Interquartile range

[Joe Tuckles]

Hello,

Please can anyone advise how I generate the interquartile range? I have a data example for age here:

. sum age, detail

                     Age at recruitment
-------------------------------------------------------------
      Percentiles      Smallest
 1%           41             40
 5%           44             40
10%           47             40       Obs                 990
25%           53             40       Sum of Wgt.         990

50%           60                      Mean            58.5101
                        Largest       Std. Dev.       7.68262
75%           65             70
90%           68             70       Variance       59.02265
95%           69             70       Skewness      -.5442946
99%           69             70       Kurtosis       2.248327

[Carlo Lazzaro]

Joe;
median (AKA 50% pecentile)=60; IQR: 53;65.

. sum age, detail

                     Age at recruitment
-------------------------------------------------------------
      Percentiles      Smallest
1%           41             40
5%           44             40
10%           47             40       Obs                 990
25%           53             40       Sum of Wgt.         990

50%           60                      Mean            58.5101
                        Largest       Std. Dev.       7.68262
75%           65             70
90%           68             70       Variance       59.02265
95%           69             70       Skewness      -.5442946
99%           69             70       Kurtosis       2.248327

[Joe Tuckles]

Thanks!

[Marcos Almeida]

Carlo gave the best approach.

If you wish to automatically calculate the IQR, this code may be helpful as well:

. sysuse auto
(1978 Automobile Data)

. quietly summarize mpg, detail

. di r(p25)
18

. di r(p75)
25

. display "interquartile range = " r(p75) - r(p25)
interquartile range = 7

[Nick Cox]

Some other things: tabstat, egen, collapse, ...

. sysuse auto, clear
(1978 Automobile Data)

. tabstat mpg, by(foreign) s(n p25 p75 iqr)

Summary for variables: mpg
     by categories of: foreign (Car type)

 foreign |         N       p25       p75       iqr
---------+----------------------------------------
Domestic |        52      16.5        22       5.5
 Foreign |        22        21        28         7
---------+----------------------------------------
   Total |        74        18        25         7
--------------------------------------------------

. egen iqr = iqr(mpg), by(foreign)

. help  collapse

[Rich Goldstein]

note also that there are several commands that directly give the iqr including -table- and -tabstat-

[Daniel Bogale Odo]

Hello,
I wanted to interpret my result by interquartile range (IQR), e.g., per one IQR. I have continuous predictor variable (x) and create this in stata:
egen IQR1_x=iqr(x)
gen IQR2_x=x/IQR1_x

then, I am going to use "IQR2_x" in my model and interpret as 'the change in the outcome var per one IQR change in the predictor (X). Am I right or, is there a way I can do that?
I appreciated any support in advance.

[Nick Cox]

Well,

value / IQR (1)

and

(value MINUS median) / IQR (1')

would be analogues of

value / SD (2)

and

(value MINUS mean) / SD (2')

and the only question is whether they do what you want. For any given variable, (1) and (2) would be perfectly correlated, but there are some other pitfalls, including a possible extreme where the IQR is zero and the result is undefined. As a way to standardize variables (1) and (1') are not guaranteed to resist outliers as they are linear transformations and the IQR could be relatively small in a highly skewed distribution.

[Daniel Bogale Odo]

Great thanks! Nick Cox, these points are really helpful. Taking your these suggestions into account, I prefer to standardize the value so that decided to use 'value MINUS median) / IQR'.

Thanks again for prompt assistance!