about me
art
biz
Chess
corrections
economics
EconoSchool
Finance
friends
fun
game theory
games
geo
mathstat
misc
NatScience
... more
Profil
Logout
Subscribe Weblog

 
hondavsferrariGraphic Discovery, Howard Wainer: [E]ven the magic of logarithms does not always tame profound differences. One example of this appeared on July 8, 1997, in the automobile section of the New York Times. It listed the names and prices of the forty-seven convertible car models then available. They ranged from the $15,475 Honda del Sol all the way up to the Ferrari F50, priced at a cool $487,000. The range of prices was so broad that the illustrator of the Times could not fit all of them on the same graph and so had to resort to merely listing the most expensive ones separately. "Aha," I thought, "you should've tried logs!" Then I did, figuring that they would linearize the plot. They did, but not all cars fell on the same straight line (see figure 1). The thirty-four least expensive cars fell on one straight line, then there appeared to be a jump for the next seven cars, then another jump for three exotic European cars, and then on another line with a much steeper slope were the three most expensive cars.
cars01Thus we have discovered that the cars at the upper reaches of the domain have prices that exceed what a single exponential increase would dictate. Would some other way of thinking about convertible prices provide a clear functional relationship between rank order and price?

Taking the next step (inverses) in this ladder of transformations does the trick [One approach when data are skewed is to transform them to symmetry. For mild skewness, a square root often works; when it is more extreme, a logarithm; when more extreme still, an inverse. These steps in progression are often called "Tukey's ladder of transformations."] If we make a plot showing how many of each car we could buy for one million dollars (about sixty-five Honda del Sols cars02but only two Ferrari F50s), a simple linear relationship emerges (see figure 2). By making this transformation, we not only gain a linear relationship between rank and a function of price, but we also have a metric that is easier to think about and to comunicate to others. We also discover that two other groups of cars separate themselves from the pack: "nice convertibles" and "really nice convertibles".

Source: Graphic Discovery: A Trout in the Milk and Other Visual Adventures by Howard Wainer

related items:
Notes on the use of data transformations, Osborne, Jason (2002), Practical Assessment, Research & Evaluation, 8(6)
tikhonov meinte am 19. Aug, 14:49:
I get the point of clustering cars according to their price (into 'nice convertibles', 'luxury convertibles') like you did, but what sense does it make to fit a curve to the prices? Your explanatory variable (car type) is not even ordinal and the choice of models seems a little arbitrary to me... add a few more models in a similar price range and the fit will look much worse. 
Mahalanobis antwortete am 19. Aug, 16:56:
The New York Times
listed the names and prices of the forty-seven convertible car models then available. Therefore, the argument that adding a few more models will destroy the relationship isn't valid. Car type isn't intrinsically ordinal but it can be ranked by, say, price ;-D.

I think Howard Wainer did a great job in making the data accessible. Whether this relationship shows up each and every year is of secondary importance.

>>clustering cars.. like you did

I'd rather chew glass than use Comic Sans.
bancomicsans 
kimcil (guest) antwortete am 7. Apr, 12:23:
I am preparing a research paper and collecting information on this topic. Your post is one of the better that I have read. Thank you for putting this information into one post.
alfamart official partner merchandise fifa piala dunia brazil 2014
Unit Link Terbaik di Indonesia Commonwealth Life Investra Link 
begedir antwortete am 4. May, 15:02:
I am preparing a research paper and collecting information on this topic. Your post is one of the better that I have read. Thank you for putting this information into one post. belajar grammar bahasa inggris , ingin hamil , kata kata untuk ibu 
johncloe8885 antwortete am 22. Sep, 13:16:
A small amount
A small amount: 200 USD finance company provides people with bad credit guaranteed payday loans Bank, on the other hand, if you do not want to offer loans of less than one thousand
12 month loans
dollars. and the establishment of a bank to provide overdraft, overdraft quick loans
fees are very high, typically for the purpose of the business.
loans without credit check

The financial shortcomings on the day
short term loans

These ' today, although it is possible to get the funds ' financial information logbook loans
of people, almost like a loan and does not mention the disadvantages associated with advertising for the incentive. 
johncloe8885 antwortete am 22. Sep, 13:17:
A high rate
A high rate of interest: America's consumers Association (CFA), financial best payday loans
interest is enormous. the interest rate as high as 430 per cent. 7 percent, 12 month Direct lenders
to introduce a standard credit card Apr 4-12%, taking into account the Bank fast loans
loan, but all around is a bad idea.

