class: middle center hide-slide-number monash-bg-gray80 .info-box.w-50.bg-white[ These slides are viewed best by Chrome or Firefox and occasionally need to be refreshed if elements did not load properly. See <a href=lecture-05A.pdf>here for the PDF <i class="fas fa-file-pdf"></i></a>. ] <br> .white[Press the **right arrow** to progress to the next slide!] --- class: title-slide count: false background-image: url("images/bg-01.png") # .monash-blue[ETC5521: Exploratory Data Analysis] <h1 class="monash-blue" style="font-size: 30pt!important;"></h1> <br> <h2 style="font-weight:900!important;">Working with a single variable, making transformations, detecting outliers, using robust statistics</h2> .bottom_abs.width100[ Lecturer: *Di Cook* <i class="fas fa-envelope"></i> ETC5521.Clayton-x@monash.edu <i class="fas fa-calendar-alt"></i> Week 5 - Session 1 <br> ] --- class: transition middle # Continuous variables This lecture is partly based on Chapter 3 of Unwin (2015) Graphical Data Analysis with R --- # Possible features of a single continuous variable <table class=" lightable-classic" style='font-family: "Arial Narrow", "Source Sans Pro", sans-serif; margin-left: auto; margin-right: auto;'> <thead> <tr> <th style="text-align:left;"> Feature </th> <th style="text-align:left;"> Example </th> <th style="text-align:left;"> Description </th> </tr> </thead> <tbody> <tr> <td style="text-align:left;"> Asymmetry </td> <td style="text-align:left;"> <img src="images/week4A/plots-1.png" height="54px"> </td> <td style="text-align:left;"> The distribution is not symmetrical. </td> </tr> <tr> <td style="text-align:left;"> Outliers </td> <td style="text-align:left;"> <img src="images/week4A/plots-2.png" height="54px"> </td> <td style="text-align:left;"> Some observations are that are far from the rest. </td> </tr> <tr> <td style="text-align:left;"> Multimodality </td> <td style="text-align:left;"> <img src="images/week4A/plots-3.png" height="54px"> </td> <td style="text-align:left;"> There are more than one "peak" in the observations. </td> </tr> <tr> <td style="text-align:left;"> Gaps </td> <td style="text-align:left;"> <img src="images/week4A/plots-4.png" height="54px"> </td> <td style="text-align:left;"> Some continuous interval that are contained within the range but no observations exists. </td> </tr> <tr> <td style="text-align:left;"> Heaping </td> <td style="text-align:left;"> <img src="images/week4A/plots-5.png" height="54px"> </td> <td style="text-align:left;"> Some values occur unexpectedly often. </td> </tr> <tr> <td style="text-align:left;"> Discretized </td> <td style="text-align:left;"> <img src="images/week4A/plots-6.png" height="54px"> </td> <td style="text-align:left;"> Only certain values are found, e.g. due to rounding. </td> </tr> <tr> <td style="text-align:left;"> Implausible </td> <td style="text-align:left;"> <img src="images/week4A/plots-7.png" height="54px"> </td> <td style="text-align:left;"> Values outside of plausible or likely range. </td> </tr> </tbody> </table> --- # Numerical features of a single continuous variables <img src="images/week5A/example-plot-1.png" width="432" style="display: block; margin: auto;" /> * A measure of .monash-blue[**_central tendency_**], e.g. mean, median and mode -- * A measure of .monash-blue[**_dispersion_**] (also called variability or spread), e.g. variance, standard deviation and interquartile range -- * There are other measures, e.g. .monash-blue[**_skewness_**] and .monash-blue[**_kurtosis_**] that measures "tailedness", but these are not as common as the measures of first two -- * The mean is also the _first moment_ and variance, skewness and kurtosis are _second, third, and fourth central moments_ -- **Significance tests** or **hypothesis tests** * Testing for `\(H_0: \mu = \mu_0\)` vs. `\(H_1: \mu \neq \mu_0\)` (often `\(\mu_0 = 0\)`) * The `\(t\)`-test is commonly used if the underlying data are believed to be normally distributed --- # .orange[Case study] .circle.bg-orange.white[1] 2019 Australian Federal Election .f4[Part 1/8] .flex[ .w-70[ **Context** * There are 151 seats in the House of Representative for the 2019 Australian federal election * The major parties in Australia are: * the .monash-blue[**Coalition**], comprising of the: * **Liberal**, * **Liberal National** <span class="f6">(Qld)</span>, * **National**, and * **Country Liberal** <span class="f6">(NT)</span> parties, and * the Australian .monash-blue[**Labor**] party * The .green[**Greens**] party is a small but notable party ] .w-30.center[ <img src="https://upload.wikimedia.org/wikipedia/commons/3/39/Scott_Morrison_2014_%28cropped_2%29.jpg" class="w-50 ba" alt="Scott Morrison"> <img src="https://upload.wikimedia.org/wikipedia/commons/7/7d/Bill_Shorten-crop.jpg" class="w-50 ba" alt="Bill Shorten"> ] ] --- # .orange[Case study] .circle.bg-orange.white[1] 2019 Australian Federal Election .f4[Part 2/8] .f5[<i class="fas fa-database"></i> https://results.aec.gov.au/24310/Website/Downloads/HouseFirstPrefsByCandidateByVoteTypeDownload-24310.csv] <div id="tab1A" style="width:1150px;height:auto;" class="datatables html-widget "></div> <script type="application/json" 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class=\"display\">\n <thead>\n <tr>\n <th>StateAb<\/th>\n <th>DivisionID<\/th>\n <th>DivisionNm<\/th>\n <th>CandidateID<\/th>\n <th>Surname<\/th>\n <th>GivenNm<\/th>\n <th>BallotPosition<\/th>\n <th>Elected<\/th>\n <th>HistoricElected<\/th>\n <th>PartyAb<\/th>\n <th>PartyNm<\/th>\n <th>OrdinaryVotes<\/th>\n <th>AbsentVotes<\/th>\n <th>ProvisionalVotes<\/th>\n <th>PrePollVotes<\/th>\n <th>PostalVotes<\/th>\n <th>TotalVotes<\/th>\n <th>Swing<\/th>\n <\/tr>\n <\/thead>\n<\/table>","options":{"dom":"Bft","pageLength":-1,"searching":true,"scrollX":true,"scrollY":"380px","buttons":[{"extend":"copy","filename":"Australian Federal Election 2019"},{"extend":"csv","filename":"aus-election-2019"}],"columnDefs":[{"targets":17,"render":"function(data, type, row, meta) {\n return type !== 'display' ? data : DTWidget.formatRound(data, 2, 3, \",\", \".\", null);\n }"},{"targets":11,"render":"function(data, type, row, meta) {\n return type !== 'display' ? data : DTWidget.formatRound(data, 0, 3, \",\", \".\", null);\n }"},{"targets":12,"render":"function(data, type, row, meta) {\n return type !== 'display' ? data : DTWidget.formatRound(data, 0, 3, \",\", \".\", null);\n }"},{"targets":13,"render":"function(data, type, row, meta) {\n return type !== 'display' ? data : DTWidget.formatRound(data, 0, 3, \",\", \".\", null);\n }"},{"targets":14,"render":"function(data, type, row, meta) {\n return type !== 'display' ? data : DTWidget.formatRound(data, 0, 3, \",\", \".\", null);\n }"},{"targets":15,"render":"function(data, type, row, meta) {\n return type !== 'display' ? data : DTWidget.formatRound(data, 0, 3, \",\", \".\", null);\n }"},{"targets":16,"render":"function(data, type, row, meta) {\n return type !== 'display' ? data : DTWidget.formatRound(data, 0, 3, \",\", \".\", null);\n }"},{"className":"dt-right","targets":[11,12,13,14,15,16,17]}],"order":[],"autoWidth":false,"orderClasses":false,"lengthMenu":[-1,10,25,50,100]},"callback":"function(table) {\ntable.on('click.dt', 'tbody tr', function() {\n$(this).toggleClass('selected');\n})\n}"},"evals":["options.columnDefs.0.render","options.columnDefs.1.render","options.columnDefs.2.render","options.columnDefs.3.render","options.columnDefs.4.render","options.columnDefs.5.render","options.columnDefs.6.render","callback"],"jsHooks":[]}</script> .footnote.f5[ Data source: Australian Electoral Commission. (2019). Federal Elections (website), accessed August 2021. URL: https://results.aec.gov.au/ ] --- # .orange[Case study] .circle.bg-orange.white[1] 2019 Australian Federal Election .f4[Part 3/8] .question-box[ What is the number of the seats won in the House of Representatives by parties? ] -- .panelset[ .panel[.panel-name[📊] .flex[ .w-50[ <table class=" lightable-classic" style='font-size: 20px; font-family: "Arial Narrow", "Source Sans Pro", sans-serif; width: auto !important; margin-left: auto; margin-right: auto;'> <thead> <tr> <th style="text-align:left;"> Party </th> <th style="text-align:right;"> # of seats </th> </tr> </thead> <tbody> <tr> <td style="text-align:left;"> Coalition </td> <td style="text-align:right;"> 77 </td> </tr> <tr> <td style="text-align:left;padding-left: 2em;color: #C8C8C8 !important;" indentlevel="1"> Liberal </td> <td style="text-align:right;color: #C8C8C8 !important;"> 44 </td> </tr> <tr> <td style="text-align:left;padding-left: 2em;color: #C8C8C8 !important;" indentlevel="1"> Liberal National Party Of Queensland </td> <td style="text-align:right;color: #C8C8C8 !important;"> 23 </td> </tr> <tr> <td style="text-align:left;padding-left: 2em;color: #C8C8C8 !important;" indentlevel="1"> The Nationals </td> <td style="text-align:right;color: #C8C8C8 !important;"> 10 </td> </tr> <tr> <td style="text-align:left;"> Australian Labor Party </td> <td style="text-align:right;"> 68 </td> </tr> <tr> <td style="text-align:left;"> The Greens </td> <td style="text-align:right;"> 1 </td> </tr> <tr> <td style="text-align:left;"> Centre Alliance </td> <td style="text-align:right;"> 1 </td> </tr> <tr> <td style="text-align:left;"> Katter's Australian Party (Kap) </td> <td style="text-align:right;"> 1 </td> </tr> <tr> <td style="text-align:left;"> Independent </td> <td style="text-align:right;"> 3 </td> </tr> </tbody> </table> ] .w-50[ **What does this table tell you?