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-04A.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: *Emi Tanaka* <i class="fas fa-envelope"></i> ETC5521.Clayton-x@monash.edu <i class="fas fa-calendar-alt"></i> Week 4 - 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 contiuous variables <img src="images/week4A/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, \",\", \".\");\n }"},{"targets":11,"render":"function(data, type, row, meta) {\n return type !== 'display' ? data : DTWidget.formatRound(data, 0, 3, \",\", \".\");\n }"},{"targets":12,"render":"function(data, type, row, meta) {\n return type !== 'display' ? data : DTWidget.formatRound(data, 0, 3, \",\", \".\");\n }"},{"targets":13,"render":"function(data, type, row, meta) {\n return type !== 'display' ? data : DTWidget.formatRound(data, 0, 3, \",\", \".\");\n }"},{"targets":14,"render":"function(data, type, row, meta) {\n return type !== 'display' ? data : DTWidget.formatRound(data, 0, 3, \",\", \".\");\n }"},{"targets":15,"render":"function(data, type, row, meta) {\n return type !== 'display' ? data : DTWidget.formatRound(data, 0, 3, \",\", \".\");\n }"},{"targets":16,"render":"function(data, type, row, meta) {\n return type !== 'display' ? data : DTWidget.formatRound(data, 0, 3, \",\", \".\");\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> Given this data, what questions would you ask? <div class="countdown" id="timer_61186c75" style="right:0;bottom:0;" data-warnwhen="0"> <code class="countdown-time"><span class="countdown-digits minutes">02</span><span class="countdown-digits colon">:</span><span class="countdown-digits seconds">00</span></code> </div> .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","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/week4A/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 would you ask?** <div class="countdown" id="timer_61186b3b" style="right:0;bottom:0;" data-warnwhen="0"> <code class="countdown-time"><span class="countdown-digits minutes">02</span><span class="countdown-digits colon">:</span><span class="countdown-digits seconds">00</span></code> </div> --- # Formulating questions for EDA * Think .monash-blue[**broad (open-ended) questions**] that promotes discussion and divergent thinking -- * Polar questions (i.e. the answer is yes or no) are restrictive in exploring the data -- * For example, .flex[ .w-50[ .center[ <div class="question-box w-80 tl"> Is the outlying observation the electoral district that won the seat? </div> {{content}} ] ] .w-50[ <img src="images/week4A/aus-election-plot1-1.png" width="432" style="display: block; margin: auto;" /> ] ] -- <div class="center"> <div class="question-box w-80 tl"> What is characterising the distribution of the percentage of first preference votes for the Greens party? </div> </div> -- * What promotes a higher level of exploration? --- # .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? <div class="countdown" id="timer_61186a2f" style="right:0;bottom:0;" data-warnwhen="0"> <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> --- # 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/week4A/robust-mean-1.png' class='ba pl2' height ='150px'/> <img src='images/week4A/robust-mean-2.png' class='ba pl2' height ='150px'/> <img src='images/week4A/robust-mean-3.png' class='ba pl2' height ='150px'/> <img src='images/week4A/robust-mean-4.png' class='ba pl2' height ='150px'/> <img src='images/week4A/robust-mean-5.png' class='ba pl2' height ='150px'/> <img src='images/week4A/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;"> 0.523 </td> <td style="text-align:right;color: #1E88E5 !important;"> 0.552 </td> <td style="text-align:right;color: #FFC107 !important;"> 0.531 </td> <td style="text-align:right;color: #004D40 !important;"> 0.530 </td> </tr> <tr> <td style="text-align:right;"> 5 </td> <td style="text-align:right;color: #D81B60 !important;"> 0.432 </td> <td style="text-align:right;color: #1E88E5 !important;"> 0.285 </td> <td style="text-align:right;color: #FFC107 !important;"> 0.337 </td> <td style="text-align:right;color: #004D40 !important;"> 0.361 </td> </tr> <tr> <td style="text-align:right;"> 6 </td> <td style="text-align:right;color: #D81B60 !important;"> 2.972 </td> <td style="text-align:right;color: #1E88E5 !important;"> 2.477 </td> <td style="text-align:right;color: #FFC107 !important;"> 2.624 </td> <td style="text-align:right;color: #004D40 !important;"> 2.721 </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 calculated as `$$\sqrt{\sum_{i=1}^n \frac{(x_i - \bar{x})^2}{n - 1}}$$` * <span style="color:#785EF0">**Interquartile range**</span> is the difference between 1st and 3rd quartile and is a more robust measure of spread * <span style="color:#FE6100">**Median absolute deviance**</span> (MAD) is also more robust and defined as `$$\text{median}(|x_i - \text{median}(x_i)|)$$` ] .w-50.pl3[ <img src='images/week4A/robust-mean-1.png' class='ba pl2' height ='150px'/> <img src='images/week4A/robust-mean-2.png' class='ba pl2' height ='150px'/> <img src='images/week4A/robust-mean-3.png' class='ba pl2' height ='150px'/> <img src='images/week4A/robust-mean-4.png' class='ba pl2' height ='150px'/> <img src='images/week4A/robust-mean-5.png' class='ba pl2' height ='150px'/> <img src='images/week4A/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/week4A/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) **What do you notice from this graph?** <div class="countdown" id="timer_61186973" style="right:0;bottom:0;" data-warnwhen="0"> <code class="countdown-time"><span class="countdown-digits minutes">01</span><span class="countdown-digits colon">:</span><span class="countdown-digits seconds">30</span></code> </div> ] ]] .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/week4A/aus-election-plot2-1.png" width="432" style="display: block; margin: auto;" /> ] ] --- # Closer look at the _boxplot_ <img src="images/week4A/annotated-boxplot-1.png" width="432" style="display: block; margin: auto;" /> * Observations that are outside the range of lower to upper thresholds 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/week4A/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_611869e1" style="right:0;bottom:0;" data-warnwhen="0"> <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/week4A/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/week4A/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() + labs(x = "Rooms", y = "Percentage", fill = "Price") ``` ]]] -- * Okay nothing notable as far as I can see * 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/week4A/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/week4A/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/week4A/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(Price/1e6, as.factor(Rooms))) + geom_violin() + geom_boxplot(width = 0.1) + scale_x_log10() + labs(x = "Price ($1,000,000)", y = "# of Rooms") ``` ]]] -- * You can see that drawing separate violin and box 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/week4A/melb-house-price-plot2-1.png" width="432" style="display: block; margin: auto;" /> --- # 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> --- 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: *Emi Tanaka* <i class="fas fa-envelope"></i> ETC5521.Clayton-x@monash.edu <i class="fas fa-calendar-alt"></i> Week 4 - Session 1 <br> ]