "Tukey_HSD.plot_simultaneous()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      " Mean by logo\n",
      "        sentiment\n",
      "logo             \n",
      "Logo A       8.58\n",
      "Logo B       8.44\n",
      "Logo C       7.00\n",
      "\n",
      " Standard deviation by logo\n",
      "        sentiment\n",
      "logo             \n",
      "Logo A       1.27\n",
      "Logo B       1.51\n",
      "Logo C       1.33\n"
     ]
    }
   ],
   "source": [
    "## Final Report-\n",
    " # The average sentiment on a 1 - 10 scale is as follows:\n",
    "\n",
    "logo_grouped = data[['logo','sentiment']].groupby('logo')\n",
    "\n",
    "print(' Mean by logo')\n",
    "print(logo_grouped.mean().round(2))\n",
    "print('\\n Standard deviation by logo')\n",
    "print(logo_grouped.std().round(2))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Above- \"An ANOVA revealed a signifiant effect of logo on sentiment (F = 13.61, p < .001). As shown in the table above, Logos \n",
    "#         A & B were similar in sentiment, while Logo C had reduced sentiment. The pattern of results was such that Logos A & B were \n",
    "#         statistically tied, & both performed better than Logo C. Further, the confidence intervals computed w/ Tukey HSD test \n",
    "#         supports this conclusion.\"\n",
    "\n",
    "# Could report the CIs or p-values above in a table or in paragraph form.\n",
    " # It is possible to go into same level of detail as for t-test, but people usually don't, as it get exponentially more complicated w/ all comparisions going on."
   ]
  }
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