topic Re: Calculate the median (Q1-Q3) overall from a demographic table in Statistical Procedures

Calculate the median (Q1-Q3) overall from a demographic table

NewUsrStat — Mon, 27 Mar 2023 13:28:47 GMT

Hi guys,

suppose to have the following median age (Q1-Q3) by hospitals from a demographic table:

Hospital A Hospital B Hospital C

43(39-61) 55(41-78) 57(43-59)

How can I put the median overall with Q1-Q3 without calculating that on the entire cohort from data?

I have not the original data but only the final table.

Edit: what I would like to do is to give a single number (median and Q1-Q3) that represents all the Hospitals

Thank you in advance

Re: Calculate the median (Q1-Q3) overall from a demographic table

PaigeMiller — Mon, 27 Mar 2023 12:10:18 GMT

@NewUsrStat wrote:

How can I put the median overall with Q1-Q3 without calculating that on the entire cohort from data?

I have not the original data but only the final table.

I really don't understand what you are saying, please describe in more detail.

Re: Calculate the median (Q1-Q3) overall from a demographic table

Rick_SAS — Mon, 27 Mar 2023 12:59:47 GMT

You can't. That operation is not mathematically feasible. Because of the way the median is computed, you cannot estimate the overall median from the medians of the groups. For example, the following two data sets have exactly the same medians across all classes, but different overall medians.

data A;
input Group $ Value;
datalines;
A 1
A 2
A 3
B 2
B 4
B 6
;
proc means data=A median printalltypes ;
   class Group;
   var Value;
run;


data B;
input Group $ Value;
datalines;
A 1
A 2
A 3
B 4
B 4
B 6
;
proc means data=B median printalltypes ;
   class Group;
   var Value;
run;

Re: Calculate the median (Q1-Q3) overall from a demographic table

FreelanceReinh — Mon, 27 Mar 2023 14:33:22 GMT

Hi @NewUsrStat,

I think what you can say in general about the overall quartiles Q1, Q2 (median) and Q3 is that they are in the range of the corresponding group-specific quartiles:

39 <= Q1 <= 43
43 <= Q2 <= 57
59 <= Q3 <= 78

(assuming QNTLDEF=5 and that the given group-specific quartiles are exact).

Re: Calculate the median (Q1-Q3) overall from a demographic table

NewUsrStat — Mon, 27 Mar 2023 16:24:43 GMT

Thank you very much! Maybe the mean of the means is feasible?

Re: Calculate the median (Q1-Q3) overall from a demographic table

Rick_SAS — Mon, 27 Mar 2023 17:05:41 GMT

You can do the mean of means if you know the number observations in each group.

Assume

The first group has N1 observations and the mean is M1
The second group has N2 observations and the mean is M2
The third group has N3 observations and the mean is M3

Then the overall mean is

(N1*M1 + N2*M2 + N3*M3) / (N1 + N2 + N3)

The numerator is the sum of the variable. The denominator is the total number of observations.