** {{content}} ] ]] .panel[.panel-name[data] .scroll-sign[ .f5.s400[ ```r df1 <- read_csv(here::here("data/HouseFirstPrefsByCandidateByVoteTypeDownload-24310.csv"), skip = 1, col_types = cols( .default = col_character(), OrdinaryVotes = col_double(), AbsentVotes = col_double(), ProvisionalVotes = col_double(), PrePollVotes = col_double(), PostalVotes = col_double(), TotalVotes = col_double(), Swing = col_double() ) ) ``` ```r skimr::skim(df1) ``` ``` ## ── Data Summary ──────────────────────── ## Values ## Name df1 ## Number of rows 1207 ## Number of columns 18 ## _______________________ ## Column type frequency: ## character 11 ## numeric 7 ## ________________________ ## Group variables None ## ## ── Variable type: character ──────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────── ## skim_variable n_missing complete_rate min max empty n_unique whitespace ## 1 StateAb 0 1 2 3 0 8 0 ## 2 DivisionID 0 1 3 3 0 151 0 ## 3 DivisionNm 0 1 4 15 0 151 0 ## 4 CandidateID 0 1 3 5 0 1057 0 ## 5 Surname 0 1 2 18 0 890 0 ## 6 GivenNm 0 1 1 25 0 613 0 ## 7 BallotPosition 0 1 1 3 0 14 0 ## 8 Elected 0 1 1 1 0 2 0 ## 9 HistoricElected 0 1 1 1 0 2 0 ## 10 PartyAb 151 0.875 2 4 0 40 0 ## 11 PartyNm 2 0.998 5 61 0 45 0 ## ## ── Variable type: numeric ────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────── ## skim_variable n_missing complete_rate mean sd p0 p25 p50 p75 p100 hist ## 1 OrdinaryVotes 0 1 10401. 12446. 167 1867 4317 14768. 54535 ▇▁▁▁▁ ## 2 AbsentVotes 0 1 511. 569. 13 117 246 711 3287 ▇▂▁▁▁ ## 3 ProvisionalVotes 0 1 41.4 51.7 0 8 20 56 444 ▇▁▁▁▁ ## 4 PrePollVotes 0 1 514. 607. 11 108. 211 761 5248 ▇▂▁▁▁ ## 5 PostalVotes 0 1 1033. 1476. 14 181 317 1216. 9837 ▇▁▁▁▁ ## 6 TotalVotes 0 1 12501. 14860. 250 2348 5196 18142 61202 ▇▁▁▁▁ ## 7 Swing 0 1 1.07 4.26 -28.1 -0.73 1.21 2.75 43.5 ▁▆▇▁▁ ``` ```r recode_party_names <- c( "Australian Labor Party (Northern Territory) Branch" = "Australian Labor Party", "Labor" = "Australian Labor Party", "The Greens (Vic)" = "The Greens", "The Greens (Wa)" = "The Greens", "Katter's Australian Party (KAP)" = "Katter's Australian Party", "Country Liberals (Nt)" = "Country Liberals (NT)" ) ``` ```r tdf1 <- df1 %>% filter(Elected == "Y") %>% mutate( PartyNm = str_to_title(PartyNm), PartyNm = recode(PartyNm, !!!recode_party_names) ) %>% count(PartyNm, sort = TRUE) %>% slice(2:4, 1, 8, 6, 7, 5) ``` ] ]] .panel[.panel-name[R] .f5[ <i class="fas fa-pencil-alt"></i> Note: `tidyverse` is expected to be loaded already. ```r data.frame(PartyNm = "Coalition", n = sum(tdf1$n[1:3])) %>% rbind(tdf1) %>% knitr::kable(col.names = c("Party", "# of seats")) %>% kableExtra::add_indent(2:4) %>% kableExtra::row_spec(2:4, color = "#C8C8C8") %>% kableExtra::kable_classic( full_width = FALSE, font_size = 20 ) ``` ]]] -- * The Coalition won the government * Labor and Coalition hold majority of the seats in the House of Representatives (lower house) * Parties such as The Greens, Centre Alliance and Katter's Australian Party (KAP) won _only_ a single seat {{content}} -- Only? {{content}} -- Wait... **Did the parties compete in all electoral districts?** --- # .orange[Case study] .circle.bg-orange.white[1] 2019 Australian Federal Election .f4[Part 4/8] .panelset[ .panel[.panel-name[📊] .flex[ .w-50[ <div id="tab1B" style="width:500px;height:auto;" class="datatables html-widget "></div> <script type="application/json" data-for="tab1B">{"x":{"filter":"none","vertical":false,"data":[["Australian Labor Party","Informal","The Greens","United Australia Party","Liberal","Independent","Pauline Hanson's One Nation","Fraser Anning's Conservative National Party","Animal Justice Party","Christian Democratic Party (Fred Nile Group)","Liberal National Party Of Queensland","The Nationals","Sustainable Australia","Western Australia Party","Rise Up Australia Party","Australian Christians","Liberal Democrats","Derryn Hinch's Justice Party","Labour Dlp","Shooters, Fishers And Farmers","Katter's Australian Party (Kap)","Science Party","Australian Progressives","The Great Australian Party","Australia First Party","Socialist Equality Party","Centre Alliance","Reason Australia","Socialist Alliance","Victorian Socialists","Citizens Electoral Council","Country Liberals (NT)",null,"Australian Better Families","Australian Democrats","Australian Workers Party","Child Protection Party","Involuntary Medication Objectors (Vaccination/Fluoride) Party","Love Australia Or Leave","National Party","Non-Custodial Parents Party (Equal Parenting)","Voteflux.org | Upgrade Democracy!"],[151,151,151,151,107,95,59,48,46,42,30,22,19,15,14,13,10,8,8,8,7,7,5,5,4,4,3,3,3,3,2,2,2,1,1,1,1,1,1,1,1,1]],"container":"<table class=\"display\">\n <thead>\n <tr>\n <th>Party<\/th>\n <th># of electorates<\/th>\n <\/tr>\n <\/thead>\n<\/table>","options":{"dom":"Bft","pageLength":-1,"searching":true,"scrollX":true,"scrollY":"400px","buttons":[{"extend":"copy","filename":"Australian Federal Election 2019 - Party Distribution"},{"extend":"csv","filename":"aus-election-2019-party-dist"}],"columnDefs":[{"className":"dt-right","targets":1}],"order":[],"autoWidth":false,"orderClasses":false,"lengthMenu":[-1,10,25,50,100]},"callback":"function(table) {\ntable.on('click.dt', 'tbody tr', function() {\n$(this).toggleClass('selected');\n})\n}"},"evals":["callback"],"jsHooks":[]}</script> ] .w-50[ **What do you notice from this table?** {{content}} ] ]] .panel[.panel-name[data] .f5[ ```r tdf2 <- df1 %>% mutate( PartyNm = str_to_title(PartyNm), PartyNm = recode(PartyNm, !!!recode_party_names) ) %>% count(PartyNm, sort = TRUE) ``` ]] .panel[.panel-name[R] .f5[ You can omit `table_options` and `toggle_select` or have a look at the source Rmd to find out what it is ```r tdf2 %>% DT::datatable( rownames = FALSE, escape = FALSE, width = "500px", options = table_options( scrollY = "400px", title = "Australian Federal Election 2019 - Party Distribution", csv = "aus-election-2019-party-dist" ), elementId = "tab1B", colnames = c("Party", "# of electorates"), callback = toggle_select ) ``` ]]] -- * The Greens are represented in every electoral districts * United Australia Party is the only other non-major party to be represented in every electoral district * KAP is represented in 7 electoral districts * Centre Alliance is only represented in 3 electoral districts! {{content}} -- Let's have a closer look at the Greens party... --- # .orange[Case study] .circle.bg-orange.white[1] 2019 Australian Federal Election .f4[Part 5/8] .panelset[ .panel[.panel-name[📊] .flex[ .w-70[ <img src="images/week5A/aus-election-plot1-1.png" width="720" style="display: block; margin: auto;" /> ] .w-30[ **What does this graph tell you?** {{content}} ] ]] .panel[.panel-name[data] .scroll-sign[ .f5.s500[ ```r tdf3 <- df1 %>% group_by(DivisionID) %>% summarise( DivisionNm = unique(DivisionNm), State = unique(StateAb), votes_GRN = TotalVotes[which(PartyAb == "GRN")], votes_total = sum(TotalVotes) ) %>% mutate(perc_GRN = votes_GRN / votes_total * 100) ``` ```r skimr::skim(tdf3) ``` ``` ## ── Data Summary ──────────────────────── ## Values ## Name tdf3 ## Number of rows 151 ## Number of columns 6 ## _______________________ ## Column type frequency: ## character 3 ## numeric 3 ## ________________________ ## Group variables None ## ## ── Variable type: character ──────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────── ## skim_variable n_missing complete_rate min max empty n_unique whitespace ## 1 DivisionID 0 1 3 3 0 151 0 ## 2 DivisionNm 0 1 4 15 0 151 0 ## 3 State 0 1 2 3 0 8 0 ## ## ── Variable type: numeric ────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────── ## skim_variable n_missing complete_rate mean sd p0 p25 p50 p75 p100 hist ## 1 votes_GRN 0 1 9821. 5581. 2744 6555 8676 11532. 45876 ▇▂▁▁▁ ## 2 votes_total 0 1 99925. 