Safety issues: many financial companies do business online. loans, the no credit check payday loans
borrower's social security number, and account information and controls quick loans
that contain sensitive information, such as, are expected to fill the online log book loans
application form: most of the time, the debtor, the debtor and to reveal security breaches can cause a nameless company. 
johncloe8885 antwortete am 26. Sep, 10:59:
"Financial series you want to delete the practice of consumer property development finance finance, billing and aggressiv and development And to encourage the movement forex robot
.Individual mortgage borrower card account personal best forex trading platform
loans, medical bills and car loans, home economic and family, this is asset finance
the cover.

Financing "on the loans for people on benefits
basis of the collected

When represented by counsel, you will not be able to communicate instant payday loans
directly with financial Financeor 
maskodok antwortete am 23. Nov, 12:43:
I am preparing a research paper and collecting information on this topic. Your post is one of the better that I have read. Thank you for putting this information into one post.
Pokerstar88.com agen texas poker dan domino online indonesia terpercaya, Agen Bola, Taruhan Bola, Agen Bola Terpercaya, Olb365.com Agen Judi Bola Online, Agen Judi Casino Online Indonesia Terpercaya 
typekey:junkcharts meinte am 20. Aug, 06:33:
reading the graph correctly
Please note that Howard did not cluster the prices. All he did was to rank-order them, line them up from lowest to highest; then, he found that at some points the prices jumped; from that, he inferred that there were a number of clusters.

Ironically, this clustering is much better seen in the log scale than in the reciprocal scale, the latter essentially having linearized everything. What Howard successfully did was to provide insight by comparing the "ladder of transformations". However, if we had started out with the reciprocal chart, then it would have been tough to determine the clustering. I have a few other related comments on transformations at my blog.

I do not agree that the reciprocal chart is "easier to communicate to others". It is just not a natural way for us to think about the quantity "how many cars can $1 million buy?"

I agree that the data is presented well but like the first commenter, it is fitting the straight line which irks me. Again more on my blog but the gist is that there is an implied linear regression between price and rank-order which is of limited use. 
Mahalanobis antwortete am 20. Aug, 17:54:
Ok, maybe my initial
enthusiasm stemmed from the fact that one rarely sees reciprocal charts in the wild. 
maskodok antwortete am 15. Jan, 01:16:
Interesting topic for a blog. I have been searching the Internet for fun and came upon your website. Fabulous post. Thanks a ton for sharing your knowledge! It is great to see that some people still put in an effort into managing their websites. I'll be sure to check back again real soon.
Mobil Sedan COrolla,IDrpoker.com agen Texas poker Online Indonesia Terpercaya, Mobil Sedan COrolla, Cipto Junaedy 
tikhonov meinte am 20. Aug, 19:54:
First of all sorry to Mahalanobis for mistaking you for the author of the graph, I should read more carefully next time.

