lectures/lecture-18-code.ipynb

{
  "cells": [
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "view-in-github",
        "colab_type": "text"
      },
      "source": [
        "<a href=\"https://colab.research.google.com/github/5harad/API201-students/blob/main/lectures/lecture-18-code.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
      ]
    },
    {
      "cell_type": "markdown",
      "id": "c8f6d4f7",
      "metadata": {
        "id": "c8f6d4f7"
      },
      "source": [
        "# Lecture 18: Statistical significance and its limitations\n",
        "\n"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 1,
      "id": "1b211e6c",
      "metadata": {
        "id": "1b211e6c",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "173c71e9-a83a-4cea-ba29-55a5149ec839"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stderr",
          "text": [
            "Warning message in system(\"timedatectl\", intern = TRUE):\n",
            "“running command 'timedatectl' had status 1”\n",
            "── \u001b[1mAttaching packages\u001b[22m ─────────────────────────────────────── tidyverse 1.3.1 ──\n",
            "\n",
            "\u001b[32m✔\u001b[39m \u001b[34mggplot2\u001b[39m 3.3.6      \u001b[32m✔\u001b[39m \u001b[34mpurrr  \u001b[39m 0.3.5 \n",
            "\u001b[32m✔\u001b[39m \u001b[34mtibble \u001b[39m 3.1.7      \u001b[32m✔\u001b[39m \u001b[34mdplyr  \u001b[39m 1.0.10\n",
            "\u001b[32m✔\u001b[39m \u001b[34mtidyr  \u001b[39m 1.2.1      \u001b[32m✔\u001b[39m \u001b[34mstringr\u001b[39m 1.4.1 \n",
            "\u001b[32m✔\u001b[39m \u001b[34mreadr  \u001b[39m 2.1.3      \u001b[32m✔\u001b[39m \u001b[34mforcats\u001b[39m 0.5.2 \n",
            "\n",
            "── \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"
          ]
        }
      ],
      "source": [
        "library(tidyverse)\n",
        "\n",
        "theme_set(theme_bw())"
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "set.seed(1)"
      ],
      "metadata": {
        "id": "tiC2K2yp-nVp"
      },
      "id": "tiC2K2yp-nVp",
      "execution_count": 2,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "n1 <- 3000\n",
        "p1_hat <- 201 / 3000\n",
        "\n",
        "n2 <- 3000\n",
        "p2_hat <- 141 / 3000\n",
        "\n",
        "p1_hat - p2_hat"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 34
        },
        "id": "b63Cbpiv9fSc",
        "outputId": "46bbf6e0-a5cd-4192-a2ee-2f1ec480727d"
      },
      "id": "b63Cbpiv9fSc",
      "execution_count": 3,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/html": [
              "0.02"
            ],
            "text/markdown": "0.02",
            "text/latex": "0.02",
            "text/plain": [
              "[1] 0.02"
            ]
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "s <- sqrt(p1_hat*(1-p1_hat)/n1 + p2_hat*(1-p2_hat)/n2)\n",
        "s"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 34
        },
        "id": "Q994xsdA99Nk",
        "outputId": "7107c962-4ff5-4bd2-afd1-5f57292c33e2"
      },
      "id": "Q994xsdA99Nk",
      "execution_count": 4,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/html": [
              "0.00598057968204867"
            ],
            "text/markdown": "0.00598057968204867",
            "text/latex": "0.00598057968204867",
            "text/plain": [
              "[1] 0.00598058"
            ]
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "estimates <- rnorm(1e6, mean = 0, sd = s)"
      ],
      "metadata": {
        "id": "6eF2HSdoGZut"
      },
      "id": "6eF2HSdoGZut",
      "execution_count": 5,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "ggplot(tibble(Estimate = estimates), aes(x = Estimate)) +\n",
        "  geom_histogram(bins=50) +\n",
        "  scale_y_continuous('Number of worlds') +\n",
        "  scale_x_continuous(limits=c(-.03, .03)) +\n",
        "  geom_vline(xintercept = -2*s, color='red', linetype='dashed') +\n",
        "  geom_vline(xintercept = 2*s, color='red', linetype='dashed')\n",
        "ggsave('null-diff-in-prop.png', width=4, height=4)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 437
        },
        "id": "gRwJVONOYujf",
        "outputId": "a5a15f1f-f879-4489-968d-768df51278f3"
      },
      "id": "gRwJVONOYujf",
      "execution_count": 6,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "plot without title"
            ],
            "image/png": 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pBAI0fGnQASZcyYuBNAkdgVCwCQEood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\ngg=="
          },
          "metadata": {
            "image/png": {
              "width": 420,
              "height": 420
            }
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "z <- ( (p1_hat - p2_hat) - 0 ) / s\n",
        "z"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 34
        },
        "id": "rM_jA6uhOusA",
        "outputId": "1a9f157e-606b-49ad-becc-9a53489f562f"
      },
      "id": "rM_jA6uhOusA",
      "execution_count": 7,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/html": [
              "3.34415743343945"
            ],
            "text/markdown": "3.34415743343945",
            "text/latex": "3.34415743343945",
            "text/plain": [
              "[1] 3.344157"
            ]
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "p_value <- 2*pnorm(-abs(z))\n",
        "p_value"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 34
        },
        "id": "U4zon7_hO-dx",
        "outputId": "6383133b-57d6-45f4-9c66-9fdbc6c689aa"
      },
      "id": "U4zon7_hO-dx",
      "execution_count": 8,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/html": [
              "0.000825328874622567"
            ],
            "text/markdown": "0.000825328874622567",
            "text/latex": "0.000825328874622567",
            "text/plain": [
              "[1] 0.0008253289"
            ]
          },
          "metadata": {}
        }
      ]
    }
  ],
  "metadata": {
    "colab": {
      "provenance": [],
      "collapsed_sections": [],
      "include_colab_link": true
    },
    "kernelspec": {
      "display_name": "R",
      "language": "R",
      "name": "ir"
    },
    "language_info": {
      "codemirror_mode": "r",
      "file_extension": ".r",
      "mimetype": "text/x-r-source",
      "name": "R",
      "pygments_lexer": "r",
      "version": "4.2.1"
    }
  },
  "nbformat": 4,
  "nbformat_minor": 5
}