9801. 51009 96372. 100936 105588 116216 ▁▁▁▇▅ ## 3 perc_GRN 0 1 9.87 5.63 2.89 6.43 8.55 11.4 47.8 ▇▂▁▁▁ ``` ]]] .panel[.panel-name[R] .f5[ ```r tdf3 %>% ggplot(aes(perc_GRN)) + geom_histogram(color = "white", fill = "#00843D") + labs( x = "Percentage of first preference votes per division", y = "Count", title = "First preference votes for the Greens party" ) ``` ] ]] ??? * Australia uses full-preference instant-runoff voting in single member seats * Following the full allocation of preferences, it is possible to derive a two-party-preferred figure, where the votes have been allocated between the two main candidates in the election. * In Australia, this is usually between the candidates from the Coalition parties and the Australian Labor Party. -- <ul> <li>Majority of the country does not have first preference for the Greens</li> <li>Some constituents are slightly more supportive than the others</li> </ul> {{content}} -- **What further questions does it raise?** --- # Formulating questions for EDA vs making observations from a plot .flex[ .w-50[ * BEFORE plotting or making summaries think .monash-blue[**broad (open-ended) questions**] that promotes discussion and divergent thinking * Questions with simple answers (i.e. yes or no) less helpful in encouraging exploration * For example, .center[ <div class="question-box w-80 tl"> What is the distribution of the first preference vote percentages for the Labor party across Australia? Is it evenly spread across electorates or are there clusters of popularity? </div> ] ] .w-50[ {{content}} ] ] -- * AFTER plotting or making summaries think <text style="color: #006DAE;"> **was this what you expected, are there any surprises**</text>. Detail what you learn, and how you should follow up on these observations. <img src="images/week5A/aus-election-plot1-1.png" width="432" style="display: block; margin: auto;" /> <div class="question-box w-80 tl"> Is the outlying observation the electoral district that won the seat? </div> {{content}} --- # Visual inference .flex[ .item.w-50[ Typical plot description: ```r ggplot(data, aes(x=var1)) + geom_histogram() ``` <br><br> *Is the distribution consistent with a sample from a particular statistical distribution?* ] .item.w-50[ Potential simulation methods from specific distributions ```r # Symmetric, unimodal, bell-shaped null_dist("var1", "norm") null_dist("var1", "cauchy") null_dist("var1", "t") # Skewed right null_dist("var1", "exp") null_dist("var1", "chisq") null_dist("var1", "gamma") # Constant null_dist("var1", "uniform") ``` ] ] --- # Lineup of Greens first preference percentages .panelset[ .panel[.panel-name[📊] <img src="images/week5A/votes-lineup-1.png" width="100%" style="display: block; margin: auto;" /> ] .panel[.panel-name[R] .f5[ ```r library(nullabor) set.seed(241) ggplot(lineup(null_dist("perc_GRN", "exp"), tdf3, n=10), aes(x=perc_GRN)) + geom_histogram(color = "white", fill = "#00843D", bins = 30) + facet_wrap(~.sample, ncol=5, scales="free") + theme(axis.text = element_blank(), axis.title = element_blank(), panel.grid.major = element_blank()) ``` ] ] ] --- # .orange[Case study] .circle.bg-orange.white[1] 2019 Australian Federal Election .f4[Part 6/8] .panelset[ .panel[.panel-name[📊] .flex[ .w-50[ <table class=" lightable-classic" style='font-family: "Arial Narrow", "Source Sans Pro", sans-serif; margin-left: auto; margin-right: auto;'> <thead> <tr> <th style="empty-cells: hide;" colspan="1"></th> <th style="padding-bottom:0; padding-left:3px;padding-right:3px;text-align: center; " colspan="4"><div style="border-bottom: 1px solid #111111; margin-bottom: -1px; ">% of first preference for the Greens</div></th> <th style="empty-cells: hide;" colspan="2"></th> </tr> <tr> <th style="text-align:left;"> State </th> <th style="text-align:right;"> Mean </th> <th style="text-align:right;"> Median </th> <th style="text-align:right;"> SD </th> <th style="text-align:right;"> IQR </th> <th style="text-align:right;"> Skewness </th> <th style="text-align:right;"> Kurtosis </th> </tr> </thead> <tbody> <tr> <td style="text-align:left;"> ACT </td> <td style="text-align:right;"> 16.406 </td> <td style="text-align:right;"> 13.988 </td> <td style="text-align:right;"> 5.602 </td> <td style="text-align:right;"> 5.196 </td> <td style="text-align:right;"> 0.645 </td> <td style="text-align:right;"> 1.500 </td> </tr> <tr> <td style="text-align:left;"> VIC </td> <td style="text-align:right;"> 11.400 </td> <td style="text-align:right;"> 8.570 </td> <td style="text-align:right;"> 8.210 </td> <td style="text-align:right;"> 6.717 </td> <td style="text-align:right;"> 2.603 </td> <td style="text-align:right;"> 11.360 </td> </tr> <tr> <td style="text-align:left;"> WA </td> <td style="text-align:right;"> 10.993 </td> <td style="text-align:right;"> 10.756 </td> <td style="text-align:right;"> 3.018 </td> <td style="text-align:right;"> 3.116 </td> <td style="text-align:right;"> 0.802 </td> <td style="text-align:right;"> 3.026 </td> </tr> <tr> <td style="text-align:left;"> QLD </td> <td style="text-align:right;"> 9.764 </td> <td style="text-align:right;"> 8.808 </td> <td style="text-align:right;"> 5.096 </td> <td style="text-align:right;"> 4.753 </td> <td style="text-align:right;"> 1.092 </td> <td style="text-align:right;"> 3.886 </td> </tr> <tr> <td style="text-align:left;"> TAS </td> <td style="text-align:right;"> 9.721 </td> <td style="text-align:right;"> 9.339 </td> <td style="text-align:right;"> 4.009 </td> <td style="text-align:right;"> 0.985 </td> <td style="text-align:right;"> 0.326 </td> <td style="text-align:right;"> 2.493 </td> </tr> <tr> <td style="text-align:left;"> NT </td> <td style="text-align:right;"> 9.572 </td> <td style="text-align:right;"> 9.572 </td> <td style="text-align:right;"> 2.473 </td> <td style="text-align:right;"> 1.748 </td> <td style="text-align:right;"> 0.000 </td> <td style="text-align:right;"> 1.000 </td> </tr> <tr> <td style="text-align:left;"> SA </td> <td style="text-align:right;"> 9.120 </td> <td style="text-align:right;"> 8.903 </td> <td style="text-align:right;"> 3.024 </td> <td style="text-align:right;"> 3.412 </td> <td style="text-align:right;"> 0.384 </td> <td style="text-align:right;"> 2.920 </td> </tr> <tr> <td style="text-align:left;"> NSW </td> <td style="text-align:right;"> 8.101 </td> <td style="text-align:right;"> 6.635 </td> <td style="text-align:right;"> 4.087 </td> <td style="text-align:right;"> 3.948 </td> <td style="text-align:right;"> 1.502 </td> <td style="text-align:right;"> 4.859 </td> </tr> <tr> <td style="text-align:left;border-top: 2px solid black;"> National </td> <td style="text-align:right;border-top: 2px solid black;"> 9.874 </td> <td style="text-align:right;border-top: 2px solid black;"> 8.547 </td> <td style="text-align:right;border-top: 2px solid black;"> 5.632 </td> <td style="text-align:right;border-top: 2px solid black;"> 5.001 </td> <td style="text-align:right;border-top: 2px solid black;"> 2.671 </td> <td style="text-align:right;border-top: 2px solid black;"> 15.798 </td> </tr> </tbody> </table> ] .w-50.pl3[ {{content}} ]]] .panel[.panel-name[data] .f5[ ```r tdf3 <- df1 %>% group_by(DivisionID) %>% summarise( DivisionNm = unique(DivisionNm), State = unique(StateAb), votes_GRN = TotalVotes[which(PartyAb == "GRN")], votes_total = sum(TotalVotes) ) %>% mutate(perc_GRN = votes_GRN / votes_total * 100) ``` ]] .panel[.panel-name[R] .f5[ ```r tdf3 %>% group_by(State) %>% summarise( mean = mean(perc_GRN), median = median(perc_GRN), sd = sd(perc_GRN), iqr = IQR(perc_GRN), skewness = moments::skewness(perc_GRN), kurtosis = moments::kurtosis(perc_GRN) ) %>% arrange(desc(mean)) %>% rbind(data.frame( State = "National", mean = mean(tdf3$perc_GRN), median = median(tdf3$perc_GRN), sd = sd(tdf3$perc_GRN), iqr = IQR(tdf3$perc_GRN), skewness = moments::skewness(tdf3$perc_GRN), kurtosis = moments::kurtosis(tdf3$perc_GRN) )) %>% knitr::kable(col.names = c("State", "Mean", "Median", "SD", "IQR", "Skewness", "Kurtosis"), digits = 3) %>% kableExtra::kable_classic() %>% kableExtra::add_header_above(c(" ", "% of first preference for the Greens" = 4, " " = 2)) %>% kableExtra::row_spec(9, extra_css = "border-top: 2px solid black;") ``` ]]] -- * Why are the means and the medians different? * How are the standard deviations and the interquartile ranges similar or different? * Are there some other numerical statistics we should show? --- # Robust measure of central tendency .flex[ .w-40[ * <span style="color:#D81B60">**Mean**</span> is a non-robust measure of location. * <span style="color:#1E88E5">**Median**</span> is the 50% quantile of the observations * <span style="color:#FFC107">**Trimmed mean**</span> is the sample mean after discarding observations at the tails. * <span style="color:#004D40">**Winsorized mean**</span> is the sample mean after replacing observations at the tails with the minimum or maximum of the observations that remain. ] .w-60[ <img src='images/week5A/robust-mean-1.png' class='ba pl2' height ='150px'/> <img src='images/week5A/robust-mean-2.png' class='ba pl2' height ='150px'/> <img src='images/week5A/robust-mean-3.png' class='ba pl2' height ='150px'/> <img src='images/week5A/robust-mean-4.png' class='ba pl2' height ='150px'/> <img src='images/week5A/robust-mean-5.png' class='ba pl2' height ='150px'/> <img src='images/week5A/robust-mean-6.png' class='ba pl2' height ='150px'/> <table class=" lightable-classic" style='font-size: 12px; font-family: "Arial Narrow", "Source Sans Pro", sans-serif; width: auto !important; margin-left: auto; margin-right: auto;'> <thead> <tr> <th style="text-align:right;"> Plot </th> <th style="text-align:right;"> Mean </th> <th style="text-align:right;"> Median </th> <th style="text-align:right;"> Trimmed Mean^* </th> <th style="text-align:right;"> Winsorized Mean^* </th> </tr> </thead> <tbody> <tr> <td style="text-align:right;"> 1 </td> <td style="text-align:right;color: #D81B60 !important;"> 0.109 </td> <td style="text-align:right;color: #1E88E5 !important;"> 0.114 </td> <td style="text-align:right;color: #FFC107 !important;"> 0.120 </td> <td style="text-align:right;color: #004D40 !important;"> 0.103 </td> </tr> <tr> <td style="text-align:right;"> 2 </td> <td style="text-align:right;color: #D81B60 !important;"> 0.054 </td> <td style="text-align:right;color: #1E88E5 !important;"> -0.045 </td> <td style="text-align:right;color: #FFC107 !important;"> -0.016 </td> <td style="text-align:right;color: #004D40 !important;"> -0.029 </td> </tr> <tr> <td style="text-align:right;"> 3 </td> <td style="text-align:right;color: #D81B60 !important;"> 1.177 </td> <td style="text-align:right;color: #1E88E5 !important;"> 0.729 </td> <td style="text-align:right;color: #FFC107 !important;"> 0.820 </td> <td style="text-align:right;color: #004D40 !important;"> 0.888 </td> </tr> <tr> <td style="text-align:right;"> 4 </td> <td style="text-align:right;color: #D81B60 !important;"> 0.533 </td> <td style="text-align:right;color: #1E88E5 !important;"> 0.541 </td> <td style="text-align:right;color: #FFC107 !important;"> 0.543 </td> <td style="text-align:right;color: #004D40 !important;"> 0.542 </td> </tr> <tr> <td style="text-align:right;"> 5 </td> <td style="text-align:right;color: #D81B60 !important;"> 0.468 </td> <td style="text-align:right;color: #1E88E5 !important;"> 0.329 </td> <td style="text-align:right;color: #FFC107 !important;"> 0.355 </td> <td style="text-align:right;color: #004D40 !important;"> 0.390 </td> </tr> <tr> <td style="text-align:right;"> 6 </td> <td style="text-align:right;color: #D81B60 !important;"> 5.626 </td> <td style="text-align:right;color: #1E88E5 !important;"> 6.656 </td> <td style="text-align:right;color: #FFC107 !important;"> 5.918 </td> <td style="text-align:right;color: #004D40 !important;"> 5.688 </td> </tr> </tbody> </table> .f5[ ^* Both trimmed and Winsorized mean trimmed 20% of the tails. ] ] ] --- # Robust measure of dispersion .flex[ .w-50[ * <span style="color:#648FFF">**Standard deviation**</span> or its square, **variance**, is a popular choice of measure of dispersion but is not robust to outliers * Standard deviation for sample `\(x_1, ..., x_n\)` is `$$\sqrt{\sum_{i=1}^n \frac{(x_i - \bar{x})^2}{n - 1}}$$` * <span style="color:#785EF0">**Interquartile range**</span> difference between 1st and 3rd quartile, more robust measure of spread * <span style="color:#FE6100">**Median absolute deviance**</span> (MAD) is even more robust `$$\text{median}(|x_i - \text{median}(x_i)|)$$` ] .w-50.pl3[ <img src='images/week5A/robust-mean-1.png' class='ba pl2' height ='150px'/> <img src='images/week5A/robust-mean-2.png' class='ba pl2' height ='150px'/> <img src='images/week5A/robust-mean-3.png' class='ba pl2' height ='150px'/> <img src='images/week5A/robust-mean-4.png' class='ba pl2' height ='150px'/> <img src='images/week5A/robust-mean-5.png' class='ba pl2' height ='150px'/> <img src='images/week5A/robust-mean-6.png' class='ba pl2' height ='150px'/> <table class=" lightable-classic" style='font-size: 12px; font-family: "Arial Narrow", "Source Sans Pro", sans-serif; width: auto !important; margin-left: auto; margin-right: auto;'> <thead> <tr> <th style="empty-cells: hide;" colspan="1"></th> <th style="padding-bottom:0; padding-left:3px;padding-right:3px;text-align: center; " colspan="3"><div style="border-bottom: 1px solid #111111; margin-bottom: -1px; ">Measure of dispersion</div></th> <th style="empty-cells: hide;" colspan="2"></th> </tr> <tr> <th style="text-align:right;"> Plot </th> <th style="text-align:right;"> SD </th> <th style="text-align:right;"> IQR </th> <th style="text-align:right;"> MAD </th> <th style="text-align:right;"> Skewness </th> <th style="text-align:right;"> Kurtosis </th> </tr> </thead> <tbody> <tr> <td style="text-align:right;"> 1 </td> <td style="text-align:right;color: #648FFF !important;"> 0.898 </td> <td style="text-align:right;color: #785EF0 !important;"> 1.186 </td> <td style="text-align:right;color: #FE6100 !important;"> 0.870 </td> <td style="text-align:right;"> -0.072 </td> <td style="text-align:right;"> 3.008 </td> </tr> <tr> <td style="text-align:right;"> 2 </td> <td style="text-align:right;color: #648FFF !important;"> 0.986 </td> <td style="text-align:right;color: #785EF0 !important;"> 1.411 </td> <td style="text-align:right;color: #FE6100 !important;"> 1.077 </td> <td style="text-align:right;"> 0.358 </td> <td style="text-align:right;"> 2.212 </td> </tr> <tr> <td style="text-align:right;"> 3 </td> <td style="text-align:right;color: #648FFF !important;"> 1.326 </td> <td style="text-align:right;color: #785EF0 !important;"> 1.176 </td> <td style="text-align:right;color: #FE6100 !important;"> 0.793 </td> <td style="text-align:right;"> 1.944 </td> <td style="text-align:right;"> 7.184 </td> </tr> <tr> <td style="text-align:right;"> 4 </td> <td style="text-align:right;color: #648FFF !important;"> 0.288 </td> <td style="text-align:right;color: #785EF0 !important;"> 0.450 </td> <td style="text-align:right;color: #FE6100 !important;"> 0.335 </td> <td style="text-align:right;"> -0.126 </td> <td style="text-align:right;"> 1.837 </td> </tr> <tr> <td style="text-align:right;"> 5 </td> <td style="text-align:right;color: #648FFF !important;"> 0.468 </td> <td style="text-align:right;color: #785EF0 !important;"> 0.499 </td> <td style="text-align:right;color: #FE6100 !important;"> 0.343 </td> <td style="text-align:right;"> 1.691 </td> <td style="text-align:right;"> 6.372 </td> </tr> <tr> <td style="text-align:right;"> 6 </td> <td style="text-align:right;color: #648FFF !important;"> 2.784 </td> <td style="text-align:right;color: #785EF0 !important;"> 5.362 </td> <td style="text-align:right;color: #FE6100 !important;"> 2.984 </td> <td style="text-align:right;"> -0.351 </td> <td style="text-align:right;"> 1.678 </td> </tr> </tbody> </table> ]] --- # .orange[Case study] .circle.bg-orange.white[1] 2019 Australian Federal Election .f4[Part 7/8] .panelset[ .panel[.panel-name[📊] .flex[ .w-50[ <img src="images/week5A/aus-election-plot2-1.png" width="432" style="display: block; margin: auto;" /> ] .w-50[ **We should plot the data!** * The width of the boxplot is proportional to the number of electoral districts in the corresponding state (which is roughly proportional to the population) ] ]] .panel[.panel-name[data] .f5[ ```r tdf3 <- df1 %>% group_by(DivisionID) %>% summarise( DivisionNm = unique(DivisionNm), State = unique(StateAb), votes_GRN = TotalVotes[which(PartyAb == "GRN")], votes_total = sum(TotalVotes) ) %>% mutate(perc_GRN = votes_GRN / votes_total * 100) ``` ]] .panel[.panel-name[R] .f5[ ```r tdf3 %>% mutate(State = fct_reorder(State, perc_GRN)) %>% ggplot(aes(perc_GRN, State)) + geom_boxplot(varwidth = TRUE) + labs( x = "Percentage of first preference votes per division", y = "State", title = "First preference votes for the Greens party" ) ``` ]]] --- # Outliers .info-box.w-60[ **Outliers** are *observations* that are significantly different from the majority. ] <br> .flex[ .w-50[ * Outliers can _**occur by chance in almost all distributions**_, but could be indicative of: * a measurement error, * a different population, or * an issue with the sampling process. ] .w-50[ <img src="images/week5A/aus-election-plot2-1.png" width="432" style="display: block; margin: auto;" /> ] ] --- # Closer look at the _boxplot_ <img src="images/week5A/annotated-boxplot-1.png" width="432" style="display: block; margin: auto;" /> * Observations that are outside the range of lower to upper fence (1.5 times the box length) are referred at times as .monash-blue[outliers] * Plotting boxplots for data from a skewed distribution will almost always show these "outliers" but these are not necessary outliers * Some definitions of outliers assume a symmetrical population distribution (e.g. in boxplots or observations a certain standard deviations away from the mean) and these definitions are ill-suited for asymmetrical distributions -- .center[ **But are there some things we .red[*cannot*] see from boxplots?