I do think that the example is a nice illustration of transformations, but like typekey:junkcharts I'm doubting the usefullness of regression in this case. However I do not think that reciprocals (how many cars does $1m buy?) are too hard to communicate (as least not as hard as logarithms) Just think of fuel consumption which is stated as 'miles per gallon' in the US but as 'litres per 100 km' in Europe and it is hard to say which is the 'natural' way to think about it and which is the reciprocal. 
typekey:junkcharts meinte am 20. Aug, 23:13:
value of analysis
While we disagree on the usefulness of the line-fitting, I must point out what I think is the key take-away from Howard's analysis. It illustrates that creating data graphics is an iterative activity. It would be a tragedy if the graphic designer were not to create all versions of these and then decide on which version to show to the public.
I'd have chosen the log scale in this case but it really depends on what you want to say. 
ttlwu meinte am 20. Aug, 12:24:
Pretty good post. I just stumbled upon your blog and wanted to say that I have really enjoyed reading your blog posts. Any way I'll be subscribing to your feed and I hope you post again soon. Big thanks for the useful info.
funny video to share on facebook snorting smarties 
Lazy123 antwortete am 25. Mar, 03:01:
Thanks
canopy kain adalah penutup atau tudung rumah dari bahan kain yang bisa menambah aksen pada rumah anda. Jika anda memerlukan canopy kain maka anda bisa memesan canopy kain dari kami. Ada banyak sekali pilihan canopy kain yang bisa anda pilih. silahkan baca selengkapnya . Jika anda mau memesan canopy kain hubungi kami canopy rumah .
Untuk memperindah tampilan dari rumah anda maka anda bisa mencoba memasang lantai vinyl, karena lantai vinyl ini mempunyai banyak corak yang bisa anda pakai untuk membuat tampilan ruangan anda menjadi lebih eksklusif. klik di sini . Apabila anda butuh info lengkap masalah Vinyl Kayu hubungi kami jual lantai kayu parket .
Bata merah adalah salah satu komoditas bahan bagunan yang biasa digunakan di gedung apa saja. Anda bisa membangun bangunan dengan memesan batu bata merah dari kami. Kami menawarkan bata merah dengan harga murah. lihat penjelasan lengkapnya . Jika anda ingin memesan batu merah ini hubungi bata tanpa plester .
Paket internet bolt sudah terkenal akan kecepatannya. Jika anda ingin memakai paket internet dengan kecepatan yang memuaskan ini maka anda bisa memesannya dari kami secara online. Jual online paket internet bolt kami cepat dan terpercaya. silahkan baca selengkapnya . Untuk menemukan website jual paket internet bolt silahkan buka teempat beli pulsa bolt online .
apakah anda suka melakukan taruhan saat menonton pertandingan olahraga? Saat ini sudah hadir bandar sport di mana anda bisa ikut taruhan di agen judi bola online sehingga anda bisa menyaksikan pertandingan dengan lebih seru. silahkan baca selengkapnya . Info daftar situs agen judi bola lainnya silahkan baca agen casino online .
Jika anda membutuhkan jasa badut untuk memeriahkan pesta anda silahkan hubungi kami. Jika anda juga ingin membuat baju maskot atau jual kostum badut, maka anda juga bisa melihat koleksi kami. Silahkan kunjungi kostum badut bandung. lihat penjelasan lengkapnya . Silahkan cek koleksi kostum badut lainnya gambar badut lucu .
Bassura city adalah tempat hunian apartemen yang saat ini semakin menarik minat dari banyak orang. Jual hunian apartemen di bassura city mempunyai prospek yang cerah karena ini adalah kawasan super blok dengan banyak fasilitas menarik. baca artikel . Lihat aneka penawaran bassura city hanya di sini agen pemasaran apartemen bassura city .
Jika anda ingin membangun usaha batu bata merah, maka tentunya anda memerlukan mesin cetak dari bata merah itu sendiri. Mesin cetak ini bisa anda dapatkan dengan membuat beberapa pemesanan dari internet anda akan mendapatkan harga murah. baca artikel . Untuk melihat contoh dari mesin cetak bata merah ini silahkan ke website ini Mesin Pencetak Batu Bata Merah .
Busana gamis atau busana muslim saat ini lagi trend dan ada busana muslim untuk pesta dengan desain modern dan tren warna 2015. Jika anda tertarik ingin mencoba busana ini silahkan melihat ragam busana muslimah yang kami miliki di sini. lihat penjelasan lengkapnya . Koleksi busana muslim dan gamis terlengkap kami bisa cek di sini. jual gamis busana muslim model terbaru .
Saat ini semakin banyak orang yang suka menonton motoGP yang adalah balap motor yang sangat bergengsi. Ini adalah pertaruhan antara ketangguhan mesin dan kehebatan pengendara. Jika anda suka menonton motoGP dapatkan info motoGP terbaru di sini. kunjungi website kami . Jika anda menyukai info moto GP terbaru silahkan kunjungi halaman ini. Hasil Lengkap Kualifikasi MotoGP 2015 .
Jika anda membutuhkan jasa guru privat maka anda bisa mendapatkan bantuan guru privat dari dunia maya; karena ada banyak sekali penawaran les privat yang bisa membantu anak anda belajar dengan lebih fokus. klik di sini . Dapatkan guru les privat terpercaya di Jakarta; Bogor; Depok; Tangerang; Bekasi. Guru les privat .
Apakah anda ingin membangun usaha yang membutuhkan mesin-mesin? Kami adalah pengusaha jual online mesin-mesin untuk usaha seperti genset, printer percetakan dan masih banyak lagi. Jika anda membutuhkan suplier mesin, hubungi kami lihat artikel . Jika anda membutuhkan mesin percetakan; mesin pemotong; mesing hitung dan lain sebagainya hubungi kami. jual genset .
Apakah anda suka dengan baju muslim? Jika anda suka memakai baju muslim atau gamis anda bisa mengecek model terbaru dari baju gamis yang kami tawarkan di sini. Ada banyak gamis modern yang mungkin sesuai selera anda. baca artikel . Dapatkan model jilbab dan gamis syar'i terbaru di sini. Grosir jilbab murah meriah online dan offline .
apakah anda penggemar film? Jika ya, maka pasti anda suka menonton film-film yang terbaru. Di sini anda bisa mendownload film terbaru yang baru ditayangkan di bioskop. Anda bisa mendownload film ini secara gratis, karena sudah tersedia linknya. silahkan baca selengkapnya . Jika anda ingin download film sekarang silahkan kunjungi download film movie bioskop youtube terbaru subtitle indonesia .
Apakah anda pemilik dari android? Pastinya anda ingin android anda semakin menyenangkan dan untuk itu anda bisa memasang file apk terbaru. Anda juga bisa membaca aneka tutorial android dari blog kami jika anda mau mampir. silahkan baca selengkapnya . dapatkan file APK terbaru hanya di sini Kumpulan Cara,Tips dan Trik Android  .
Dalam usaha grosir busana muslim kami menawarkan banyak barang yang yang didesain sesuai dengan syar'i dan busana muslim ini mengikuti trend busana muslim 2015. Jika anda tertarik dan ingin melihat ragam modelnya silahkan cek. lihat penjelasan lengkapnya . Silahkan memilih koleksi grosir busana muslim kami grosir baju murah bandung .
Jika anda ingin membuka usaha di rumah maka ada beberapa hal yang harus anda perhatikan karena bisnis rumahan harus bisa menghasilkan untung dengan modal yang kecil. Jadi silahkan anda pelajari cara membangun bisnis rumahan berikut. kunjungi website kami . Baca profil usaha rumahan ini dan kenali potensinya Usaha dirumah tanpa modal .
Apakah anda sedang mencari cartridge printer bekas karena yang baru terlalu mahal. Jika anda ingin mendapatkan cartridge printer bekas yang masih baik silahkan kunjungi toko printer online kami. Ada banyak sekali jenis kosongan yang kami sediakan. klik di sini . Silahkan beli cartridge kosongan dari printer di sini Jual Beli Cartridge Bekas .
Jika anda ingin membeli playstation, maka pastikan anda membeli dari penjual playstation yang terpercaya. Anda bisa mendapatkan PS2 dan PS3 dengan harga murah karena dipasarkan secara online dan bebas pajak usaha. lihat artikel . beli playstation harga bersaing hanya di sini harga playstation 3 .
Silahkan lihat penawaran kredit mobil yang kami miliki. Kami menawarkan kredit mobil toyota; daihatsu dan honda dengan harga yang bersaing dan bunga kredit yang rendah. Jadi anda akan bisa mendapatkan keuntungan berganda. lihat penjelasan lengkapnya . Silahkan cek penawaran kredit yang kami miliki di sini Simulasi Kredit .
Apakah anda membutuhkan genteng untuk rumah anda? Kami membuat genteng press tanah liat dengan harga murah dan kami bisa mengantarkan genteng tanah liat ini ke rumah anda dengan pemesanan minimal 2000 genteng. baca artikel . jual genteng press tanah liat yang ada di sini. jual genteng press kodok .
Jika anda ingin membeli busana untuk keseharian anda maka anda bisa membeli dari blog fashion. Ada banyak sekali blog yang menawarkan busana wanita dengan aneka ragam motif. Silahkan cek motif dari baju wanita dan tas wanita di sini. kunjungi website kami . Anda juga bisa belajar membuat blog dan bermain SEO jika anda mempunyai cukup waktu luang; karena blogging harus dilakukan dengan serius. Silahkan pelajari cara melakukan SEO ini jual aksesoris dan tas online
kurasakisan meinte am 23. Sep, 17:03:
using other source again, oh man

