proposal (3).ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# **STAT-201 Project Proposal**\n",
    "## Analysis of data science salaries\n",
    "\n",
    "Prabh Sehgal, Rainie Fu, Rishabh Mathur, Dennis Truong"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Introduction\n",
    "A key factor in employee happiness is financial compensation, and past work during the COVID-19 pandemic have shown that working remotely can also have a positive impact on happiness thanks to increased employee autonomy. (Card et al., 2012; Galanti et al., 2021). Our analysis aims to explore the relationships between different data science jobs, their salaries, and their proportions doing remote work. Our analyses can inform prospective emplyees about each position's remote work flexibility and typical salary. Employees may use these inferences to discover new data science occupations that better align with their work-life goals."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Research Question\n",
    "\n",
    "If full-time Data Scientists and Data Analysts were compared, is there a difference in the means of salaries and difference in proportions of remote work?\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Dataset\n",
    "\n",
    "Our research utilizes the dataset \"Data Science Job Salaries\" by Ruchi Bhatia (2022) from [Kaggle](https://www.kaggle.com/datasets/ruchi798/data-science-job-salaries). Observations include the year the salary was paid, experience level, work kind, title, salary, remote ratio, firm size, and company location. The main observations we aim to use are the ```job_title``` to tell us the job type, the ```salary_in_USD``` to inform us about each role's salary, and the ```remote_ratio``` to give us the proportion of poeple working remotely in that respective role.\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Preliminary Results"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Exploring our Data\n",
    "\n",
    "We downloaded the data to our repository and read it from there since Kaggle does not let datasets to be read straight from the website."
   ]
  },
  {
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    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Warning message in system(\"timedatectl\", intern = TRUE):\n",
      "“running command 'timedatectl' had status 1”\n",
      "── \u001b[1mAttaching packages\u001b[22m ─────────────────────────────────────── tidyverse 1.3.2 ──\n",
      "\u001b[32m✔\u001b[39m \u001b[34mggplot2\u001b[39m 3.4.0      \u001b[32m✔\u001b[39m \u001b[34mpurrr  \u001b[39m 1.0.0 \n",
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      "── \u001b[1mConflicts\u001b[22m ────────────────────────────────────────── tidyverse_conflicts() ──\n",
      "\u001b[31m✖\u001b[39m \u001b[34mdplyr\u001b[39m::\u001b[32mfilter()\u001b[39m masks \u001b[34mstats\u001b[39m::filter()\n",
      "\u001b[31m✖\u001b[39m \u001b[34mdplyr\u001b[39m::\u001b[32mlag()\u001b[39m    masks \u001b[34mstats\u001b[39m::lag()\n",
      "\n",
      "Attaching package: ‘gridExtra’\n",
      "\n",
      "\n",
      "The following object is masked from ‘package:dplyr’:\n",
      "\n",
      "    combine\n",
      "\n",
      "\n",
      "Registered S3 method overwritten by 'GGally':\n",
      "  method from   \n",
      "  +.gg   ggplot2\n",
      "\n"
     ]
    },
    {
     "data": {
      "text/html": [
       "<table class=\"dataframe\">\n",
       "<caption>A tibble: 6 × 11</caption>\n",
       "<thead>\n",
       "\t<tr><th scope=col>work_year</th><th scope=col>experience_level</th><th scope=col>employment_type</th><th scope=col>job_title</th><th scope=col>salary</th><th scope=col>salary_currency</th><th scope=col>salary_in_usd</th><th scope=col>employee_residence</th><th scope=col>remote_ratio</th><th scope=col>company_location</th><th scope=col>company_size</th></tr>\n",
       "\t<tr><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;chr&gt;</th><th scope=col>&lt;chr&gt;</th><th scope=col>&lt;chr&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;chr&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;chr&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;chr&gt;</th><th scope=col>&lt;chr&gt;</th></tr>\n",
       "</thead>\n",
       "<tbody>\n",
       "\t<tr><td>2020</td><td>MI</td><td>FT</td><td>Data Scientist            </td><td> 70000</td><td>EUR</td><td> 79833</td><td>DE</td><td>  0</td><td>DE</td><td>L</td></tr>\n",
       "\t<tr><td>2020</td><td>SE</td><td>FT</td><td>Machine Learning Scientist</td><td>260000</td><td>USD</td><td>260000</td><td>JP</td><td>  0</td><td>JP</td><td>S</td></tr>\n",
       "\t<tr><td>2020</td><td>SE</td><td>FT</td><td>Big Data Engineer         </td><td> 85000</td><td>GBP</td><td>109024</td><td>GB</td><td> 50</td><td>GB</td><td>M</td></tr>\n",
       "\t<tr><td>2020</td><td>MI</td><td>FT</td><td>Product Data Analyst      </td><td> 20000</td><td>USD</td><td> 20000</td><td>HN</td><td>  0</td><td>HN</td><td>S</td></tr>\n",
       "\t<tr><td>2020</td><td>SE</td><td>FT</td><td>Machine Learning Engineer </td><td>150000</td><td>USD</td><td>150000</td><td>US</td><td> 50</td><td>US</td><td>L</td></tr>\n",
       "\t<tr><td>2020</td><td>EN</td><td>FT</td><td>Data Analyst              </td><td> 72000</td><td>USD</td><td> 72000</td><td>US</td><td>100</td><td>US</td><td>L</td></tr>\n",
       "</tbody>\n",
       "</table>\n"
      ],
      "text/latex": [
       "A tibble: 6 × 11\n",
       "\\begin{tabular}{lllllllllll}\n",
       " work\\_year & experience\\_level & employment\\_type & job\\_title & salary & salary\\_currency & salary\\_in\\_usd & employee\\_residence & remote\\_ratio & company\\_location & company\\_size\\\\\n",