** ] --- # .orange[Case study] .circle.bg-orange.white[1] 2019 Australian Federal Election .f4[Part 8/8] .panelset[ .panel[.panel-name[📊] .flex[ .w-50[ <img src="images/week5A/aus-election-2019-plot3-1.png" width="432" style="display: block; margin: auto;" /> ] .w-50[ {{content}} ] ]] .panel[.panel-name[data] .f5[ ```r tdf3 <- df1 %>% group_by(DivisionID) %>% summarise( DivisionNm = unique(DivisionNm), State = unique(StateAb), votes_GRN = TotalVotes[which(PartyAb == "GRN")], votes_total = sum(TotalVotes) ) %>% mutate(perc_GRN = votes_GRN / votes_total * 100) ``` ]] .panel[.panel-name[R] .f5[ ```r tdf3 %>% mutate(State = fct_reorder(State, perc_GRN)) %>% ggplot(aes(perc_GRN, State)) + ggbeeswarm::geom_quasirandom(groupOnX = FALSE, varwidth = TRUE) + labs( x = "Percentage of first preference votes per division", y = "State", title = "First preference votes for the Greens party" ) ``` ]]] -- **Now what do you notice from this graph that you didn't notice before?** {{content}} -- * There are only two electoral districts in NT! * And only 3 and 5 electoral districts in ACT and TAS, respectively! {{content}} -- * We have _not_ computed the number of electoral districts for each state so far! {{content}} -- <div class="info-box"> <i class="fas fa-book-reader"></i> Both numerical and graphical summaries can either <i>reveal</i> and/or <i>hide</i> aspects of the data </div> --- class: transition # Transformations --- # .orange[Case study] .bg-orange.circle.white[2] Melbourne Housing Prices .f4[Part 1/5] .flex[ .w-50[ <table class=" lightable-classic" style='font-size: 12px; font-family: "Arial Narrow", "Source Sans Pro", sans-serif; margin-left: auto; margin-right: auto;'> <thead> <tr> <th style="text-align:left;"> Suburb </th> <th style="text-align:right;"> Rooms </th> <th style="text-align:left;"> Type </th> <th style="text-align:right;"> Price ($) </th> <th style="text-align:left;"> Date </th> </tr> </thead> <tbody> <tr> <td style="text-align:left;"> Abbotsford </td> <td style="text-align:right;"> 3 </td> <td style="text-align:left;"> Home </td> <td style="text-align:right;"> 1,490,000 </td> <td style="text-align:left;"> 2017-04-01 </td> </tr> <tr> <td style="text-align:left;"> Abbotsford </td> <td style="text-align:right;"> 3 </td> <td style="text-align:left;"> Home </td> <td style="text-align:right;"> 1,220,000 </td> <td style="text-align:left;"> 2017-04-01 </td> </tr> <tr> <td style="text-align:left;"> Abbotsford </td> <td style="text-align:right;"> 3 </td> <td style="text-align:left;"> Home </td> <td style="text-align:right;"> 1,420,000 </td> <td style="text-align:left;"> 2017-04-01 </td> </tr> <tr> <td style="text-align:left;"> Aberfeldie </td> <td style="text-align:right;"> 3 </td> <td style="text-align:left;"> Home </td> <td style="text-align:right;"> 1,515,000 </td> <td style="text-align:left;"> 2017-04-01 </td> </tr> <tr> <td style="text-align:left;"> Airport West </td> <td style="text-align:right;"> 2 </td> <td style="text-align:left;"> Home </td> <td style="text-align:right;"> 670,000 </td> <td style="text-align:left;"> 2017-04-01 </td> </tr> <tr> <td style="text-align:left;"> Airport West </td> <td style="text-align:right;"> 2 </td> <td style="text-align:left;"> Townhouse </td> <td style="text-align:right;"> 530,000 </td> <td style="text-align:left;"> 2017-04-01 </td> </tr> <tr> <td style="text-align:left;"> Airport West </td> <td style="text-align:right;"> 2 </td> <td style="text-align:left;"> Unit </td> <td style="text-align:right;"> 540,000 </td> <td style="text-align:left;"> 2017-04-01 </td> </tr> <tr> <td style="text-align:left;"> Airport West </td> <td style="text-align:right;"> 3 </td> <td style="text-align:left;"> Home </td> <td style="text-align:right;"> 715,000 </td> <td style="text-align:left;"> 2017-04-01 </td> </tr> <tr> <td style="text-align:left;"> Albanvale </td> <td style="text-align:right;"> 6 </td> <td style="text-align:left;"> Home </td> <td style="text-align:right;"> NA </td> <td style="text-align:left;"> 2017-04-01 </td> </tr> <tr> <td style="text-align:left;"> Albert Park </td> <td style="text-align:right;"> 3 </td> <td style="text-align:left;"> Home </td> <td style="text-align:right;"> 1,925,000 </td> <td style="text-align:left;"> 2017-04-01 </td> </tr> <tr> <td style="text-align:left;"> Albion </td> <td style="text-align:right;"> 3 </td> <td style="text-align:left;"> Unit </td> <td style="text-align:right;"> 515,000 </td> <td style="text-align:left;"> 2017-04-01 </td> </tr> <tr> <td style="text-align:left;"> Albion </td> <td style="text-align:right;"> 4 </td> <td style="text-align:left;"> Home </td> <td style="text-align:right;"> 717,000 </td> <td style="text-align:left;"> 2017-04-01 </td> </tr> <tr> <td style="text-align:left;"> Alphington </td> <td style="text-align:right;"> 2 </td> <td style="text-align:left;"> Home </td> <td style="text-align:right;"> 1,675,000 </td> <td style="text-align:left;"> 2017-04-01 </td> </tr> <tr> <td style="text-align:left;"> Alphington </td> <td style="text-align:right;"> 4 </td> <td style="text-align:left;"> Home </td> <td style="text-align:right;"> 2,008,000 </td> <td style="text-align:left;"> 2017-04-01 </td> </tr> <tr> <td style="text-align:left;"> Altona </td> <td style="text-align:right;"> 2 </td> <td style="text-align:left;"> Home </td> <td style="text-align:right;"> 860,000 </td> <td style="text-align:left;"> 2017-04-01 </td> </tr> <tr> <td style="text-align:left;"> Altona Meadows </td> <td style="text-align:right;"> 4 </td> <td style="text-align:left;"> Home </td> <td style="text-align:right;"> NA </td> <td style="text-align:left;"> 2017-04-01 </td> </tr> <tr> <td style="text-align:left;"> Altona North </td> <td style="text-align:right;"> 3 </td> <td style="text-align:left;"> Home </td> <td style="text-align:right;"> 720,000 </td> <td style="text-align:left;"> 2017-04-01 </td> </tr> <tr> <td style="text-align:left;"> Armadale </td> <td style="text-align:right;"> 2 </td> <td style="text-align:left;"> Unit </td> <td style="text-align:right;"> 836,000 </td> <td style="text-align:left;"> 2017-04-01 </td> </tr> <tr> <td style="text-align:left;"> Armadale </td> <td style="text-align:right;"> 2 </td> <td style="text-align:left;"> Home </td> <td style="text-align:right;"> 2,110,000 </td> <td style="text-align:left;"> 2017-04-01 </td> </tr> <tr> <td style="text-align:left;"> Armadale </td> <td style="text-align:right;"> 3 </td> <td style="text-align:left;"> Home </td> <td style="text-align:right;"> 1,386,000 </td> <td style="text-align:left;"> 2017-04-01 </td> </tr> </tbody> </table> ] .w-50.pl3[ * This data was scrapped each week from domain.com.au from 2016-01-28 to 2018-10-13 * In total there are **63,023** observations * All variables shown .f5[(there are more variables not shown here)], except price, have complete records * The are **48,433** property prices across Melbourne (roughly 23% missing) {{content}} ]] .footnote.f5[ Data source: Tony Pio (2018) Melbourne Housing Market, Version 27. Retrieved August 2021 from https://www.kaggle.com/anthonypino/melbourne-housing-market. ] -- **How would you explore this data first?