can someone provide details what does decile do and how should be used
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Olive: In turn, what is "decile" precisely? Are you referring or alluding to a particular Stata command or function? Are you asking about the statistical idea of a decile or deciles? You ask for details but provide none yourself. Please expand your question (greatly).Comment
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Hi Olive, how are you getting on with Nick's question?Comment
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Originally posted by David Benson View Post
Hi everyone,
Two questions:
1. How would you interpret the results of sumdist?
I attempted an interpretation below - this is using David's example.
OUTPUTHTML Code:sumdist income if year==2010, n(10) qgp(gp)
INTERPRETATION
$17,974 is the first decile group.
10% of the observations are smaller than it.
$33,631 is the second decile group.
20% of the observations are smaller than it.
...
$113,743 is the ninth decile group.
90% of the observations are smaller than it.
2. How would you find the total income by decile?
The output would show 10 series. Each series would sum the income of the bottom 10%, next 10%, ..., top 10%.
I tried this code on David's example, but I don't think it is correct. It shows the counts and not the total income by decile.
HTML Code:xtile dec = income, nq(10) tabstat income, stat(n) by(dec)
Last edited by Malina Rokis; 19 Aug 2020, 13:20.Comment
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"$17,974 is the first decile" (not decile group) and 10% of the obs have an income less than the first decile. There are 9 deciles and they characterize 10 decile groups. -sumdist- shows you the share of total income that is held by each quantile group (decile group in this example), and saves results in r(). Also left behind in r() are the overall mean and the sample (sum of weights). From the latter 2 stored results you can get an estimate of total income for the sample as a whole. This total x decile group share = total income held by that decile group.
Code:. sysuse auto (1978 Automobile Data) . sumdist mpg, ng(5) Distributional summary statistics, 5 quantile groups --------------------------------------------------------------------------- Quantile | group | Quantile % of median Share, % L(p), % GL(p) ----------+---------------------------------------------------------------- 1 | 17.000 85.000 17.132 17.132 3.649 2 | 19.000 95.000 19.924 37.056 7.892 3 | 22.000 110.000 17.449 54.505 11.608 4 | 25.000 125.000 18.401 72.906 15.527 5 | 27.094 100.000 21.297 --------------------------------------------------------------------------- Share = quantile group share of total mpg; L(p)=cumulative group share; GL(p)=L(p)*mean(mpg) . return list scalars: r(gl5) = 21.29729729729729 r(cush5) = .9999999999999998 r(sh5) = .2709390862944162 r(qrel4) = 1.25 r(q4) = 25 r(gl4) = 15.52702702702702 r(cush4) = .7290609137055836 r(sh4) = .1840101522842639 r(qrel3) = 1.1 r(q3) = 22 r(gl3) = 11.60810810810811 r(cush3) = .5450507614213197 r(sh3) = .174492385786802 r(qrel2) = .95 r(q2) = 19 r(gl2) = 7.891891891891891 r(cush2) = .3705583756345177 r(sh2) = .199238578680203 r(qrel1) = .85 r(q1) = 17 r(gl1) = 3.648648648648649 r(cush1) = .1713197969543147 r(sh1) = .1713197969543147 r(ngps) = 5 r(p95) = 34 r(p90) = 29 r(p75) = 25 r(p50) = 20 r(p25) = 18 r(p10) = 14 r(p5) = 14 r(median) = 20 r(N) = 74 r(sum_w) = 74 r(mean) = 21.2972972972973 matrices: r(relquantiles) : 1 x 4 r(shares) : 1 x 5 r(quantiles) : 1 x 4 . di "total income held by poorest fifth = " r(sh1) * r(N) * r(mean) total income held by poorest fifth = 270Comment
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Your reply helped, thanks Stephen!
How would the exercise change if we were to find the total income by decile? Specifically, if the deciles are based on the population - so say there are 40M individuals, and we then want the total income of the 4M with the lowest income, next 4M with the lowest income, and so forth.
For example, I adapted your code slightly and added an extra line of code. From these 74 observations, how would we divide the data into equally sized groups?