Shadow Fight 2 Apk 
ttlwu meinte am 15. Oct, 12:04:
I really thank you for the valuable info on this great subject and look forward to more great posts. Thanks a lot for enjoying this beauty article with me. I am appreciating it very much! Looking forward to another great article. Good luck to the author! All the best!
nashville seo company 
ttlwu meinte am 26. Nov, 10:11:
I read that Post and got it fine and informative. Please share more like that...
best thermogenic 
ttlwu meinte am 23. Dec, 08:36:
That is really nice to hear. thank you for the update and good luck.
funny pictures daylight savings time 
justcool1122 meinte am 15. Jan, 12:54:
The information you have posted is very useful. The sites you have referred was good. Thanks for sharing.. safety jogger 
ttlwu meinte am 17. Jan, 11:12:
Wonderful illustrated information. I thank you about that. No doubt it will be very useful for my future projects. Would like to see some other posts on the same subject!
most effective treatment for neuropathy without medication 
SerieALivescore meinte am 23. Jan, 08:11:
www.scorespro.com
EUFA Champions League is world renowned football group held yearly, where champions of the European land leagues from recently are group within this awesome UEFA Champion League for you to play a new win your trophy that could declare them the top Football Crew of The european countries. www.scorespro.com 
AsharSeo meinte am 22. Mar, 07:24:
Auf über 300 m2 Fläche nden wir für Ihre Kunstwerke, Bilder und Fotos den passenden Rahmen, mit oder ohne Passepartout. Unsere top ausgestatte Rahmenwerkstatt ermöglicht uns schnell und in höchster Qualität auf jeden Kundenwunsch zu reagieren. Unsere über 20 Jahre Erfahrung sind ein großer Pluspunkt für unsere Kunden.Bilderschienen