       " <dbl> & <chr> & <chr> & <chr> & <dbl> & <chr> & <dbl> & <chr> & <dbl> & <chr> & <chr>\\\\\n",
       "\\hline\n",
       "\t 2020 & MI & FT & Data Scientist             &  70000 & EUR &  79833 & DE &   0 & DE & L\\\\\n",
       "\t 2020 & SE & FT & Machine Learning Scientist & 260000 & USD & 260000 & JP &   0 & JP & S\\\\\n",
       "\t 2020 & SE & FT & Big Data Engineer          &  85000 & GBP & 109024 & GB &  50 & GB & M\\\\\n",
       "\t 2020 & MI & FT & Product Data Analyst       &  20000 & USD &  20000 & HN &   0 & HN & S\\\\\n",
       "\t 2020 & SE & FT & Machine Learning Engineer  & 150000 & USD & 150000 & US &  50 & US & L\\\\\n",
       "\t 2020 & EN & FT & Data Analyst               &  72000 & USD &  72000 & US & 100 & US & L\\\\\n",
       "\\end{tabular}\n"
      ],
      "text/markdown": [
       "\n",
       "A tibble: 6 × 11\n",
       "\n",
       "| work_year &lt;dbl&gt; | experience_level &lt;chr&gt; | employment_type &lt;chr&gt; | job_title &lt;chr&gt; | salary &lt;dbl&gt; | salary_currency &lt;chr&gt; | salary_in_usd &lt;dbl&gt; | employee_residence &lt;chr&gt; | remote_ratio &lt;dbl&gt; | company_location &lt;chr&gt; | company_size &lt;chr&gt; |\n",
       "|---|---|---|---|---|---|---|---|---|---|---|\n",
       "| 2020 | MI | FT | Data Scientist             |  70000 | EUR |  79833 | DE |   0 | DE | L |\n",
       "| 2020 | SE | FT | Machine Learning Scientist | 260000 | USD | 260000 | JP |   0 | JP | S |\n",
       "| 2020 | SE | FT | Big Data Engineer          |  85000 | GBP | 109024 | GB |  50 | GB | M |\n",
       "| 2020 | MI | FT | Product Data Analyst       |  20000 | USD |  20000 | HN |   0 | HN | S |\n",
       "| 2020 | SE | FT | Machine Learning Engineer  | 150000 | USD | 150000 | US |  50 | US | L |\n",
       "| 2020 | EN | FT | Data Analyst               |  72000 | USD |  72000 | US | 100 | US | L |\n",
       "\n"
      ],
      "text/plain": [
       "  work_year experience_level employment_type job_title                  salary\n",
       "1 2020      MI               FT              Data Scientist              70000\n",
       "2 2020      SE               FT              Machine Learning Scientist 260000\n",
       "3 2020      SE               FT              Big Data Engineer           85000\n",
       "4 2020      MI               FT              Product Data Analyst        20000\n",
       "5 2020      SE               FT              Machine Learning Engineer  150000\n",
       "6 2020      EN               FT              Data Analyst                72000\n",
       "  salary_currency salary_in_usd employee_residence remote_ratio\n",
       "1 EUR              79833        DE                   0         \n",
       "2 USD             260000        JP                   0         \n",
       "3 GBP             109024        GB                  50         \n",
       "4 USD              20000        HN                   0         \n",
       "5 USD             150000        US                  50         \n",
       "6 USD              72000        US                 100         \n",
       "  company_location company_size\n",
       "1 DE               L           \n",
       "2 JP               S           \n",
       "3 GB               M           \n",
       "4 HN               S           \n",
       "5 US               L           \n",
       "6 US               L           "
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "library(tidyverse)\n",
    "# install.packages(\"infer\")\n",
    "library(infer)\n",
    "library(repr)\n",
    "library(ggplot2)\n",
    "library(gridExtra)\n",
    "# library(tidyverse)\n",
    "# library(datateachr)\n",
    "# library(digest)\n",
    "# library(infer)\n",
    "# library(repr)\n",
    "# library(taxyvr)\n",
    "# library(tidyverse)\n",
    "# library(broom)\n",
    "# library(digest)\n",
    "library(GGally)\n",
    "# library(scales)\n",
    "# library(gridExtra)\n",
    "\n",
    "set.seed(4204)\n",
    "\n",
    "# load the url where the dataset is at \n",
    "url <- \"https://raw.githubusercontent.com/vindennt/stat-201-project-group-10/main/ds_salaries.csv\"\n",
    "\n",
    "#use suppressMessages() to avoid the warning message when it automatically gives a\n",
    "#name to the first column, which is just indecies\n",
    "salaries <- suppressMessages(\n",
    "read_delim(url, delim = \",\") %>%\n",
    "select(!...1))\n",
    "\n",
    "# get a preview of the dataset\n",
    "head(salaries)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "vscode": {
     "languageId": "r"
    }
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   "outputs": [
    {
     "data": {
      "text/html": [
       "<ol>\n",
       "\t<li>'Data Scientist'</li>\n",
       "\t<li>'Machine Learning Engineer'</li>\n",
       "\t<li>'Data Analyst'</li>\n",
       "\t<li>'Data Engineer'</li>\n",
       "</ol>\n"
      ],
      "text/latex": [
       "\\begin{enumerate}\n",
       "\\item 'Data Scientist'\n",
       "\\item 'Machine Learning Engineer'\n",
       "\\item 'Data Analyst'\n",
       "\\item 'Data Engineer'\n",
       "\\end{enumerate}\n"
      ],
      "text/markdown": [
       "1. 'Data Scientist'\n",
       "2. 'Machine Learning Engineer'\n",
       "3. 'Data Analyst'\n",
       "4. 'Data Engineer'\n",
       "\n",
       "\n"
      ],
      "text/plain": [
       "[[1]]\n",
       "[1] \"Data Scientist\"\n",
       "\n",
       "[[2]]\n",
       "[1] \"Machine Learning Engineer\"\n",
       "\n",
       "[[3]]\n",
       "[1] \"Data Analyst\"\n",