Is there a better way to xtile?HTML Code:sysuse auto sumdist mpg, ng(5) qgp(group) return list di "total income held by poorest fifth = " r(sh1) * r(N) * r(mean) tabstat mpg, stat(sum n) by(group) Summary for variables: mpg by categories of: group (Quantile group) group | sum N ---------+-------------------- 1 | 270 18 2 | 314 17 3 | 275 13 4 | 290 12 5 | 427 14 ---------+-------------------- Total | 1576 74 ------------------------------
HTML Code:xtile gp=mpg, n(5) tab gp
Last edited by Malina Rokis; 19 Aug 2020, 17:42.Comment
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Type -help sumdist- and you'll see that there's an option to derive quantile group membership! (As it happens, -sumdist- calls -xtile- to do its work, as a "viewsource sumdist.ado" would show you.) With a membership variable created (with values 1,..., 10, for the decile group case, you can then loop to derive group totals
Notice, importantly, that the number of cases per decile group is not the same. This is a well-known (and common) issue, often discussed on Statalist (you can search), and arises because of the discrete nature of the finite sample data. Observe that the number of observations divided by ten does not give an integer result: 2246/10 = 224.6.Code:. sysuse nlsw88.dta, (NLSW, 1988 extract) . sumdist wage, ng(10) qgp(group) Distributional summary statistics, 10 quantile groups --------------------------------------------------------------------------- Quantile | group | Quantile % of median Share, % L(p), % GL(p) ----------+---------------------------------------------------------------- 1 | 3.221 51.347 3.803 3.803 0.295 2 | 4.026 64.184 5.088 8.891 0.691 3 | 4.694 74.838 4.705 13.595 1.056 4 | 5.435 86.648 6.541 20.136 1.564 5 | 6.272 99.998 7.461 27.597 2.143 6 | 7.311 116.557 8.750 36.347 2.823 7 | 8.671 138.251 10.368 46.716 3.628 8 | 10.274 163.796 12.105 58.821 4.569 9 | 12.778 203.719 15.127 73.948 5.743 10 | 26.052 100.000 7.767 --------------------------------------------------------------------------- Share = quantile group share of total wage; L(p)=cumulative group share; GL(p)=L(p)*mean(wage) . ta group Quantile | group | Freq. Percent Cum. ------------+----------------------------------- 1 | 245 10.91 10.91 2 | 242 10.77 21.68 3 | 188 8.37 30.05 4 | 226 10.06 40.12 5 | 222 9.88 50.00 6 | 225 10.02 60.02 7 | 227 10.11 70.12 8 | 222 9.88 80.01 9 | 231 10.28 90.29 10 | 218 9.71 100.00 ------------+----------------------------------- Total | 2,246 100.00 . ge gtotal = . (2,246 missing values generated) . forval g = 1/10 { 2. sum wage if group == `g' 3. replace gtotal = r(sum) if group == `g' 4. } Variable | Obs Mean Std. Dev. Min Max -------------+--------------------------------------------------------- wage | 245 2.707919 .4634796 1.004952 3.220612 (245 real changes made) Variable | Obs Mean Std. Dev. Min Max -------------+--------------------------------------------------------- wage | 242 3.667434 .2614696 3.239966 4.025765 (242 real changes made) Variable | Obs Mean Std. Dev. Min Max -------------+--------------------------------------------------------- wage | 188 4.365382 .1798131 4.033815 4.694041 (188 real changes made) Variable | Obs Mean Std. Dev. Min Max -------------+--------------------------------------------------------- wage | 226 5.048622 .2051734 4.703177 5.434783 (226 real changes made) Variable | Obs Mean Std. Dev. Min Max -------------+--------------------------------------------------------- wage | 222 5.86305 .2401936 5.442833 6.27214 (222 real changes made) Variable | Obs Mean Std. Dev. Min Max -------------+--------------------------------------------------------- wage | 225 6.784099 .2933849 6.272401 7.310784 (225 real changes made) Variable | Obs Mean Std. Dev. Min Max -------------+--------------------------------------------------------- wage | 227 7.967731 .3787266 7.318838 8.671494 (227 real changes made) Variable | Obs Mean Std. Dev. Min Max -------------+--------------------------------------------------------- wage | 222 9.512104 .4832126 8.679548 10.27375 (222 real changes made) Variable | Obs Mean Std. Dev. Min Max -------------+--------------------------------------------------------- wage | 231 