** <div class="countdown" id="timer_c408e70c" data-update-every="1" tabindex="0" style="right:0;bottom:0;"> <div class="countdown-controls"><button class="countdown-bump-down">−</button><button class="countdown-bump-up">+</button></div> <code class="countdown-time"><span class="countdown-digits minutes">01</span><span class="countdown-digits colon">:</span><span class="countdown-digits seconds">00</span></code> </div> --- # .orange[Case study] .bg-orange.circle.white[2] Melbourne Housing Prices .f4[Part 2/5] .panelset[ .panel[.panel-name[📊] .flex[ .w-50[ Observations arranged by Suburb and Date: <img src="images/week5A/melb-house-plot-miss-1.png" width="432" style="display: block; margin: auto;" /> ] .w-50[ Comparing distribution of room number for observations with missing and non-missing price records: <img src="images/week5A/melb-house-plot-room-miss-1.png" width="576" style="display: block; margin: auto;" /> {{content}} ]]] .panel[.panel-name[data] .scroll-sign[ .f5.s400[ ```r df2 <- read_csv(here::here("data/MELBOURNE_HOUSE_PRICES_LESS.csv"), col_types = cols( .default = col_character(), Rooms = col_double(), Price = col_double(), Date = col_date(format = "%d/%m/%Y"), Propertycount = col_double(), Distance = col_double() ) ) ``` ```r skimr::skim(df2) ``` ``` ## ── Data Summary ──────────────────────── ## Values ## Name df2 ## Number of rows 63023 ## Number of columns 13 ## _______________________ ## Column type frequency: ## character 8 ## Date 1 ## numeric 4 ## ________________________ ## Group variables None ## ## ── Variable type: character ──────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────── ## skim_variable n_missing complete_rate min max empty n_unique whitespace ## 1 Suburb 0 1 3 18 0 380 0 ## 2 Address 0 1 7 27 0 57754 0 ## 3 Type 0 1 1 1 0 3 0 ## 4 Method 0 1 1 2 0 9 0 ## 5 SellerG 0 1 1 27 0 476 0 ## 6 Postcode 0 1 4 4 0 225 0 ## 7 Regionname 0 1 16 26 0 8 0 ## 8 CouncilArea 0 1 17 30 0 34 0 ## ## ── Variable type: Date ───────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────── ## skim_variable n_missing complete_rate min max median n_unique ## 1 Date 0 1 2016-01-28 2018-10-13 2017-09-03 112 ## ## ── Variable type: numeric ────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────── ## skim_variable n_missing complete_rate mean sd p0 p25 p50 p75 p100 hist ## 1 Rooms 0 1 3.11 0.958 1 3 3 4 31 ▇▁▁▁▁ ## 2 Price 14590 0.768 997898. 593499. 85000 620000 830000 1220000 11200000 ▇▁▁▁▁ ## 3 Propertycount 0 1 7618. 4424. 39 4380 6795 10412 21650 ▅▇▅▂▁ ## 4 Distance 0 1 12.7 7.59 0 7 11.4 16.7 64.1 ▇▆▁▁▁ ``` ]]] .panel[.panel-name[R] .f5[ ```r df2 %>% select(Suburb, Rooms, Type, Price, Date) %>% arrange(Suburb, Date) %>% visdat::vis_miss() df2 %>% mutate(miss = ifelse(is.na(Price), "Missing", "Recorded")) %>% count(Rooms, miss) %>% group_by(miss) %>% mutate(perc = n / sum(n) * 100) %>% ggplot(aes(as.factor(Rooms), perc, fill = miss)) + geom_col(position = "dodge") + scale_fill_viridis_d(begin=0.3, end=0.7) + labs(x = "Rooms", y = "Percentage", fill = "Price") ``` ]] .panel[.panel-name[lineup] <img src="images/week5A/melb-house-lineup-1.png" width="80%" style="display: block; margin: auto;" /> ] .panel[.panel-name[R] .f5[ ```r library(nullabor) df2_d <- df2 %>% mutate(miss = ifelse(is.na(Price), "Missing", "Recorded")) %>% select(Rooms, miss) df2_l <- lineup(null_permute("miss"), df2_d, n=10, pos=7) df2_l_agg <- df2_l %>% group_by(.sample) %>% count(Rooms, miss) %>% ungroup() %>% group_by(miss) %>% mutate(perc = n / sum(n) * 100) %>% mutate(Rooms = as.factor(Rooms)) ggplot(df2_l_agg, aes(x=Rooms, y=perc, fill = miss)) + geom_col(position = "dodge") + scale_fill_viridis_d(begin=0.3, end=0.7) + facet_wrap(~.sample, ncol=5) + theme(legend.position = "none", axis.text = element_blank(), axis.title = element_blank(), panel.grid.major.x = element_blank()) ``` ]]] -- * Seems to be okay nothing very notable - but check with a <text style="color: #D93F00;"> lineup </text> * What next? --- # .orange[Case study] .bg-orange.circle.white[2] Melbourne Housing Prices .f4[Part 3/5] .panelset[ .panel[.panel-name[📊] .flex[ .w-50[ <img src="images/week5A/melb-house-price-plot1-1.png" width="432" style="display: block; margin: auto;" /> ] .w-50[ **What can we say from this plot?** {{content}} ]]] .panel[.panel-name[data] .f5[ ```r df2 <- read_csv(here::here("data/MELBOURNE_HOUSE_PRICES_LESS.csv"), col_types = cols( .default = col_character(), Rooms = col_double(), Price = col_double(), Date = col_date(format = "%d/%m/%Y"), Propertycount = col_double(), Distance = col_double() ) ) ``` ]] .panel[.panel-name[R] .f5[ ```r df2 %>% ggplot(aes(Price / 1e6)) + geom_histogram(color = "white") + labs( x = "Price ($1,000,000)", y = "Count" ) ``` ]]] -- * The housing prices are right-skewed {{content}} -- * There appears to be a lot of outlying housing prices (how can we tell?) --- # .orange[Case study] .bg-orange.circle.white[2] Melbourne Housing Prices .f4[Part 4/5] .panelset[ .panel[.panel-name[📊] .flex[ .w-50[ <img src="images/week5A/melb-house-price-plot2-1.png" width="432" style="display: block; margin: auto;" /> ] .w-50[ {{content}} ]]] .panel[.panel-name[data] .f5[ ```r df2 <- read_csv(here::here("data/MELBOURNE_HOUSE_PRICES_LESS.csv"), col_types = cols( .default = col_character(), Rooms = col_double(), Price = col_double(), Date = col_date(format = "%d/%m/%Y"), Propertycount = col_double(), Distance = col_double() ) ) ``` ]] .panel[.panel-name[R] .f5[ ```r df2 %>% ggplot(aes(Price / 1e6)) + geom_histogram(color = "white") + labs( x = "Price ($1,000,000)", y = "Count" ) + scale_x_log10() ``` ]]] -- * The x-axis has been `\(\log_{10}\)`-transformed in this plot {{content}} -- * The plot appears more symmetrical now {{content}} -- * What is a measure of central tendancy here? <span class='f4'>With no transformation:</span> <table class=" lightable-classic" style='font-family: "Arial Narrow", "Source Sans Pro", sans-serif; margin-left: auto; margin-right: auto;'> <thead> <tr> <th style="text-align:right;"> Mean </th> <th style="text-align:right;"> Median </th> <th style="text-align:right;"> Trimmed Mean </th> <th style="text-align:right;"> Winsorised Mean </th> </tr> </thead> <tbody> <tr> <td style="text-align:right;"> $997,898 </td> <td style="text-align:right;"> $830,000 </td> <td style="text-align:right;"> $871,375 </td> <td style="text-align:right;"> $903,823 </td> </tr> </tbody> </table> <span class='f4'>With log transformation (and back transformed to original scale):</span> <table class=" lightable-classic" style='font-family: "Arial Narrow", "Source Sans Pro", sans-serif; margin-left: auto; margin-right: auto;'> <thead> <tr> <th style="text-align:right;"> Mean </th> <th style="text-align:right;"> Median </th> <th style="text-align:right;"> Trimmed Mean </th> <th style="text-align:right;"> Winsorised Mean </th> </tr> </thead> <tbody> <tr> <td style="text-align:right;"> $874,166 </td> <td style="text-align:right;"> $830,000 </td> <td style="text-align:right;"> $847,973 </td> <td style="text-align:right;"> $859,325 </td> </tr> </tbody> </table> --- class: transition # Multi-modality --- # .orange[Case study] .bg-orange.circle.white[2] Melbourne Housing Prices .f4[Part 5/5] .panelset[ .panel[.panel-name[📊] .flex[ .w-50[ <img src="images/week5A/melb-house-by-room-1.png" width="432" style="display: block; margin: auto;" /> ] .w-50[ {{content}} ]]] .panel[.panel-name[data] .f5.s500[ ```r df2 <- read_csv(here::here("data/MELBOURNE_HOUSE_PRICES_LESS.csv"), col_types = cols( .default = col_character(), Rooms = col_double(), Price = col_double(), Date = col_date(format = "%d/%m/%Y"), Propertycount = col_double(), Distance = col_double() ) ) ``` ]] .panel[.panel-name[R] .f5[ ```r df2 %>% ggplot(aes(x=as.factor(Rooms), y=Price / 1e6, )) + ggbeeswarm::geom_quasirandom(varwidth=TRUE, alpha=0.3) + scale_y_log10() + labs(y = "Price ($1,000,000)", x = "# of Rooms") ``` ]]] -- * You can see that drawing separate univariate plots for each room number show that higher number of rooms generally are pricier * You could not see this, however, when the data are combined <img src="images/week5A/melb-house-price-plot2-1.png" width="432" style="display: block; margin: auto;" /> --- class: transition # Bins and Bandwidths: More details --- # .orange[Case study] .circle.bg-orange.white[3] Boston housing data .f4[Part 1/4] .panelset[ .panel[.panel-name[📊] .grid[ .item[ <img src="images/week5A/boston-plot1-1.png" width="460.8" style="display: block; margin: auto;" /> ] .item[ {{content}} ] ] ] .panel[.panel-name[data] .h300.f4.scroll-sign[ ```r data(bostonc, package = "DAAG") df3 <- read_tsv(I(bostonc[10:length(bostonc)])) skimr::skim(df3) ``` ``` ## ── Data Summary ──────────────────────── ## Values ## Name df3 ## Number of rows 506 ## Number of columns 21 ## _______________________ ## Column type frequency: ## character 2 ## numeric 19 ## ________________________ ## Group variables None ## ## ── Variable type: character ──────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────── ## skim_variable n_missing complete_rate min max empty n_unique whitespace ## 1 TOWN 0 1 4 23 0 92 0 ## 2 TRACT 0 1 4 4 0 506 0 ## ## ── Variable type: numeric ────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────── ## skim_variable n_missing complete_rate mean sd p0 p25 p50 p75 p100 hist ## 1 OBS. 0 1 254. 146. 1 127. 254. 380. 