       "\n",
       "[[4]]\n",
       "[1] \"Data Engineer\"\n"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<table class=\"dataframe\">\n",
       "<caption>A grouped_df: 6 × 7</caption>\n",
       "<thead>\n",
       "\t<tr><th scope=col>work_year</th><th scope=col>experience_level</th><th scope=col>job_title</th><th scope=col>salary_in_usd</th><th scope=col>remote_ratio</th><th scope=col>company_size</th><th scope=col>n</th></tr>\n",
       "\t<tr><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;chr&gt;</th><th scope=col>&lt;chr&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;chr&gt;</th><th scope=col>&lt;chr&gt;</th><th scope=col>&lt;int&gt;</th></tr>\n",
       "</thead>\n",
       "<tbody>\n",
       "\t<tr><td>2020</td><td>MI</td><td>Data Scientist           </td><td>79833</td><td>in person</td><td>L</td><td>140</td></tr>\n",
       "\t<tr><td>2020</td><td>EN</td><td>Data Scientist           </td><td>51321</td><td>in person</td><td>S</td><td>140</td></tr>\n",
       "\t<tr><td>2020</td><td>MI</td><td>Data Scientist           </td><td>40481</td><td>in person</td><td>L</td><td>140</td></tr>\n",
       "\t<tr><td>2020</td><td>EN</td><td>Data Scientist           </td><td>39916</td><td>in person</td><td>M</td><td>140</td></tr>\n",
       "\t<tr><td>2020</td><td>MI</td><td>Machine Learning Engineer</td><td>43331</td><td>in person</td><td>M</td><td> 41</td></tr>\n",
       "\t<tr><td>2020</td><td>SE</td><td>Data Engineer            </td><td>33511</td><td>in person</td><td>S</td><td>129</td></tr>\n",
       "</tbody>\n",
       "</table>\n"
      ],
      "text/latex": [
       "A grouped\\_df: 6 × 7\n",
       "\\begin{tabular}{lllllll}\n",
       " work\\_year & experience\\_level & job\\_title & salary\\_in\\_usd & remote\\_ratio & company\\_size & n\\\\\n",
       " <dbl> & <chr> & <chr> & <dbl> & <chr> & <chr> & <int>\\\\\n",
       "\\hline\n",
       "\t 2020 & MI & Data Scientist            & 79833 & in person & L & 140\\\\\n",
       "\t 2020 & EN & Data Scientist            & 51321 & in person & S & 140\\\\\n",
       "\t 2020 & MI & Data Scientist            & 40481 & in person & L & 140\\\\\n",
       "\t 2020 & EN & Data Scientist            & 39916 & in person & M & 140\\\\\n",
       "\t 2020 & MI & Machine Learning Engineer & 43331 & in person & M &  41\\\\\n",
       "\t 2020 & SE & Data Engineer             & 33511 & in person & S & 129\\\\\n",
       "\\end{tabular}\n"
      ],
      "text/markdown": [
       "\n",
       "A grouped_df: 6 × 7\n",
       "\n",
       "| work_year &lt;dbl&gt; | experience_level &lt;chr&gt; | job_title &lt;chr&gt; | salary_in_usd &lt;dbl&gt; | remote_ratio &lt;chr&gt; | company_size &lt;chr&gt; | n &lt;int&gt; |\n",
       "|---|---|---|---|---|---|---|\n",
       "| 2020 | MI | Data Scientist            | 79833 | in person | L | 140 |\n",
       "| 2020 | EN | Data Scientist            | 51321 | in person | S | 140 |\n",
       "| 2020 | MI | Data Scientist            | 40481 | in person | L | 140 |\n",
       "| 2020 | EN | Data Scientist            | 39916 | in person | M | 140 |\n",
       "| 2020 | MI | Machine Learning Engineer | 43331 | in person | M |  41 |\n",
       "| 2020 | SE | Data Engineer             | 33511 | in person | S | 129 |\n",
       "\n"
      ],
      "text/plain": [
       "  work_year experience_level job_title                 salary_in_usd\n",
       "1 2020      MI               Data Scientist            79833        \n",
       "2 2020      EN               Data Scientist            51321        \n",
       "3 2020      MI               Data Scientist            40481        \n",
       "4 2020      EN               Data Scientist            39916        \n",
       "5 2020      MI               Machine Learning Engineer 43331        \n",
       "6 2020      SE               Data Engineer             33511        \n",
       "  remote_ratio company_size n  \n",
       "1 in person    L            140\n",
       "2 in person    S            140\n",
       "3 in person    L            140\n",
       "4 in person    M            140\n",
       "5 in person    M             41\n",
       "6 in person    S            129"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# As the salaries of part-time positions can vary due to various factors, we exclude them from our analysis \n",
    "# and focus solely on the salaries for full-time positions.\n",
    "\n",
    "# In preparation for potential hypothesis testing using the Central Limit Theorem, we need to identify which \n",
    "# job titles have a sample size that is sufficiently large (we consider n > 30 to be a large sample size, \n",
    "# as discussed in class).\n",
    "salaries <- salaries %>%\n",
    "    filter(employment_type == \"FT\") %>%\n",
    "    group_by(job_title) %>%\n",
    "    mutate(n = n()) %>%\n",
    "    filter(n > 30)\n",
    "\n",
    "# Output the list of job titles that we are considering working with.\n",
    "large_job_groups <- as.list(unique(salaries$job_title))\n",
    "large_job_groups\n",
    "\n",
    "# Now let's only gather the information that we are interested in about these four titles:\n",
    "# 1. salaries in usd (to enable salary comparison)\n",
    "# 2. remote ratio, change the numerical values into categorical values for ease of visualization \n",
    "inperson <- salaries %>%\n",
    "    filter(remote_ratio == 0) %>%\n",
    "    mutate(remote_ratio = \"in person\")\n",
    "hybrid <- salaries %>%\n",
    "    filter(remote_ratio == 50) %>%\n",
    "    mutate(remote_ratio = \"hybrid\")\n",
    "remote <- salaries %>%\n",