11.42343 .6994007 10.32206 12.77777 (231 real changes made) Variable | Obs Mean Std. Dev. Min Max -------------+--------------------------------------------------------- wage | 218 20.84741 9.051053 12.82608 40.74659 (218 real changes made) . ta group , su(gtotal) Quantile | Summary of gtotal group | Mean Std. Dev. Freq. ------------+------------------------------------ 1 | 663.44012 0 245 2 | 887.51904 0 242 3 | 820.69177 0 188 4 | 1140.9886 0 226 5 | 1301.597 0 222 6 | 1526.4224 0 225 7 | 1808.6749 0 227 8 | 2111.687 0 222 9 | 2638.8113 0 231 10 | 4544.7354 0 218 ------------+------------------------------------ Total | 1737.1135 1093.8109 2,246 . tabstat gtotal, by(group) stats(mean count) Summary for variables: gtotal by categories of: group (Quantile group) group | mean N ---------+-------------------- 1 | 663.4401 245 2 | 887.519 242 3 | 820.6918 188 4 | 1140.989 226 5 | 1301.597 222 6 | 1526.422 225 7 | 1808.675 227 8 | 2111.687 222 9 | 2638.811 231 10 | 4544.735 218 ---------+-------------------- Total | 1737.114 2246 ------------------------------
I appreciate that you're new to Statalist -- welcome. But, please, read help-files in their entirety. before posting. And it'd be a good idea to read the Forum FAQ as well.Comment
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Stephen Jenkins gives excellent advice as always.
Here's another way to do it, without a loop.
Naturally the number of decimal places for mean and total wage is ridiculous, except to show that you get the same answers.Code:. sysuse nlsw88, clear (NLSW, 1988 extract) . sumdist wage, ng(10) qgp(group) Distributional summary statistics, 10 quantile groups --------------------------------------------------------------------------- Quantile | group | Quantile % of median Share, % L(p), % GL(p) ----------+---------------------------------------------------------------- 1 | 3.221 51.347 3.803 3.803 0.295 2 | 4.026 64.184 5.088 8.891 0.691 3 | 4.694 74.838 4.705 13.595 1.056 4 | 5.435 86.648 6.541 20.136 1.564 5 | 6.272 99.998 7.461 27.597 2.143 6 | 7.311 116.557 8.750 36.347 2.823 7 | 8.671 138.251 10.368 46.716 3.628 8 | 10.274 163.796 12.105 58.821 4.569 9 | 12.778 203.719 15.127 73.948 5.743 10 | 26.052 100.000 7.767 --------------------------------------------------------------------------- Share = quantile group share of total wage; L(p)=cumulative group share; GL(p)=L(p)*mean(wage) . egen mean = mean(wage), by(group) . egen count = count(wage), by(group) . gen gtotal = mean * count . tabdisp group, c(mean count gtotal) ---------------------------------------------- Quantile | group | mean count gtotal ----------+----------------------------------- 1 | 2.707919 245 663.4401 2 | 3.667434 242 887.5191 3 | 4.365382 188 820.6918 4 | 5.048622 226 1140.989 5 | 5.86305 222 1301.597 6 | 6.784099 225 1526.422 7 | 7.967731 227 1808.675 8 | 9.512104 222 2111.687 9 | 11.42342 231 2638.811 10 | 20.84741 218 4544.735 ----------------------------------------------
I will add a personal hobby-horse. Historically, deciles and other named quantiles are levels of a variable. The bins, classes or intervals they delimit are also often also called deciles (or whatever). The ambiguity doesn't usually bite hard, but spelling out that you mean bins, classes or intervals is painless and will impress those you want to impress.
The fullest list of such terms I know, with dates of known first use, is at
https://stats.stackexchange.com/ques.../235334#235334
which itself updates a list published in the Stata Journal in 2016. Further contributions to the menagerie are most welcome;Last edited by Nick Cox; 20 Aug 2020, 03:27.Comment
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Thank you very much Stephen and Nick!Comment
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Thank you all very much.Comment
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Hi everyone. Pls what is the stata code for estimating descriptive statistic by quantile. i want nq(4).
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Hi everyone. Pls, what is the stata code for estimating descriptive statistic by quantile. i want nq(4). i have panel data
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