class: center, middle, inverse, title-slide .title[ # <font size="7" color="Black">Comparing Potential Sampling Plans</font> ] .author[ ### <font size="5" color="Black"> Kyle Weber and Ian Vanwright </font> ] .institute[ ### <font size="6" color="gold">Prepared For: STA 490 </font><br> ] .date[ ### <font color="gold" size="6"> West Chester University of Pennsylvania <br> </font> <font color="gold" size="6"> </font> <br><br> <font color="white" size="3"> Slides available at: <a href="https://rpubs.com/IV246" class="uri">https://rpubs.com/IV246</a> AND <a href="https://github.com/Kyle-Weber/STA490" class="uri">https://github.com/Kyle-Weber/STA490</a></font> ] --- class: top, center ## Table of Contents: .left[ - Data Cleaning - Combining Categories - Default Rate - Analyzing Four Sampling Plans - Comparing Default Rates - Default Rate Visualization - Conclusion ] --- class: top, center ## Data Cleaning .left[ - Original data set contained 899,150 observations, was split into 9 files - All 9 data files were combined into 1 data set when loaded - Removed all missing values for MIS_Status and State - Changed currency values to numerical - Remaining observations is 897153 ] --- class: top, center ## Combining Categories .left[ - Variable "State" combined into 5 regions - Represent geographical region - Frequency Table of Regions - Lowest is SouthWest ] |Region | Frequency| |:------|---------:| |MW | 202581| |NE | 202423| |SE | 140841| |SW | 90202| |W | 263103| --- ## Calculating Default Rates .left[ - Original rates for data set - Provides a comparison to the sampling plans - Southeast has the highest rate ] <!--If need time can talk about why they are important--> |State | Default Rate| |:-----|------------:| |MW | 0.1583021| |NE | 0.1611872| |SE | 0.2141990| |SW | 0.1934325| |W | 0.1719593| --- class: top, center ## Simple Random Sampling Process .left[ - Random Sample of 4000 <!-- why 4000 less than 5% of original data set --> - Taken from Cleaned Data Set - Frequency and Default Rate Table ] |Size | Var.count| |:---------|---------:| |Size | 4000| |Var.count | 28| |Region | Sample_Default_Rate| |:------|-------------------:| |SE | 0.2083333| |W | 0.1719418| |MW | 0.1455982| |SW | 0.2198391| |NE | 0.1445148| --- class: top, center ## Systematic Sample .left[ - Jump size of 4000 observations - Selects observations from fixed intervals - Representative of entire population - Rounding Error ] | Size| Var.count| |----:|---------:| | 4014| 28| |Region | Sample_Default_Rate| |:------|-------------------:| |SE | 0.1855346| |NE | 0.1571429| |W | 0.1692177| |MW | 0.1399317| |SW | 0.1985472| --- class: top, center ## Stratified Sampling .left[ - Strata size for regions ] | MW| NE| SE| SW| W| |---:|---:|---:|---:|----:| | 901| 901| 627| 401| 1170| |Region | Sample_Default_Rate| |:------|-------------------:| |MW | 0.1642619| |NE | 0.1653718| |SE | 0.2216906| |SW | 0.1695761| |W | 0.1632479| --- class: top, center ## Cluster Sampling .left[ - ZipCode used to Define Clusters - Finally, a cluster sample of Zip code is taken with the size and variable count shown below. ] |Size | Var.count| |:---------|---------:| |Size | 283| |Var.count | 28| |Region | Default Rate| |:------|------------:| |MW | 0.0714286| |NE | 0.1931818| |SE | 0.2575758| |SW | 0.0000000| |W | 0.2127660| --- class: top, center ## Default Rate Comparison .left[ - Comparison of Default Rates across regions - Sample Default Rate vs Subpopulation Default Rate - Systematic or Stratified ] <div class="figure"> <div class="datatables html-widget html-fill-item" id="htmlwidget-30c4907b4720388a5c2e" style="width:100%;height:auto;"></div> <script type="application/json" data-for="htmlwidget-30c4907b4720388a5c2e">{"x":{"filter":"none","vertical":false,"data":[["1","2","3","4","5","6","7","8","9","10","11","12","13","14","15","16","17","18","19","20"],["Simple Random","Simple Random","Simple Random","Simple Random","Simple Random","Systematic","Systematic","Systematic","Systematic","Systematic","Clustering","Clustering","Clustering","Clustering","Clustering","Stratified","Stratified","Stratified","Stratified","Stratified"],["SE","W","MW","SW","NE","SE","NE","W","MW","SW","NE","SE","W","MW","SW","MW","NE","SE","SW","W"],[0.20833,0.17194,0.1456,0.21984,0.14451,0.18553,0.15714,0.16922,0.13993,0.19855,0.19318,0.25758,0.21277,0.07142999999999999,0,0.16426,0.16537,0.22169,0.16958,0.16325],[0.2142,0.17196,0.1583,0.19343,0.16119,0.2142,0.16119,0.17196,0.1583,0.19343,0.16119,0.2142,0.17196,0.1583,0.19343,0.1583,0.16119,0.2142,0.19343,0.17196]],"container":"<table class=\"display\">\n <thead>\n <tr>\n <th> <\/th>\n <th>Sampling_Plan<\/th>\n <th>Region<\/th>\n <th>Sample_Default_Rate<\/th>\n <th>Subpopulation_Default_Rate<\/th>\n <\/tr>\n <\/thead>\n<\/table>","options":{"dom":"t","pageLength":61,"scrollY":"200px","scrollCollapse":true,"columnDefs":[{"className":"dt-right","targets":[3,4]},{"orderable":false,"targets":0},{"name":" ","targets":0},{"name":"Sampling_Plan","targets":1},{"name":"Region","targets":2},{"name":"Sample_Default_Rate","targets":3},{"name":"Subpopulation_Default_Rate","targets":4}],"order":[],"autoWidth":false,"orderClasses":false,"lengthMenu":[10,25,50,61,100]}},"evals":[],"jsHooks":[]}</script> <p class="caption">Summary of inferential statistics of the full model</p> </div> --- ## Comparrison Between Each other - Default Rate for each Region Based on Sampling Plan <img src="490Grp2.Rmd_files/figure-html/interactive-comparison-1.png" width="120%" /> --- ## Visualization for final choice ``` ## <ggproto object: Class FacetWrap, Facet, gg> ## compute_layout: function ## draw_back: function ## draw_front: function ## draw_labels: function ## draw_panels: function ## finish_data: function ## init_scales: function ## map_data: function ## params: list ## setup_data: function ## setup_params: function ## shrink: TRUE ## train_scales: function ## vars: function ## super: <ggproto object: Class FacetWrap, Facet, gg> ``` <img src="490Grp2.Rmd_files/figure-html/interactive sample defaul-1.png" width="120%" /> --- <img src="490Grp2.Rmd_files/figure-html/interactive sample default-1.png" width="120%" /> --- ## Visualization for final choice <img src="490Grp2.Rmd_files/figure-html/interactive-sample default 2-1.png" width="130%" /> --- ## Conclusion - why this is important - uses - Questions