506 ▇▇▇▇▇ ## 2 TOWN# 0 1 47.5 27.6 0 26.2 42 78 91 ▅▆▅▃▇ ## 3 LON 0 1 -71.1 0.0754 -71.3 -71.1 -71.1 -71.0 -70.8 ▁▂▇▂▁ ## 4 LAT 0 1 42.2 0.0618 42.0 42.2 42.2 42.3 42.4 ▁▃▇▃▁ ## 5 MEDV 0 1 22.5 9.20 5 17.0 21.2 25 50 ▂▇▅▁▁ ## 6 CMEDV 0 1 22.5 9.18 5 17.0 21.2 25 50 ▂▇▅▁▁ ## 7 CRIM 0 1 3.61 8.60 0.00632 0.0820 0.257 3.68 89.0 ▇▁▁▁▁ ## 8 ZN 0 1 11.4 23.3 0 0 0 12.5 100 ▇▁▁▁▁ ## 9 INDUS 0 1 11.1 6.86 0.46 5.19 9.69 18.1 27.7 ▇▆▁▇▁ ## 10 CHAS 0 1 0.0692 0.254 0 0 0 0 1 ▇▁▁▁▁ ## 11 NOX 0 1 0.555 0.116 0.385 0.449 0.538 0.624 0.871 ▇▇▆▅▁ ## 12 RM 0 1 6.28 0.703 3.56 5.89 6.21 6.62 8.78 ▁▂▇▂▁ ## 13 AGE 0 1 68.6 28.1 2.9 45.0 77.5 94.1 100 ▂▂▂▃▇ ## 14 DIS 0 1 3.80 2.11 1.13 2.10 3.21 5.19 12.1 ▇▅▂▁▁ ## 15 RAD 0 1 9.55 8.71 1 4 5 24 24 ▇▂▁▁▃ ## 16 TAX 0 1 408. 169. 187 279 330 666 711 ▇▇▃▁▇ ## 17 PTRATIO 0 1 18.5 2.16 12.6 17.4 19.0 20.2 22 ▁▃▅▅▇ ## 18 B 0 1 357. 91.3 0.32 375. 391. 396. 397. ▁▁▁▁▇ ## 19 LSTAT 0 1 12.7 7.14 1.73 6.95 11.4 17.0 38.0 ▇▇▅▂▁ ``` ]] .panel[.panel-name[R] .f5[ ```r ggplot(df3, aes(MEDV)) + geom_histogram(binwidth = 1, color = "black", fill = "#008A25") + labs(x = "Median housing value (US$1000)", y = "Frequency") ``` ]] ] .footnote.f6[ Harrison, David, and Daniel L. Rubinfeld (1978) Hedonic Housing Prices and the Demand for Clean Air, *Journal of Environmental Economics and Management* **5** 81-102. Original data.<br> Gilley, O.W. and R. Kelley Pace (1996) On the Harrison and Rubinfeld Data. *Journal of Environmental Economics and Management* **31** 403-405. Provided corrections and examined censoring.<br> Maindonald, John H. and Braun, W. John (2020). DAAG: Data Analysis and Graphics Data and Functions. R package version 1.24 ] -- * There is a large frequency in the final bin. * There is a decline in observations in the $40-49K range as well as dip in observations around $26K and $34K. -- * The histogram is using a bin width of 1 unit and is **left-open** (or **right-closed**): (4.5, 5.5], (5.5, 6.5] ... (49.5, 50.5], so that 5.5 is in the smaller bin, where as right-open would place it in the larger bin. * Occasionally, whether it is **left-** or **right-open** can make a difference. Or, you might also **set the breaks** controlling the min value where binning starts. --- # .orange[Case study] .circle.bg-orange.white[3] Boston housing data .f4[Part 2/4] .panelset[ .panel[.panel-name[📊] .grid[ .item[ <img src="images/week5A/boston-plot2-1.png" width="432" style="display: block; margin: auto;" /> ] .item[ * Density plots depend on the **bandwidth** (binwidth) chosen and more than often do not estimate well at boundary cases * There are various way to present features of the data using a plot and what works for one person, may not be as straightforward for another * Be prepared to do multiple plots! ] ] ] .panel[.panel-name[data] .h300.f4.scroll-sign[ ```r data(bostonc, package = "DAAG") df3 <- read_tsv(I(bostonc[10:length(bostonc)])) skimr::skim(df3) ``` ``` ## ── Data Summary ──────────────────────── ## Values ## Name df3 ## Number of rows 506 ## Number of columns 21 ## _______________________ ## Column type frequency: ## character 2 ## numeric 19 ## ________________________ ## Group variables None ## ## ── Variable type: character ──────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────── ## skim_variable n_missing complete_rate min max empty n_unique whitespace ## 1 TOWN 0 1 4 23 0 92 0 ## 2 TRACT 0 1 4 4 0 506 0 ## ## ── Variable type: numeric ────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────── ## skim_variable n_missing complete_rate mean sd p0 p25 p50 p75 p100 hist ## 1 OBS. 0 1 254. 146. 1 127. 254. 380. 506 ▇▇▇▇▇ ## 2 TOWN# 0 1 47.5 27.6 0 26.2 42 78 91 ▅▆▅▃▇ ## 3 LON 0 1 -71.1 0.0754 -71.3 -71.1 -71.1 -71.0 -70.8 ▁▂▇▂▁ ## 4 LAT 0 1 42.2 0.0618 42.0 42.2 42.2 42.3 42.4 ▁▃▇▃▁ ## 5 MEDV 0 1 22.5 9.20 5 17.0 21.2 25 50 ▂▇▅▁▁ ## 6 CMEDV 0 1 22.5 9.18 5 17.0 21.2 25 50 ▂▇▅▁▁ ## 7 CRIM 0 1 3.61 8.60 0.00632 0.0820 0.257 3.68 89.0 ▇▁▁▁▁ ## 8 ZN 0 1 11.4 23.3 0 0 0 12.5 100 ▇▁▁▁▁ ## 9 INDUS 0 1 11.1 6.86 0.46 5.19 9.69 18.1 27.7 ▇▆▁▇▁ ## 10 CHAS 0 1 0.0692 0.254 0 0 0 0 1 ▇▁▁▁▁ ## 11 NOX 0 1 0.555 0.116 0.385 0.449 0.538 0.624 0.871 ▇▇▆▅▁ ## 12 RM 0 1 6.28 0.703 3.56 5.89 6.21 6.62 8.78 ▁▂▇▂▁ ## 13 AGE 0 1 68.6 28.1 2.9 45.0 77.5 94.1 100 ▂▂▂▃▇ ## 14 DIS 0 1 3.80 2.11 1.13 2.10 3.21 5.19 12.1 ▇▅▂▁▁ ## 15 RAD 0 1 9.55 8.71 1 4 5 24 24 ▇▂▁▁▃ ## 16 TAX 0 1 408. 169. 187 279 330 666 711 ▇▇▃▁▇ ## 17 PTRATIO 0 1 18.5 2.16 12.6 17.4 19.0 20.2 22 ▁▃▅▅▇ ## 18 B 0 1 357. 91.3 0.32 375. 391. 396. 397. ▁▁▁▁▇ ## 19 LSTAT 0 1 12.7 7.14 1.73 6.95 11.4 17.0 38.0 ▇▇▅▂▁ ``` ]] .panel[.panel-name[R] .f4[ ```r library(patchwork) library(lvplot) library(ggbeeswarm) h1 <- ggplot(df3, aes(MEDV, y = "")) + geom_boxplot(fill = "#008A25") + labs(x = "Median housing value (US$1000)", y = "") + theme(axis.line.y = element_blank()) h2 <- ggplot(df3, aes(y=MEDV, x = 1)) + geom_lv(aes(fill = after_stat(LV))) + scale_fill_brewer() + xlim(c(0.4, 1.6)) + labs(y = "Median housing value (US$1000)", x = "") + theme(axis.line.x = element_blank(), axis.text.y = element_blank()) + coord_flip() h3 <- ggplot(df3, aes(y=MEDV, x = "")) + geom_quasirandom() + labs(y = "Median housing value (US$1000)", x = "") + theme(axis.line.x = element_blank()) + coord_flip() h4 <- ggplot(df3, aes(MEDV)) + geom_density() + geom_rug() + labs(x = "Median housing value (US$1000)", y = "") + theme(axis.line.y = element_blank()) (h1 + h3)/(h2 + h4) ``` ] ] ] --- # .orange[Case study] .circle.bg-orange.white[3] Boston housing data .f4[Part 3/4] .panelset[ .panel[.panel-name[📊] .grid[ .item[ <img src="images/week5A/boston-plot5-1.png" width="432" style="display: block; margin: auto;" /> <img src="images/week5A/boston-plot6-1.png" width="432" style="display: block; margin: auto;" /> <img src="images/week5A/boston-plot7-1.png" width="432" style="display: block; margin: auto;" /> ] .item[ <img src="images/week5A/boston-plot8-1.png" width="432" style="display: block; margin: auto;" /> <img src="images/week5A/boston-plot9-1.png" width="432" style="display: block; margin: auto;" /> <img src="images/week5A/boston-plot10-1.png" width="432" style="display: block; margin: auto;" /> ] ] ] .panel[.panel-name[data] .h300.f4.scroll-sign[ ```r data(bostonc, package = "DAAG") df3 <- read_tsv(I(bostonc[10:length(bostonc)])) skimr::skim(df3) ``` ``` ## ── Data Summary ──────────────────────── ## Values ## Name df3 ## Number of rows 506 ## Number of columns 21 ## _______________________ ## Column type frequency: ## character 2 ## numeric 19 ## ________________________ ## Group variables None ## ## ── Variable type: character ──────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────── ## skim_variable n_missing complete_rate min max empty n_unique whitespace ## 1 TOWN 0 1 4 23 0 92 0 ## 2 TRACT 0 1 4 4 0 506 0 ## ## ── Variable type: numeric ────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────── ## skim_variable n_missing complete_rate mean sd p0 p25 p50 p75 p100 hist ## 1 OBS. 0 1 254. 146. 1 127. 254. 380. 506 ▇▇▇▇▇ ## 2 TOWN# 0 1 47.5 27.6 0 26.2 42 78 91 ▅▆▅▃▇ ## 3 LON 0 1 -71.1 0.0754 -71.3 -71.1 -71.1 -71.0 -70.8 ▁▂▇▂▁ ## 4 LAT 0 1 42.2 0.0618 42.0 42.2 42.2 42.3 42.4 ▁▃▇▃▁ ## 5 MEDV 0 1 22.5 9.20 5 17.0 21.2 25 50 ▂▇▅▁▁ ## 6 CMEDV 0 1 22.5 9.18 5 17.0 21.2 25 50 ▂▇▅▁▁ ## 7 CRIM 0 1 3.61 8.60 0.00632 0.0820 0.257 3.68 89.0 ▇▁▁▁▁ ## 8 ZN 0 1 11.4 23.3 0 0 0 12.5 100 ▇▁▁▁▁ ## 9 INDUS 0 1 11.1 6.86 0.46 5.19 9.69 18.1 27.7 ▇▆▁▇▁ ## 10 CHAS 0 1 0.0692 0.254 0 0 0 0 1 ▇▁▁▁▁ ## 11 NOX 0 1 0.555 0.116 0.385 0.449 0.538 0.624 0.871 ▇▇▆▅▁ ## 12 RM 0 1 6.28 0.703 3.56 5.89 6.21 6.62 8.78 ▁▂▇▂▁ ## 13 AGE 0 1 68.6 28.1 2.9 45.0 77.5 94.1 100 ▂▂▂▃▇ ## 14 DIS 0 1 3.80 2.11 1.13 2.10 3.21 5.19 12.1 ▇▅▂▁▁ ## 15 RAD 0 1 9.55 8.71 1 4 5 24 24 ▇▂▁▁▃ ## 16 TAX 0 1 408. 169. 187 279 330 666 711 ▇▇▃▁▇ ## 17 PTRATIO 0 1 18.5 2.16 12.6 17.4 19.0 20.2 22 ▁▃▅▅▇ ## 18 B 0 1 357. 91.3 0.32 375. 391. 396. 