{
  "cells": [
    {
      "metadata": {
        "slideshow": {
          "slide_type": "slide"
        },
        "toc": "true"
      },
      "cell_type": "markdown",
      "source": "<h1>Table of Contents<span class=\"tocSkip\"></span></h1>\n<div class=\"toc\"><ul class=\"toc-item\"><li><span><a href=\"#Terminology\" data-toc-modified-id=\"Terminology-1\"><span class=\"toc-item-num\">1&nbsp;&nbsp;</span>Terminology</a></span></li><li><span><a href=\"#Sampling-Distribution\" data-toc-modified-id=\"Sampling-Distribution-2\"><span class=\"toc-item-num\">2&nbsp;&nbsp;</span>Sampling Distribution</a></span></li><li><span><a href=\"#Central-Limit-Theorem\" data-toc-modified-id=\"Central-Limit-Theorem-3\"><span class=\"toc-item-num\">3&nbsp;&nbsp;</span>Central Limit Theorem</a></span></li><li><span><a href=\"#z-Score-and-t-Values\" data-toc-modified-id=\"z-Score-and-t-Values-4\"><span class=\"toc-item-num\">4&nbsp;&nbsp;</span>z Score and t Values</a></span></li></ul></div>"
    },
    {
      "metadata": {
        "slideshow": {
          "slide_type": "slide"
        }
      },
      "cell_type": "markdown",
      "source": "## Terminology"
    },
    {
      "metadata": {
        "slideshow": {
          "slide_type": "slide"
        }
      },
      "cell_type": "markdown",
      "source": "**Population:**  population is the broader group of people to whom you intend to generalize the results of your study.\n  \n**Sample:**   sample is the group of individuals who participate in your study, always be a subset of your population.     \n  \n**Statistic:**  A statistic is a characteristic of a sample  \n  \n**Parameter:**  A parameter is a characteristic of a population  "
    },
    {
      "metadata": {
        "run_control": {
          "frozen": false,
          "read_only": false
        },
        "slideshow": {
          "slide_type": "slide"
        }
      },
      "cell_type": "markdown",
      "source": "![Imgur](https://i.imgur.com/ewSO3nQ.png?1)"
    },
    {
      "metadata": {
        "slideshow": {
          "slide_type": "slide"
        }
      },
      "cell_type": "markdown",
      "source": "**sampling**   \nRandomly choosing a value such that the probability of picking any particular value is given by a probability distribution. This is known as sampling from the distribution. For example, here are 10 samples from a Bernoulli(0.7) distribution: false, true, false, false, true, true, true, false, true and true. If we took a very large number of samples from a Bernoulli(0.7) distribution then the percentage of the samples equal to true would be very close to 70%."
    },
    {
      "metadata": {
        "slideshow": {
          "slide_type": "slide"
        }
      },
      "cell_type": "markdown",
      "source": "## Sampling Distribution"
    },
    {
      "metadata": {
        "slideshow": {
          "slide_type": "slide"
        }
      },
      "cell_type": "markdown",
      "source": "> A sampling distribution is a probability distribution of a statistic obtained through a large number of samples drawn from a specific population."
    },
    {
      "metadata": {
        "slideshow": {
          "slide_type": "slide"
        }
      },
      "cell_type": "markdown",
      "source": "![Imgur](https://i.imgur.com/herhDH0.jpg)"
    },
    {
      "metadata": {
        "slideshow": {
          "slide_type": "slide"
        }
      },
      "cell_type": "markdown",
      "source": "## Central Limit Theorem"
    },
    {
      "metadata": {
        "slideshow": {
          "slide_type": "slide"
        }
      },
      "cell_type": "markdown",
      "source": "> The CLT says that if you take many repeated samples from a population, and calculate the averages or sum of each one, the collection of those averages will be normally distributed… and it doesn’t matter what the shape of the source distribution is!\n\n* CLT applies for reasonably large sample size (e.g., n = 30)\n\n"
    },
    {
      "metadata": {
        "slideshow": {
          "slide_type": "fragment"
        }
      },
      "cell_type": "markdown",
      "source": "**Central Limit Theorem applet**  \nhttp://bioinformatics.cruk.cam.ac.uk/apps/stats/central-limit-theorem/"
    },
    {
      "metadata": {
        "slideshow": {
          "slide_type": "slide"
        }
      },
      "cell_type": "markdown",
      "source": "![Imgur](https://i.imgur.com/QlZvCwT.png)"
    },
    {
      "metadata": {
        "run_control": {
          "frozen": false,
          "read_only": false
        },
        "scrolled": false,
        "slideshow": {
          "slide_type": "slide"
        },
        "trusted": false
      },
      "cell_type": "code",
      "source": " y = runif(1000)\n     par(mfrow = c(2,1))\n     hist(y)\n     out = vector()\n     for (i in 1:1000){\n     out_i = mean(sample(y, size = 3))\n     out = c(out, out_i)\n     }\n     hist(out)    ",
      "execution_count": 16,
      "outputs": [
        {
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pS8we7w8DBJkvmF4tL1R7YTpFqtVpog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\nEOwAACIh2AEAREKwAwCIhGAHABCJ/w8XStXIU0Gp/gAAAABJRU5ErkJggg==",