    "    filter(remote_ratio == 100) %>%\n",
    "    mutate(remote_ratio = \"remote\")\n",
    "salaries_new <- rbind(inperson, hybrid, remote) %>%\n",
    "    select(-salary_currency, -salary, -employee_residence, -company_location, -employment_type)\n",
    "\n",
    "head(salaries_new)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
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    {
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SPkU/PgAAckMeBAAUSy74\nUpmo71auvdx+2tQqhixvJEVFJZgTDi2ZuuHohShT6WrN+gwd2LqcReTSx6+/9mXQ4y8t7lTR\ncvP4ljkzpq0Iei+0oTlTa/s//5wx1RxYOe21Z0hI+ajDf12S8sf/uFKxrnwxK3THkcs230oN\ne456sk8tr/SG165dO3bsWPrLkJAQb2/vQo5Rp9NZLJZCdlLMmc1mRVFcHYWzGAwGETGZTHq9\nXkSMRmPKS4tFPfdYGY1GdR+oKftOr9ereIyigatNyn60WCyFueDodLqii6gIkAdVoLgdVC5X\nEnc3eVAd1L0T5a7kwbteENrPfPT+LyEDl9e6c8uxNp2vJdZWduCYXkHy3w+bls9+IWzK0onN\nruzZ9XflB6d0vcdLRALufWxQm53Tv/xhdMM2mTJhTGSEzauC1+3B+vj4yK2IWxIeFi7/frWn\n9vjn3nnGJ+K3D+bMmb7Qb9lLbdPuwjl+/Pjzzz+f3mzJkiXlypUr5Ch1Op2Xl1fe65Vknp6e\nrg7B6dzdU2+oMptTX6pvr6r7GioiJpPJZDK5OgrnUv3VRgp9wbHb7UUVSREgD0KNSu7uJg+q\nQMk9/Bzn1Dx4twvC2ANbdsZ3nt7BL5v3fDq/tK5z2osKlZ6znx725q6Doxu7XboqJ5cP6708\nw7pVr4bZv9/Qb+5BERHx6z1r9QDJpvjVScoCU6tHRjYtrxPxbD5iaJt90/b/HNe2U+rNNlWr\nVh03blx6k9KlS8fExBRmjO7u7oqixMXFFaaT4i82NlbFnxCazWaTyRQfH5+cnCwiSUlmEVN8\nfHxMTHKebUsKk8mk0+kSExNdHYiz6HQ6d3d3m82WkJDg6licyN3dPTY21tVROJGbm5vBYCjk\nBSflYCjCqAqDPKgOVusdt+xqWyGPGZcgD6oDedARuefBu1wQxhzc96Nnq1dDst4lkx1rxYql\n5VBYmL6K2SRNxm19pX3me2MkdsTChY+IiIjRO1g8In1NkZERiqTmPom4FSG+fr7i7+8v7h4e\naSnSEBjoL+du3hRJvZRXrFhx2LBh6b1GREQUModpIRGKSHx8fPH6o3uR0uv1JpMpISEhKSlJ\nRJKSdCKmhISEuLgkV4dWZBRF0ev1Kj5QDQaDu7t7cnKyiscoIlarVd0DNJvNBoMhLi6uMIkw\n5WAowqgKgTyoEqr/WCm/SuLuJg+qA3nQEbnnwbv7QFTMD9//am3arHa2N7Eq5/ctX/zJSVva\n6/gLF67rgoODdGXLBsu5M2fTpyA27EpUsoi4B1RKVc7PIvrqNaom/XnidNpqkcdP/OsbElJG\n/KtV8ws7eTIsdXnif/9d1wcFlXbaIAEAyAF5EABQzNzdgvDUX38lB5UtkykPnvlq2ZLPjieK\n6PzNNw6tWbR4z19XboRd/H3H/NWHPbv2aeUmFbr2rBf55Xvv/3Y93p4ceWr3wknjZn99447O\n/dv1ahm7852VB89eC7t4bNv8jX9W7dOjtk70dXr0qnLyg4Vbj14MDzu9/931B906dmuq8nup\nAQDFEXkQAFDM3NVbRhNv3ojR+fv7Z1p4+ejnn0dWGtarjtmrdeircWtXb581YVmsyb98zbZT\nZg261yIi/t0nvhy5Yt3CcdsjFat/pQZ9po3p4n9n915tQqdHLF+1cVro9WTvinW6TnmpXzmd\niEiFfi++ELts3bwJG6MNATXbjX9tREO3uzFeAAAyIg8CAIobnYq/F6RgIiIiUh4bK7BSpUrZ\n7fabN28WVUgFFhoa6rzOFy9erOJnCD08PKxWa/rBMGuW+7x57lu3RrRrp55nCN3c3PR6vYqf\nwzYYDH5+fgkJCVFRUa6OxYn8/f1v3LjzoyL18PHxMZlM4eHhhXx2ws8vuy9xQXbUlAedx9fX\nd+jQoa6OIlVMTMCnny6qWPFQ69ZvuyqGRYsWuWrTBUYeVAfyoCNyz4Pq+VE1AAAAAEC+UBAC\nAAAAgEZREAIAAACARlEQAgAAAIBGURACAAAAgEZREAIAAACARlEQAgAAAIBGURACAAAAgEZR\nEAIAAACARlEQAgAAAIBGURACAAAAgEZREAIAAACARlEQAgAAAIBGURACAAAAgEZREAIAAACA\nRlEQAgAAAIBGURACAAAAgEZREAIAAACARlEQAgAAAIBGURACAAAAgEZREAIAAACARhldHQCg\nBqGhoc7rfNGiRc7rHAAAAFrGJ4QAAAAAoFEUhAAAAACgURSEAAAAAKBRFIQAAAAAoFEUhAAA\nAACgURSEAAAAAKBRFIQAAAAAoFEUhAAAAACgURSEAAAAAKBRFIQAAAAAoFEUhAAAAACgURSE\nAAAAAKBRRlcHUOyYTCajsbDTotPprFZrkcRTbLm5uSmK4uoonCXlGLBYLCn/MJlMKS+tVhec\nMk46loxGo16vV/GBqtPpRMRgMKh4jKKBq41erxcRq9VamAtOysEAB5EHHZFyZCJdSdzd5EF1\n0MjVxql5kIIwG0VS56i4WEqhKIqKx5gytPQxZnnpkmCc1LOKd2L6tU/FY0yh+gGK2o/VYog8\nmCd1j64ASuiEqPvaQh5UE6ceqxSEWSUlJSUlJRWmBw8PD0VR4uPjiyqk4ikhIcFut7s6Cmcx\nGAwikpiYmHIw2Gx6EXNiYmJ8fKGOjYJx3rGk1+tVfKAaDAZ3d/fk5GQVj1FE3N3d1T1Ai8Vi\nMBji4+MLkwgNBoOHh0cRRqVu5EFHuLm5uTqE4qWE7m7yoAqQBx2Rex7khgcAAAAA0CgKQgAA\nAADQKApCAAAAANAoCkIAAAAA0CgKQgAAAADQKApCAAAAANAoCkIAAAAA0CgKQgAAAADQKApC\nAAAAANAoCkIAAAAA0ChHCsKkpCSnxwEAQHFFHgQAqJYjBeEnw8rWf3D8vO1HriY6PR4AAIob\n8iAAQLUcKQgrNagbu2/xxH6Ny5e5t+fYOVt+upzg9LgAACguyIMAANVypCBs+ty+f65d/GX7\n2xO7+Z1YO/mRZhWCa98/+o0PDv0X5/T4AABwNfIgAEC1HP1SGUtwowfHvvH+t2eu/ffjR2+N\nrBP+2bRBrSoF1+j6+GubfrzCsxUAAHUjDwIAVCnf3zJqLdu03/g3lq1e8eqjta2R/3y18uVH\nm1eq1PqJ5T/fUJwRIAAAxQl5EACgJvkrCBOv/rpt3vje9cuWqdvjuc2XK/d4+q2PDh7+dGb3\nxG2jWzR56osbTooSAIDigDwIAFAZo0NrJV795bONa9au2bT793Cb3qdmpxGzRowY1rdZGYuI\niLRs3r1/s94Nn3p69uhTbzRwZrgAALgAeRAAoFKOFIRfPVnmgeU3bDrPKu2HTB8xYnj/+ypY\ns6xiuufx0T0n9D1zRoRECABQF/IgAEC1HCkIkzxqD3x5+Ijhj7Sv7KHLaSVDo5HvrJRmRRga\nAADFAnkQAKBajjxD6GaKiwhs2eHOLJj00RCf2lOOpLyo0H7kiPblizg8AABcjjwIAFAtRz4h\nvHH6l2O6mDsW2yL/PP5P5Gn7RZFGRR8YiruxY8c6qedFixY5qefQ0NCCNTx2bIBI33feeeej\nj/4o2pAcUeCw87Ry5Uon9QyoC3kQAKBauReEWx/SDfgo5Z9NdW9mt4ahUZ9aRR4UAADFAnkQ\nAKByuReEPRcf/ar/N2teHf+Jqc8jTQMyv6kzeZWt1/vxUdWdGB4AAC5EHgQAqFzuBaFbcP3O\ng+q7ndllKDtn5XAyHgBAW8iDAACVc+QZwvumfH6f0wMBAKCYIg8CAFQrl4Lwy/G1Qn8b9v7+\nF8LG1wr9IsfVui06ubCrEyIDAMClyIMAAPXLpSA0efj6eluNKf/wzXE1D5MTwgIAwNXIgwAA\n9culIOww8/DhlH+l/wMAAM0gDwIA1M+RH6YXEZHY86cvJ6X+O+70V2sWvPnWe3vOxDkpLAAA\nihfyIABAjRwqCJNOLuteucoja8+LiNiOvda2Xtfhzzw/aVSXRh3m/GpzboAAALgaeRAAoFaO\nFITRW6dM2hf0+EsDyonIzQ9emfmzZ98lP5059fXLdf54deZH0c6OEQAAVyIPAgBUy5GC8Nfv\nv0/o8fxbD1a1isTv3rY7ru7Ts55qUrlqhxee7hrzww8nnB4kAAAuRB4EAKiWIwXhrVu3vMuU\n8RARSf5u7/7EKg/cX1NERKylS3tevXrVmfEBAOBq5EEAgGo58sP0QUFBt/48c1M6+CV+vfWz\nm6UHdG+c8kbEv/9GlapWyqENXdocOnrjuQwL3DpO2zKhUZa1ok9+vHztl8fOhiV5lq3ZauDo\nYS0CDQ51n0fz2FO7Vq3YfuBUeLJnubpdho55tGmAw1+nAwDQOPIgAEC1HCkI63ftWnrBSw+O\nOdXgn03vXa/6zPC2ehGxXft62sK91tbDGji0oeioaGn0xPKxLdK2qHfzybpOxL4F0z+I7jFx\n6jOVLeG/vD/vzRmWeYseq+xoysqxefjeuS9vTu43btbEivrLhzYtW7GpRp1xzdwd7BYAoHHk\nQQCAajlSEFq6vbp63PFhS9/41h7Q9rXPXm5iEBHbx6EPLDjfbO76Bx1LKFHRUWb/4OCAgJxX\nCftm50/ePecPblpZRAK7jX7k4JDVu39/dEx9nXLztw9Xbtz3x4XrsYZS1Zr3HfV496pWh5uf\n3bH5WO1hqwY08RaRwD6Tl/ZxKGIAAESEPAgAUDFHCkLRlbl/4aFrcyJvJFj9vUypDdtO+uzH\nhe2bBpkc2k5SVFSCOeHQkqkbjl6IMpWu1qzP0IGty1kyrmL/558zppoDK6e99gwJKR91+K9L\nUl/38euvfRn0+EuLO1W03Dy+Zc6MaSuC3gttaBaHmpc//seVinXli1mhO45ctvlWathz1JN9\nank5FDYAAORBAIB6OVQQpjB7+2dMPYFNugQ63jjWpvO1xNrKDhzTK0j++2HT8tkvhE1ZOrGZ\nx+1VYiIjbF4VvHTpC3x8fORWxC05/cuuvys/OKXrPV4iEnDvY4Pa7Jz+5Q+jG7bJlAlzbB4e\nFi7/frWn9vjn3nnGJ+K3D+bMmb7Qb9lLbdPu1Dlz5szOnTvTmz3wwANly5Z1fGTZ0uv1Hh4e\nea+H7DB1d43JZFLxbOt0OhExGo0qHqOI6HQ6dQ/QYDCIiLt7sbi7kTzoONXnQb2eZzAzKYm7\n22AwqPsSSh5Uh7uQBx0rCK99/9ZzU5Z/9fuFKzfj7Vne6/+hsvWhPHvw6fzSus5pLypUes5+\netibuw6ObtYl8/5LOXIzLhBd8qVLV+Xk8mG9l2dYXvVqmP37Df3mHhQREb/es1YPyKG5iIiY\nWj0ysml5nYhn8xFD2+ybtv/nuLadUm+2OX/+/Nq1a9ObNG/evGrVqnkOKE9W6x0388AxTN1d\nYzKZTCbHPtwosQwGg+qPKNUPUAo9Rrs9a+rKN/Jg/mnhyES6kru7yYMqoPoBipPzoCMF4a0t\nY/tM2q67t137vl383bO2aFI520a5s1asWFoOhYWJ3E6EHr6+psjICEVSk5dE3IoQXz9fvdls\nkibjtr7SPvO9MRI7YuHCR1JG4R0sHpHZNxd/f39x9/BIS5GGwEB/OXfzpkjqtDZp0mT9+vXp\nvZYqVerWrVsFGFM6Hx8fRVEiIyML04mWFXL+4bj4+Pj4+HhXR+Eser3e29s7MTExNjbW1bE4\nkbe3t7qvNp6enkajMSIiQlGUAneScjAUIgryYP5oIQ96eXHPbSYlMXebzWa9Xk8eLOnIg47I\nPQ86UhAe/fprw+Ctf6/v41vgIJTz+1Z8Ftl2dJ9aKRuMv3Dhui44OChToNVrVE365MRppWk1\nnYhI5PET//qGhJTReZcNli/PnFXa10xJZrFhV5L9gr0M7gGVKmV4Nj+H5uJfrZpf2MmTYVIt\nQEQk8b//ruuDgkqnt/Py8goJCUl/GRERkZSUVOCRpo5XUWw2WyE70Sym7q6x2+0qnu2UWyy0\ncDKqe4Ap+c9msxUmEaYcDIVAHsz/eNV+6hXmgFSlkri7jUajlMzIHUQeVIe7kAcduQM+Li4u\npFWrgmdBEdH5m28cWrNo8Z6/rtwIu/j7jvmrD3t27dPKTUTOfLVsyWfHE0XEv12vlrE731l5\n8Oy1sIvHts3f+GfVPj1q66RC1571Ir987/3frsfbkyNP7V44adzsr2/csY2cmuvr9OhV5eQH\nC7cevRgednr/u+sPunXs1lTltwcAAIoOeRAAoFqOfELYoHHjM8ePJ0n7QiQPr9ahr8atXb19\n1oRlsSb/8jXbTpk16F6LiMjlo59/HllpWK86ZvFqEzo9YvmqjdNCryd7V6zTdcpL/crpRMS/\n+8SXI1esWzhue6Ri9a/UoM+0MV38s9lGDs2lQr8XX4hdtm7ehI3RhoCa7ca/NqKhW8GHAgDQ\nGPIgAEC1dI58+Bj3y+wHxhx5ZMH8kS3LqP4vioW/VaZUqVJ2u/3mzZtFFVKBhYaGujqEgli0\naJGTei7whBw7NuD48b4dOswMDv6jaENyrZUrV6r4uQKDweDn55eQkBAVFeXqWJzI39//xo07\nPypSDx8fH5PJFB4eXshbZfz8/AoTBnkwX4pPHnQeX1/foUOHujqKVDExAZ9+uqhixUOtW7/t\nqhicl7udx83NTa/XkwdLOvKgI3LPg458QvjtrPHbbl7+46lWm8e6BwSX9sjc5oGl55bcX+Do\nAAAo7siDAADVcqQgtCt6a6kaLTrVyPbdYM+ijQgAgOKFPAgAUC1HCsL2r37b3slhAABQbJEH\nAQCq5dgP06eIv3ry97/O/XcrsE3vRgGi2Gx2o7GQ3+QNAECJQR4EAKiOIz87ISK3Drz1UK3A\nMiHN2t3fb8z7p0REfp3avP7wDWfU/LMfAACkIA8CANTJoYLw3xWPdJ+0W+nwzNxlY5qkLku2\n1qwav+F/g+afcmJ0AAAUA+RBAIBaOVIQnlqz+MtSoz898slbE4e1DEpdaAgZ+sGWZ6v/uHL1\n786MDwAAVyMPAgBUy5GC8K+///bp3r+Txx1tG7Vv43X27FknhAUAQLFBHgQAqJYjBaG3t7ct\nPj75zjfiIyISrFZrkQcFAEAxQh4EAKiWIwVh7Xr14rfOfetEXKalyo39z8/4xN6iRWPnRAYA\nQPFAHgQAqJYjPztR6rEpY+d2ntys3p5Herj9LVE3V0wOXfbbF9u//DuuxnPLBvs7PUgAAFyI\nPAgAUC2HfofQs/28b78IHv/svPULryeJ/LNq9kGxlGn26JzZb/1fa+6UAQCoHHkQAKBWDv4w\nvb5Mp+e3HJkcd+3smUs348U9oFLVSn5m54YGAEBxQR4EAKiTgwVhCp01sEqdQGeFAqQIDQ11\ndQgAkC3yIABAbXIpCD8e4jl4e17t7Uk91yd80L8oQwIAoDggDwIA1C+Xb72c1wAAIABJREFU\ngrBM4549k1L/rYQf3bXnjKVmk0Y1y/qYk2Oun/vj59/+szbq379lt+p3JVAAAO4u8iAAQP1y\nKQibT/jgg5R/Xdn6WMvjQ3afX9i9jCn97ei/Nj314EtJXZfUc3KIAAC4AnkQAKB+jvwO4V/v\nTv+w2SvzM2ZBEfGsOWj++MqrXn73lJNCAwCgWCAPAgBUy5GC8O+///bw97fc+YZPQIDx5MmT\nRR4UAADFCHkQAKBajhSEAQEBt3au3n4ty2Ll2vat+23+/vwgLwBA1ciDAADVcuRnJ5r97/H6\nS6cPqHOsW88O9e4p7WWShMgrZ458vXPvnxG1nh/czOlBAgDgQuRBAIBqOVIQGhpO/eIL94mT\nF3y0ZtGu9KXmgHv7vLx+4dRm+fopQwAAShryIABAtRzLYrqgDs9t+PHZVTf/PX3uSkS8YvIq\nXbHqPaWtjtxwCgBASUceBACoVH7+rKkz+1UM8avotFgAACjOyIMAANXhb5sAAAAAoFEUhAAA\nAACgURSEAAAAAKBRFIQAAAAAoFEUhAAAAACgURSEAAAAAKBRFIQAAAAAoFEUhAAAAACgURSE\nAAAAAKBRRlcHAAAASoDQ0FAn9bxo0SIn9ey8mHE3OW8/rly50kk9O1VJPBlRnPEJIQAAAABo\nFJ8QZuXm5ubu7l6YHnQ6nV6v9/HxKaqQACdxc3MzmUyujsJZdDqdiJhMJnWfjDqdTt0DNBqN\nIuLt7V2YThRFKaJwNKHweTC/1H0Ma0QJ3YnqzoMFUBL3I3nQEbnnQQrCrBITE5OTkwvTg4+P\nj6IoMTExRRUS4CSJiYnx8fGujsJZ9Hq9t7e3zWaLjY11dSxO5O3tre6rjaenp9FojI2NLUxR\np9frzWZzEUalboXPg/ml7mNYI0roTlR3HiyAkrgfyYOOyD0PUhBmZbfbbTZbITtRFKXwnQDO\nViRHe7FlMBhEGyejugeYkv9sNlthEmHKwQAH3f0rg7qPYY0ooTtR3XmwAErobJTQsB10F/Ig\nzxACAAAAgEZREAIAAACARlEQAgAAAIBGURACAAAAgEZREAIAAACARlEQAgAAAIBGURACAAAA\ngEZREAIAAACARlEQAgAAAIBGURACAAAAgEZREAIAAACARlEQAgAAAIBGGV0dACQ0NNTVIUCj\nRo0a5aSeFy1a5KSeAQAAUIT4hBAAAAAANIqCEAAAAAA0ioIQAAAAADSKghAAAAAANIqCEAAA\nAAA0ioIQAAAAADSKghAAAAAANIqCEAAAAAA0ioIQAAAAADSKghAAAAAANIqCEAAAAAA0ioIQ\nAAAAADSKghAAAAAANIqCEAAAAAA0ioIQAAAAADSKghAAAAAANIqCEAAAAAA0ioIQAAAAADSK\nghAAAAAANIqCEAAAAAA0ioIQAAAAADTKeNe2pNw4tnXVhq9+O3cj0Vq6SuNew0c8UMMz8yqX\nNoeO3nguwwK3jtO2TGjk+DaiT368fO2Xx86GJXmWrdlq4OhhLQINIiISe2rXqhXbD5wKT/Ys\nV7fL0DGPNg2gFAYA3E3kQQBAMXTXCsKL216bsc3ca8L0SVWt4UfeX/DOjBWBK59p4pZxneio\naGn0xPKxLdKi0rv55GMTEfsWTP8gusfEqc9UtoT/8v68N2dY5i16rLJewvfOfXlzcr9xsyZW\n1F8+tGnZik016oxr5l50gwMAIA/kQQBAcXS3CsKoq3Gl7/vf4GHNK4hIYNeh93/xzWd//CtN\nqmdaKTrK7B8cHBCQtbVy87cPV27c98eF67GGUtWa9x31ePeq1qwrhX2z8yfvnvMHN60sIoHd\nRj9ycMjq3b8/Oqb+2R2bj9UetmpAE28RCewzeWkfpw0TAIBskQcBAMXS3SoIvRoNfuH2PS/2\n8Bu39EFBWRJeUlRUgjnh0JKpG45eiDKVrtasz9CBrctZRC59/PprXwY9/tLiThUtN49vmTNj\n2oqg90IbmjO1tv/zzxlTzYGV0157hoSUjzr81yUpf/yPKxXryhezQnccuWzzrdSw56gn+9Ty\ncu54AQDIiDwIACiW7t4zhLdFHVvx9ufWB6d18su8/P/bu+/Apso1juPvyepuupFRpowyBKmg\nIogKF2QWcbGkUhHrgItMURSUK8qQJcOLgIAsgYvIFlBAkaIsQaCgUECGQEvbpG3oTO4ftEBL\nU1LSNMk5389f5PCeN+/Jc5IfT3ISTLlSgIcpt1KPN7pUEBd+XT534qik9+YMbX55+6Y/a3R7\nr111PyFESKPePVtt/HDrr7EPtiqUhBlGQ65fuJ90c4NerxephlRxLemaOL9te/1/j5j1tt5w\neMWkSR9OD/xi9OMFV+Hs379/+vTpN3cbPnx4/fr17Tk+SZJUKlVAQIA9kwBuz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      "text/plain": [
       "plot without title"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 240,
       "width": 600
      }
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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EUJEReOnLh87y5SYgppPmLu2BYitw4dOisi9Rs10oj8unNnVKpWiXumd+/Qoevb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\nCQkJjvRgMBisVmtUVFR+heSC/Pz8bt++7cZ/GfX09DSbzdHR0Q4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SInLzk9emHfDqtWD/2dPfv1rrzzemfXbb2TECAFCYyIMAALdlT0H4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      "text/plain": [
       "plot without title"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 240,
       "width": 600
      }