397. ▁▁▁▁▇ ## 19 LSTAT 0 1 12.7 7.14 1.73 6.95 11.4 17.0 38.0 ▇▇▅▂▁ ``` ]] .panel[.panel-name[R] .f4.scroll-sign[.s500[ ```r ggplot(df3, aes(PTRATIO)) + geom_histogram(fill = "#9651A0", color = "black", binwidth = 0.2) + labs( x = "Pupil-teacher ratio by town", y = "", title = "Bin width = 0.2, Left-open" ) ggplot(df3, aes(PTRATIO)) + geom_histogram(fill = "#9651A0", color = "black", binwidth = 0.5) + labs( x = "Pupil-teacher ratio by town", y = "", title = "Bin width = 0.5, Left-open" ) ggplot(df3, aes(PTRATIO)) + geom_histogram(fill = "#9651A0", color = "black", bins = 30) + labs( x = "Pupil-teacher ratio by town", y = "", title = "Bin number = 30, Left-open" ) ggplot(df3, aes(PTRATIO)) + geom_histogram(fill = "#9651A0", color = "black", binwidth = 0.2, closed = "left") + labs( x = "Pupil-teacher ratio by town", y = "", title = "Bin width = 0.2, Right-open" ) ggplot(df3, aes(PTRATIO)) + geom_histogram(fill = "#9651A0", color = "black", binwidth = 0.5, closed = "left") + labs( x = "Pupil-teacher ratio by town", y = "", title = "Bin width = 0.5, Right-open" ) ggplot(df3, aes(PTRATIO)) + geom_histogram( fill = "#9651A0", color = "black", bins = 30, closed = "left" ) + labs( x = "Pupil-teacher ratio by town", y = "", title = "Bin number = 30, Right-open" ) ``` ]]] ] --- # .orange[Case study] .circle.bg-orange.white[3] Boston housing data .f4[Part 4/4] .panelset[ .panel[.panel-name[📊] .grid[ .item[ <img src="images/week5A/boston-plotx-1.png" width="576" style="display: block; margin: auto;" /> ] .item.f4[ * CRIM: per capita crime rate by town * INDUS: proportion of non-retail business acres per town * NOX: nitrogen oxides concentration (parts per 10 million) * RM: average number of room per dwelling * AGE: proportion of owner-occupied units built prior to 1940 * DIS: weighted mean of distances to 5 Boston employment centres * RAD: index of accessibility to radial highways * TAX: full-value property tax rate per $10K * PTRATIO: pupil-teacher ratio by town * LSTAT: lower status of the population (%) * MEDV: median value of owner-occupied homes in $1000s ] ] ] .panel[.panel-name[data] .h300.f4.scroll-sign[ ```r df3long <- df3 %>% pivot_longer(MEDV:LSTAT, names_to = "var", values_to = "value" ) %>% filter(!var %in% c("CHAS", "B", "ZN")) skimr::skim(df3long) ``` ``` ## ── Data Summary ──────────────────────── ## Values ## Name df3long ## Number of rows 6072 ## Number of columns 8 ## _______________________ ## Column type frequency: ## character 3 ## numeric 5 ## ________________________ ## Group variables None ## ## ── Variable type: character ──────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────── ## skim_variable n_missing complete_rate min max empty n_unique whitespace ## 1 TOWN 0 1 4 23 0 92 0 ## 2 TRACT 0 1 4 4 0 506 0 ## 3 var 0 1 2 7 0 12 0 ## ## ── Variable type: numeric ────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────── ## skim_variable n_missing complete_rate mean sd p0 p25 p50 p75 p100 hist ## 1 OBS. 0 1 254. 146. 1 127 254. 380 506 ▇▇▇▇▇ ## 2 TOWN# 0 1 47.5 27.5 0 26 42 78 91 ▅▆▅▃▇ ## 3 LON 0 1 -71.1 0.0753 -71.3 -71.1 -71.1 -71.0 -70.8 ▁▂▇▂▁ ## 4 LAT 0 1 42.2 0.0617 42.0 42.2 42.2 42.3 42.4 ▁▃▇▃▁ ## 5 value 0 1 49.0 120. 0.00632 4 12.3 23.4 711 ▇▁▁▁▁ ``` ]] .panel[.panel-name[R] .f4[ ```r ggplot(df3long, aes(value)) + geom_histogram(color = "white") + facet_wrap(~var, scale = "free") + labs(x = "", y = "") + theme(axis.text = element_text(size = 12)) ``` ] ] ] --- # .orange[Case study] .circle.bg-orange.white[4] Hidalgo stamps thickness .panelset[ .panel[.panel-name[📊] <img src="images/week5A/hidalgo-plot-1.png" width="576" style="display: block; margin: auto;" /> * A stamp collector, Walton von Winkle, bought several collections of Mexican stamps from 1872-1874 and measured the thickness of all of them. * The different **bandwidth** for the density plot suggest either that there are two or seven modes. ] .panel[.panel-name[data] .h300.f4.scroll-sign[ ```r load(here::here("data/Hidalgo1872.rda")) skimr::skim(Hidalgo1872) ``` ``` ## ── Data Summary ──────────────────────── ## Values ## Name Hidalgo1872 ## Number of rows 485 ## Number of columns 3 ## _______________________ ## Column type frequency: ## numeric 3 ## ________________________ ## Group variables None ## ## ── Variable type: numeric ────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────── ## skim_variable n_missing complete_rate mean sd p0 p25 p50 p75 p100 hist ## 1 thickness 0 1 0.0860 0.0150 0.06 0.075 0.08 0.098 0.131 ▅▇▃▂▁ ## 2 thicknessA 195 0.598 0.0922 0.0162 0.068 0.0772 0.092 0.105 0.131 ▇▃▆▃▂ ## 3 thicknessB 289 0.404 0.0768 0.00508 0.06 0.072 0.078 0.08 0.097 ▁▃▇▁▁ ``` ]] .panel[.panel-name[R] .f4[ ```r ggplot(Hidalgo1872, aes(thickness)) + geom_histogram(binwidth = 0.001, aes(y = stat(density)), fill="grey80") + labs(x = "Thickness (0.001 mm)", y = "Density") + geom_density(color = "#E16A86", size = 2) + geom_density(color = "#00AD9A", size = 2, bw = "SJ") ``` ] ] ] --- class: transition # Focus --- # .orange[Case study] .circle.bg-orange.white[5] Movie length .panelset[ .panel[.panel-name[📊] .grid[ .item[ <img src="images/week5A/movies-plot1-1.png" width="432" style="display: block; margin: auto;" /> <img src="images/week5A/movies-plot2-1.png" width="381.6" style="display: block; margin: auto;" /> ] .item[ {{content}} ] ] ] .panel[.panel-name[data] .h300.f4.scroll-sign[ ```r data(movies, package = "ggplot2movies") skimr::skim(movies) ``` ``` ## ── Data Summary ──────────────────────── ## Values ## Name movies ## Number of rows 58788 ## Number of columns 24 ## _______________________ ## Column type frequency: ## character 2 ## numeric 22 ## ________________________ ## Group variables None ## ## ── Variable type: character ──────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────── ## skim_variable n_missing complete_rate min max empty n_unique whitespace ## 1 title 0 1 1 121 0 56007 0 ## 2 mpaa 0 1 0 5 53864 5 0 ## ## ── Variable type: numeric ────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────── ## skim_variable n_missing complete_rate mean sd p0 p25 p50 p75 p100 hist ## 1 year 0 1 1976. 23.7 1893 1958 1983 1997 2005 ▁▁▃▃▇ ## 2 length 0 1 82.3 44.3 1 74 90 100 5220 ▇▁▁▁▁ ## 3 budget 53573 0.0887 13412513. 23350085. 0 250000 3000000 15000000 200000000 ▇▁▁▁▁ ## 4 rating 0 1 5.93 1.55 1 5 6.1 7 10 ▁▃▇▆▁ ## 5 votes 0 1 632. 3830. 5 11 30 112 157608 ▇▁▁▁▁ ## 6 r1 0 1 7.01 10.9 0 0 4.5 4.5 100 ▇▁▁▁▁ ## 7 r2 0 1 4.02 5.96 0 0 4.5 4.5 84.5 ▇▁▁▁▁ ## 8 r3 0 1 4.72 6.45 0 0 4.5 4.5 84.5 ▇▁▁▁▁ ## 9 r4 0 1 6.37 7.59 0 0 4.5 4.5 100 ▇▁▁▁▁ ## 10 r5 0 1 9.80 9.73 0 4.5 4.5 14.5 100 ▇▁▁▁▁ ## 11 r6 0 1 13.0 11.0 0 4.5 14.5 14.5 84.5 ▇▂▁▁▁ ## 12 r7 0 1 15.5 11.6 0 4.5 14.5 24.5 100 ▇▃▁▁▁ ## 13 r8 0 1 13.9 11.3 0 4.5 14.5 24.5 100 ▇▃▁▁▁ ## 14 r9 0 1 8.95 9.44 0 4.5 4.5 14.5 100 ▇▁▁▁▁ ## 15 r10 0 1 16.9 15.7 0 4.5 14.5 24.5 100 ▇▃▁▁▁ ## 16 Action 0 1 0.0797 0.271 0 0 0 0 1 ▇▁▁▁▁ ## 17 Animation 0 1 0.0628 0.243 0 0 0 0 1 ▇▁▁▁▁ ## 18 Comedy 0 1 0.294 0.455 0 0 0 1 1 ▇▁▁▁▃ ## 19 Drama 0 1 0.371 0.483 0 0 0 1 1 ▇▁▁▁▅ ## 20 Documentary 0 1 0.0591 0.236 0 0 0 0 1 ▇▁▁▁▁ ## 21 Romance 0 1 0.0807 0.272 0 0 0 0 1 ▇▁▁▁▁ ## 22 Short 0 1 0.161 0.367 0 0 0 0 1 ▇▁▁▁▂ ``` ]] .panel[.panel-name[R] .f4[ ```r ggplot(movies, aes(length)) + geom_histogram(color = "white") + labs(x = "Length of movie (minutes)", y = "Frequency") ggplot(movies, aes(length)) + geom_histogram(color = "white") + labs(x = "Length of movie (minutes)", y = "Frequency") + scale_x_log10() movies %>% filter(length < 180) %>% ggplot(aes(length)) + geom_histogram(binwidth = 1, fill = "#795549", color = "black") + labs(x = "Length of movie (minutes)", y = "Frequency") ``` ] ] ] -- * Upon further exploration, you can find the two movies that are well over 16 hours long are "<i>Cure for Insomnia</i>", "<i>Four Stars</i>", and "<i>Longest Most Meaningless Movie in the World</i>" {{content}} -- * We can restrict our attention to films under 3 hours: <img src="images/week5A/movies-plot3-1.png" width="648" style="display: block; margin: auto;" /> {{content}} -- * Notice that there is a peak at particular times. Why do you think so? --- # Take away messages .flex[ .w-70.f2[ <ul class="fa-ul"> {{content}} </ul> ] ] -- <li><span class="fa-li"><i class="fas fa-paper-plane"></i></span>Numerical and graphical summaries can reveal, but also hide, aspects of data</li> {{content}} -- <li><span class="fa-li"><i class="fas fa-paper-plane"></i></span><b>Do many numerical and graphical summaries of the data!</b></li> --- # Resources and Acknowledgement - Slides originally written by Emi Tanaka and constructed with [`xaringan`](https://github.com/yihui/xaringan), [remark.js](https://remarkjs.com), [`knitr`](http://yihui.name/knitr), and [R Markdown](https://rmarkdown.rstudio.com). --- background-size: cover class: title-slide background-image: url("images/bg-01.png") <a rel="license" href="http://creativecommons.org/licenses/by-sa/4.0/"><img alt="Creative Commons License" style="border-width:0" src="https://i.creativecommons.org/l/by-sa/4.0/88x31.png" /></a><br />This work is licensed under a <a rel="license" href="http://creativecommons.org/licenses/by-sa/4.0/">Creative Commons Attribution-ShareAlike 4.0 International License</a>. .bottom_abs.width100[ Lecturer: *Di Cook* <i class="fas fa-envelope"></i> ETC5521.Clayton-x@monash.edu <i class="fas fa-calendar-alt"></i> Week 5 - Session 1 <br> ]