            "text/plain": "Plot with title \"Histogram of out\""
          },
          "metadata": {},
          "output_type": "display_data"
        }
      ]
    },
    {
      "metadata": {
        "slideshow": {
          "slide_type": "slide"
        }
      },
      "cell_type": "markdown",
      "source": "![Imgur](https://i.imgur.com/MWhdTgh.png?1)"
    },
    {
      "metadata": {
        "slideshow": {
          "slide_type": "slide"
        }
      },
      "cell_type": "markdown",
      "source": "**Sampling Distributions Applet:**  \nhttp://onlinestatbook.com/stat_sim/sampling_dist/index.html"
    },
    {
      "metadata": {
        "slideshow": {
          "slide_type": "slide"
        }
      },
      "cell_type": "markdown",
      "source": "![Imgur](https://i.imgur.com/ZyTw7rQ.png)"
    },
    {
      "metadata": {
        "collapsed": true,
        "run_control": {
          "frozen": false,
          "read_only": false
        },
        "slideshow": {
          "slide_type": "slide"
        },
        "trusted": false
      },
      "cell_type": "code",
      "source": "sdm.sim <- function(n,src.dist=NULL,param1=NULL,param2=NULL) {\n   r <- 10000  # Number of replications/samples - DO NOT ADJUST\n   # This produces a matrix of observations with  \n   # n columns and r rows. Each row is one sample:\n   my.samples <- switch(src.dist,\n\"E\" = matrix(rexp(n*r,param1),r),\n\"N\" = matrix(rnorm(n*r,param1,param2),r),\n\"U\" = matrix(runif(n*r,param1,param2),r),\n\"P\" = matrix(rpois(n*r,param1),r),\n\"B\" = matrix(rbinom(n*r,param1,param2),r),\n\"G\" = matrix(rgamma(n*r,param1,param2),r),\n\"X\" = matrix(rchisq(n*r,param1),r),\n\"T\" = matrix(rt(n*r,param1),r))\n   all.sample.sums <- apply(my.samples,1,sum)\n   all.sample.means <- apply(my.samples,1,mean)   \n   all.sample.vars <- apply(my.samples,1,var) \n   par(mfrow=c(2,2))\n   hist(my.samples[1,],col=\"gray\",main=\"Distribution of One Sample\")\n   hist(all.sample.sums,col=\"gray\",main=\"Sampling Distribution\\nof\nthe Sum\")\n   hist(all.sample.means,col=\"gray\",main=\"Sampling Distribution\\nof the Mean\")\n   hist(all.sample.vars,col=\"gray\",main=\"Sampling Distribution\\nof\nthe Variance\")\n}",
      "execution_count": 17,
      "outputs": []
    },
    {
      "metadata": {
        "run_control": {
          "frozen": false,
          "read_only": false
        },
        "slideshow": {
          "slide_type": "slide"
        },
        "trusted": false
      },
      "cell_type": "code",
      "source": "sdm.sim(50,src.dist=\"E\",param1=1)\n#source: https://qualityandinnovation.com/2015/03/30/sampling-distributions-and-central-limit-theorem-in-r/",
      "execution_count": 18,
      "outputs": [
        {
          "data": {
            "image/png": 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NhFtHUADLBWguKzs7PEQZJ2AjAMbR0AA6yboPjevXvqiEzaOR6Py6wYAGhFWwfA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\n7fVXX301a3Xf93Pf6YChfv755+wHf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            "text/plain": "Plot with title \"Sampling Distribution\nof\nthe Variance\""
          },
          "metadata": {},
          "output_type": "display_data"
        }
      ]
    },
    {
      "metadata": {
        "slideshow": {
          "slide_type": "slide"
        }
      },
      "cell_type": "markdown",
      "source": "![Imgur](https://i.imgur.com/4shGH5I.png)"
    },
    {
      "metadata": {
        "slideshow": {
          "slide_type": "slide"
        }
      },
      "cell_type": "markdown",
      "source": "## z Score and t Values"
    },
    {
      "metadata": {
        "slideshow": {
          "slide_type": "slide"
        }
      },
      "cell_type": "markdown",
      "source": "![Imgur](https://i.imgur.com/kqfCUH6.png)"
    },
    {
      "metadata": {
        "slideshow": {
          "slide_type": "slide"
        }
      },
      "cell_type": "markdown",
      "source": "![Imgur](https://i.imgur.com/Hy8jXsc.png)"
    },
    {
      "metadata": {
        "run_control": {
          "marked": false
        },
        "slideshow": {
          "slide_type": "slide"
        }
      },
      "cell_type": "markdown",
      "source": "<span style=\"color:red; font-family:Comic Sans MS\">References</span>   \n<a href=\"http://www.mbmlbook.com/MurderMystery.html\" target=\"_blank\">http://www.mbmlbook.com/MurderMystery.html</a>\n"
    }
  ],
  "metadata": {
    "celltoolbar": "Slideshow",
    "hide_input": false,
    "kernelspec": {
      "name": "r",
      "display_name": "R",
      "language": "R"
    },
    "language_info": {
      "codemirror_mode": "r",
      "file_extension": ".r",
      "mimetype": "text/x-r-source",
      "name": "R",
      "pygments_lexer": "r",
      "version": "3.4.3"
    },
    "nav_menu": {},
    "toc": {
      "nav_menu": {},
      "number_sections": true,
      "sideBar": true,
      "skip_h1_title": false,
      "base_numbering": 1,
      "title_cell": "Table of Contents",
      "title_sidebar": "Contents",
      "toc_cell": true,
      "toc_position": {},
      "toc_section_display": "block",
      "toc_window_display": false
    }
  },
  "nbformat": 4,
  "nbformat_minor": 2
}