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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KFJGoGDHutmliubn57yZZQ0HjpMfeZKaj5wVE83Cd80a/6pu5d/RO2f9dZumwQ+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\nvV5vMpkSEhKc/8jMDz8/P9ceoLe3t06ni4qKys8no3q9npJSvfz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69lNNK1ft8MLTXW7/9NOJQg8SAIBiRB4EALgsNQXhrVu3vIKD3UVE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FMMhAAAAAAgUwyEAAAAACBTDIQAAAAAIFMKm83m6hqk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      "text/plain": [
       "plot without title"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 240,
       "width": 600
      }
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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PhCV4lKjxyMCRTzXwt/vndAAAKkceBAC4LHsKwlrt2xd9f/JjI8/U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\nAAAAgEz9P7IoThpMZed/AAAAAElFTkSuQmCC",
      "text/plain": [
       "plot without title"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 240,
       "width": 600
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "\n",
    "options(repr.plot.width = 10, repr.plot.height = 4)\n",
    "\n",
    "salaries_ds_large <- salaries_new %>%\n",
    "    filter(company_size == \"L\") %>%\n",
    "    filter(job_title == \"Data Scientist\")\n",
    "\n",
    "ds_salary_dist <- salaries_ds_large %>% # data scientist salary distribution for large companies\n",
    "    ggplot(aes(x = salary_in_usd, y = after_stat(density))) +\n",
    "    geom_histogram(binwidth = 20000) +\n",
    "    geom_vline(xintercept = mean(salaries_ds_large$salary_in_usd),\n",
    "              color = \"blue\") +\n",
    "    labs(x = \"Salary (USD)\", title = \"Data scientist salary\") +\n",
    "    scale_x_continuous(labels = scales::dollar_format()) + # so salaries aren't in scientific notation\n",
    "    coord_cartesian(xlim = c(0, 300000), ylim = c(0, 1e-05)) # same width x-axes\n",
    "\n",
    "salaries_pda_large <- salaries_new %>%\n",
    "    filter(company_size == \"L\") %>%\n",
    "    filter(job_title == \"Data Analyst\")\n",
    "\n",
    "pda_salary_dist <- salaries_pda_large %>% # data analyst salary distribution for large companies\n",
    "    ggplot(aes(x = salary_in_usd, y = after_stat(density))) +\n",
    "    geom_histogram(binwidth = 20000) +\n",
    "    geom_vline(xintercept = mean(salaries_pda_large$salary_in_usd),\n",
    "              color = \"blue\") +\n",
    "    labs(x = \"Salary (USD)\", title = \"Data analyst salary\") +\n",
    "    scale_x_continuous(labels = scales::dollar_format()) + # so salaries aren't in scientific notation\n",
    "    coord_cartesian(xlim = c(0, 300000), ylim = c(0, 1e-05)) # same width x-axes\n",
    "\n",
    "grid.arrange(ds_salary_dist, pda_salary_dist, ncol = 2, top = \"Salary differences of large company sizes\")\n",
    "\n",
    "#======#======#======#======#======#======#======#======#======#======#======#======#======#======#======#======\n",
    "\n",
    "salaries_ds_medium <- salaries_new %>%\n",
    "    filter(company_size == \"M\") %>%\n",
    "    filter(job_title == \"Data Scientist\")\n",
    "\n",
    "ds_salary_dist <- salaries_ds_medium %>% # data analyst distribution\n",
    "    ggplot(aes(x = salary_in_usd, y = after_stat(density))) +\n",
    "    geom_histogram(binwidth = 20000) +\n",
    "    geom_vline(xintercept = mean(salaries_ds_medium$salary_in_usd),\n",
    "              color = \"blue\") +\n",
    "    labs(x = \"Salary (USD)\", title = \"Salary for data scientist\") +\n",
    "    scale_x_continuous(labels = scales::dollar_format()) + # so salaries aren't in scientific notation\n",
    "    coord_cartesian(xlim = c(0, 300000), ylim = c(0, 1e-05)) # same width x-axes\n",
    "\n",
    "salaries_pda_medium <- salaries_new %>%\n",
    "    filter(company_size == \"M\") %>%\n",
    "    filter(job_title == \"Data Analyst\")\n",
    "\n",
    "pda_salary_dist <- salaries_pda_medium %>% # data analyst distribution\n",
    "    ggplot(aes(x = salary_in_usd, y = after_stat(density))) +\n",
    "    geom_histogram(binwidth = 20000) +\n",
    "    geom_vline(xintercept = mean(salaries_pda_medium$salary_in_usd),\n",
    "              color = \"blue\") +\n",
    "    labs(x = \"Salary (USD)\", title = \"Salary for data analyst\") +\n",
    "    scale_x_continuous(labels = scales::dollar_format()) + # so salaries aren't in scientific notation\n",
    "    coord_cartesian(xlim = c(0, 300000), ylim = c(0, 1e-05)) # same width x-axes\n",
    "\n",
    "grid.arrange(ds_salary_dist, pda_salary_dist, ncol = 2, top = \"Salary differences of medium company sizes\")\n",
    "\n",
    "#======#======#======#======#======#======#======#======#======#======#======#======#======#======#======#======\n",
    "\n",
    "salaries_ds_small <- salaries_new %>%\n",
    "    filter(company_size == \"S\") %>%\n",
    "    filter(job_title == \"Data Scientist\")\n",
    "\n",
    "ds_salary_dist <- salaries_ds_small %>% # data analyst distribution\n",
    "    ggplot(aes(x = salary_in_usd, y = after_stat(density))) +\n",
    "    geom_histogram(binwidth = 20000) +\n",
    "    geom_vline(xintercept = mean(salaries_ds_small$salary_in_usd),\n",
    "              color = \"blue\") +\n",
    "    labs(x = \"Salary (USD)\", title = \"Salary for data scientist\") +\n",
    "    scale_x_continuous(labels = scales::dollar_format()) + # so salaries aren't in scientific notation\n",
    "    coord_cartesian(xlim = c(0, 300000), ylim = c(0, 1e-05)) # same width x-axes\n",
    "\n",
    "salaries_pda_small <- salaries_new %>%\n",
    "    filter(company_size == \"S\") %>%\n",
    "    filter(job_title == \"Data Analyst\")\n",
