BookmarkSubscribeRSS Feed
🔒 This topic is solved and locked. Need further help from the community? Please sign in and ask a new question.
Azeddine
Obsidian | Level 7

I use Proc severity and proc univariate to estimate my parameters of continuous probability function.

I don't understand why statistics of Kolmogorov Smirnov is different with the two proc.

At the same time, statistics have the same definition in the documentation :

http://support.sas.com/documentation/cdl/en/procstat/63104/HTML/default/viewer.htm#procstat_univaria...

http://support.sas.com/documentation/cdl/en/etsug/63348/HTML/default/viewer.htm#etsug_severity_sect0...

 

Other statistics like Anderson Darling and Cramer-von Mises are the same.

 

 

1 ACCEPTED SOLUTION

Accepted Solutions
Rick_SAS
SAS Super FREQ

I'm away from the office so I can't check D’Agostino, R. and Stephens, M. (1986), Goodness-of-Fit Techniques.

However, my guess is that SEVERITY is using an asymptotic test statistic. Under the null hypothesis, sqrt(N)*D  converges in distribution to another distribution (called the Brownian bridge).  In contrast, UNIVARIATE is probably using table and formulas that describe the distribution of D itself.

 

For large samples, I would think that the p-values would be similar.

View solution in original post

4 REPLIES 4
Rick_SAS
SAS Super FREQ

I'm away from the office so I can't check D’Agostino, R. and Stephens, M. (1986), Goodness-of-Fit Techniques.

However, my guess is that SEVERITY is using an asymptotic test statistic. Under the null hypothesis, sqrt(N)*D  converges in distribution to another distribution (called the Brownian bridge).  In contrast, UNIVARIATE is probably using table and formulas that describe the distribution of D itself.

 

For large samples, I would think that the p-values would be similar.

PGStats
Opal | Level 21

You didn't post your code. According to the documentation, the two procedures will be equivalent only when edf=STANDARD is chosen in proc SEVERITY, in the absence of censoring.

PG
Rick_SAS
SAS Super FREQ

To follow up, the main difference seems to be that UNIVARIATE, which does not support censoring, uses one modification of the D statistic, whereas SEVERITY, which does support censoring, uses a slightly different modification. 

 

The PROC SEVERITY formula

D*sqrt(n) + 0.19/sqrt(n))

 

appears on p. 113 in D'Agostino and Stephens. The formula handles the possibility of censored data and converges to an asymptotic distribution, which is tabulated in Table 4.4 and credited to Koztol and Byar (1975).

 

Azeddine
Obsidian | Level 7
Thank you very much

sas-innovate-2024.png

Join us for SAS Innovate April 16-19 at the Aria in Las Vegas. Bring the team and save big with our group pricing for a limited time only.

Pre-conference courses and tutorials are filling up fast and are always a sellout. Register today to reserve your seat.

 

Register now!

What is ANOVA?

ANOVA, or Analysis Of Variance, is used to compare the averages or means of two or more populations to better understand how they differ. Watch this tutorial for more.

Find more tutorials on the SAS Users YouTube channel.

Discussion stats
  • 4 replies
  • 1641 views
  • 5 likes
  • 3 in conversation