    "\n",
    "pda_salary_dist <- salaries_pda_small %>% # data analyst distribution\n",
    "    ggplot(aes(x = salary_in_usd, y = after_stat(density))) +\n",
    "    geom_histogram(binwidth = 20000) +\n",
    "    geom_vline(xintercept = mean(salaries_pda_small$salary_in_usd),\n",
    "              color = \"blue\") +\n",
    "    labs(x = \"Salary (USD)\", title = \"Salary for data analyst\") +\n",
    "    scale_x_continuous(labels = scales::dollar_format()) + # so salaries aren't in scientific notation\n",
    "    coord_cartesian(xlim = c(0, 300000), ylim = c(0, 1e-05)) # same width x-axes\n",
    "\n",
    "grid.arrange(ds_salary_dist, pda_salary_dist, ncol = 2, top = \"Salary differences of small company sizes\")\n",
    "\n",
    "#======#======#======#======#======#======#======#======#======#======#======#======#======#======#======#======\n",
    "# since we can see that \n",
    "\n",
    "\n",
    "ds_salary_dist <- salaries_new %>% # data analyst distribution\n",
    "    filter(job_title == \"Data Scientist\") %>%\n",
    "    ggplot(aes(x = salary_in_usd, y = after_stat(density))) +\n",
    "    geom_histogram(binwidth = 20000) +\n",
    "    geom_vline(xintercept = mean(filter(salaries_new, job_title == \"Data Scientist\")$salary_in_usd),\n",
    "              color = \"blue\") +\n",
    "    labs(x = \"Salary (USD)\", title = \"Salary for data scientist\") +\n",
    "    scale_x_continuous(labels = scales::dollar_format()) + # so salaries aren't in scientific notation\n",
    "    coord_cartesian(xlim = c(0, 300000), ylim = c(0, 1e-05)) # same width x-axes\n",
    "\n",
    "pda_salary_dist <- salaries_new %>% # data analyst distribution\n",
    "    filter(job_title == \"Data Analyst\") %>%\n",
    "    ggplot(aes(x = salary_in_usd, y = after_stat(density))) +\n",
    "    geom_histogram(binwidth = 20000) +\n",
    "    geom_vline(xintercept = mean(filter(salaries_new, job_title == \"Data Analyst\")$salary_in_usd),\n",
    "              color = \"blue\") +\n",
    "    labs(x = \"Salary (USD)\", title = \"Salary for data analyst\") +\n",
    "    scale_x_continuous(labels = scales::dollar_format()) + # so salaries aren't in scientific notation\n",
    "    coord_cartesian(xlim = c(0, 300000), ylim = c(0, 1e-05)) # same width x-axes\n",
    "\n",
    "grid.arrange(ds_salary_dist, pda_salary_dist, ncol = 2, top = \"Salary differences of all company sizes\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "vscode": {
     "languageId": "r"
    }
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Warning message in job_title == \"Data Analyst\" || job_title == \"Data Scientist\":\n",
      "“'length(x) = 96 > 1' in coercion to 'logical(1)'”\n",
      "Warning message in job_title == \"Data Analyst\" || job_title == \"Data Scientist\":\n",
      "“'length(x) = 129 > 1' in coercion to 'logical(1)'”\n",
      "Warning message in job_title == \"Data Analyst\" || job_title == \"Data Scientist\":\n",
      "“'length(x) = 129 > 1' in coercion to 'logical(1)'”\n",
      "Warning message in job_title == \"Data Analyst\" || job_title == \"Data Scientist\":\n",
      "“'length(x) = 140 > 1' in coercion to 'logical(1)'”\n",
      "Warning message in job_title == \"Data Analyst\" || job_title == \"Data Scientist\":\n",
      "“'length(x) = 140 > 1' in coercion to 'logical(1)'”\n",
      "Warning message in job_title == \"Data Analyst\" || job_title == \"Data Scientist\":\n",
      "“'length(x) = 41 > 1' in coercion to 'logical(1)'”\n",
      "Warning message in job_title == \"Data Analyst\" || job_title == \"Data Scientist\":\n",
      "“'length(x) = 41 > 1' in coercion to 'logical(1)'”\n"
     ]
    },
    {
     "data": {
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8Nbjhj/YRHNo79+mD19kmb23O5FUh4lLNVj3tIOcUkPH2z/fMKJKuUdRB6GhUvl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",
      "text/plain": [
       "plot without title"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 240,
       "width": 420
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# We also want to visualize data for the proportions of remote work employees, and we only consider remote workers as those who work fully remotely \n",
    "\n",
    "options(repr.plot.width = 7, repr.plot.height = 4)\n",
    "\n",
    "remote_prop_visual <- salaries_new %>%\n",
    "    filter(job_title == \"Data Analyst\" || job_title == \"Data Scientist\") %>%\n",
    "    ggplot(aes(x = job_title, fill = remote_ratio == \"remote\")) +\n",
    "    geom_bar(position = \"fill\", width = 0.7) +\n",
    "    xlab(\"Job title\") +\n",
    "    ylab(\"Proportion\") +\n",
    "    ggtitle(\"Proportions of data science jobs working remotely\") +\n",
    "    labs(fill = \"Fully remote\")\n",
    "\n",
    "remote_prop_visual"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Estimates"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "vscode": {
     "languageId": "r"
    }
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table class=\"dataframe\">\n",
       "<caption>A tibble: 4 × 6</caption>\n",
       "<thead>\n",
       "\t<tr><th scope=col>job_title</th><th scope=col>n</th><th scope=col>salary_mean</th><th scope=col>salary_sd</th><th scope=col>remote_prop</th><th scope=col>remote_sd</th></tr>\n",
       "\t<tr><th scope=col>&lt;chr&gt;</th><th scope=col>&lt;int&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;dbl&gt;</th></tr>\n",
       "</thead>\n",
       "<tbody>\n",
       "\t<tr><td>Data Analyst             </td><td> 96</td><td> 93752.84</td><td>39258.60</td><td>0.7291667</td><td>0.4443902</td></tr>\n",
       "\t<tr><td>Data Engineer            </td><td>129</td><td>114224.82</td><td>57349.85</td><td>0.7131783</td><td>0.4522776</td></tr>\n",
       "\t<tr><td>Data Scientist           </td><td>140</td><td>108922.79</td><td>64372.43</td><td>0.5571429</td><td>0.4967240</td></tr>\n",
       "\t<tr><td>Machine Learning Engineer</td><td> 41</td><td>104880.15</td><td>63218.63</td><td>0.5365854</td><td>0.4986597</td></tr>\n",
       "</tbody>\n",
       "</table>\n"
      ],
      "text/latex": [
       "A tibble: 4 × 6\n",
       "\\begin{tabular}{llllll}\n",
       " job\\_title & n & salary\\_mean & salary\\_sd & remote\\_prop & remote\\_sd\\\\\n",
       " <chr> & <int> & <dbl> & <dbl> & <dbl> & <dbl>\\\\\n",
       "\\hline\n",
       "\t Data Analyst              &  96 &  93752.84 & 39258.60 & 0.7291667 & 0.4443902\\\\\n",
       "\t Data Engineer             & 129 & 114224.82 & 57349.85 & 0.7131783 & 0.4522776\\\\\n",
       "\t Data Scientist            & 140 & 108922.79 & 64372.43 & 0.5571429 & 0.4967240\\\\\n",
       "\t Machine Learning Engineer &  41 & 104880.15 & 63218.63 & 0.5365854 & 0.4986597\\\\\n",
       "\\end{tabular}\n"
      ],
      "text/markdown": [
       "\n",
       "A tibble: 4 × 6\n",
       "\n",
       "| job_title &lt;chr&gt; | n &lt;int&gt; | salary_mean &lt;dbl&gt; | salary_sd &lt;dbl&gt; | remote_prop &lt;dbl&gt; | remote_sd &lt;dbl&gt; |\n",
       "|---|---|---|---|---|---|\n",
       "| Data Analyst              |  96 |  93752.84 | 39258.60 | 0.7291667 | 0.4443902 |\n",
       "| Data Engineer             | 129 | 114224.82 | 57349.85 | 0.7131783 | 0.4522776 |\n",
       "| Data Scientist            | 140 | 108922.79 | 64372.43 | 0.5571429 | 0.4967240 |\n",
       "| Machine Learning Engineer |  41 | 104880.15 | 63218.63 | 0.5365854 | 0.4986597 |\n",
       "\n"
      ],
      "text/plain": [
       "  job_title                 n   salary_mean salary_sd remote_prop remote_sd\n",
       "1 Data Analyst               96  93752.84   39258.60  0.7291667   0.4443902\n",
       "2 Data Engineer             129 114224.82   57349.85  0.7131783   0.4522776\n",
       "3 Data Scientist            140 108922.79   64372.43  0.5571429   0.4967240\n",
       "4 Machine Learning Engineer  41 104880.15   63218.63  0.5365854   0.4986597"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Here, we will calcualte basic point estimate statistics for future inferences.\n",
    "\n",
    "data_estimates <- salaries_new %>%\n",
    "    group_by(job_title) %>%\n",
    "    summarize(n = n(),\n",
    "              salary_mean = mean(salary_in_usd), \n",
    "              salary_sd = sd(salary_in_usd), \n",
    "              remote_prop = mean(remote_ratio == \"remote\"), \n",
    "              remote_sd = sqrt(remote_prop * (1 - remote_prop)))\n",
    "\n",
    "head(data_estimates)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "tags": []
   },
   "source": [
    "# Methods"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Up till now, the report has demonstrated differences in mean salaries and proportions of remote work among Data Scientists and Data Analysts. To ensure randomness, representative samples of full-time employees with sample sizes greater than 30 were used.\n",
    "However, relying on point estimates and plots alone is not enough to establish these differences. Therefore, to address this issue, the report proposes using the Central Limit Theorem, as the samples are roughly normally distributed and less computationally intensive than resampling methods.\n",
    "By letting Data Scientists be population 1, and Data Analysts as population 2, we aim to test the following hypothesis for the mean salary:\n",
    "$$H_0 : \\mu_2 - \\mu_1 = 0$$\n",
    "$$H_1 : \\mu_2 - \\mu_1 \\neq 0$$\n",
    "\n",
    "for the proportion of remote work:\n",
    "$$H_0 : p_2 - p_1 = 0$$\n",
    "$$H_1 : p_2 - p_1 \\neq 0$$\n",
    "\n",
    "where $\\mu$ is the population's mean salary and $p$ is its proportion of employees working remotely. \n",
    "\n",
    "We expect to reject both null hypotheses, and will include a 90% confidence interval in our final report.\n",
    "\n",
    "### Impact\n",
    "\n",
    "The outcomes of these findings could affect the decisions of newly graduated data scientists in terms of which job positions to seek and which career paths to focus on during their undergraduate studies.\n",
    "\n",
    "### Future\n",
    "\n",
    "This prompts further questions about how differences in experience, company location, and company size may affect the comparison of job titles in the field of Data Science. Additionally, with more data, these issues can be explored for the other professions that were not thoroughly examined due to limitations in sample size and distribution."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# References"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Bhatia, R. (2022). *Data science job salaries*. https://www.kaggle.com/datasets/ruchi798/data-science-job-salaries\n",
    "\n",
    "Card, D., Mas, A., Moretti, E., & Saez, E. (2012). Inequality at work: The effect of peer salaries on job satisfaction. *American Economic Review*, 102(6), 2981–3003. https://doi.org/10.1257/aer.102.6.2981\n",
    "\n",
    "Galanti, T., Guidetti, G., Mazzei, E., Zappalà, S., & Toscano, F. (2021). Work from home during the COVID-19 outbreak: the impact on employees' remote work productivity, engagement, and stress. *Journal of Occupational and Environmental Medicine*, 63(7), e426–e432. https://doi.org/10.1097/JOM.0000000000002236"
   ]
  }
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