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Date:         Tue, 7 Jun 2005 14:49:13 -0500
Reply-To:     "Swank, Paul R" <Paul.R.Swank@UTH.TMC.EDU>
Sender:       "SAS(r) Discussion" <SAS-L@LISTSERV.UGA.EDU>
From:         "Swank, Paul R" <Paul.R.Swank@UTH.TMC.EDU>
Subject:      Re: A stat question
Comments: To: Lu Liu <Lu.Liu@TALBOTS.COM>
Content-Type: text/plain; charset="us-ascii"

Unless you are considering this a sample from a time continuum then Peter is correct. There is no inference to be made. In addition, the data are very skewed and the effect sizes are very small. Even if this were a sample with very large sample sizes, the degree of skew will play havoc with the t distribution since the distribution of the standard deviation does not become normal nearly as quickly as the sampling distribution of the mean.

Given the distribution and the fact that you are dealing with all customers at a particular time point, I think I would forget about a significance test and look carefully at the cost factors relative to the returns. Those ought to the the numbers the decision makers want anyway.

Paul R. Swank, Ph.D. Professor, Developmental Pediatrics Medical School UT Health Science Center at Houston

-----Original Message----- From: SAS(r) Discussion [mailto:SAS-L@LISTSERV.UGA.EDU] On Behalf Of Lu Liu Sent: Tuesday, June 07, 2005 12:19 PM To: SAS-L@LISTSERV.UGA.EDU Subject: Re: A stat question

Hi Dr. Swank,

Below are the group size and their respective std. dev and means for each variable. I also want to mention that in this case, I actually split the entire population ~52,000 into 2 equal groups so they are not samples.

Group A Size = 26,004 Order Sales AOS Std. Dev 0.0503 14.0272 13.8897 Means 0.0024 0.5802 0.5706

Group B Size = 26,005 Order Sales AOS Std. Dev 0.0600 23.0460 23.0216 Means 0.0035 0.8463 0.8425

Thank you! Lu

-----Original Message----- From: SAS(r) Discussion [mailto:SAS-L@LISTSERV.UGA.EDU]On Behalf Of Swank, Paul R Sent: Tuesday, June 07, 2005 1:48 PM To: SAS-L@LISTSERV.UGA.EDU Subject: Re: A stat question

And what did the distribution for all these variables look like and what was the sample size? I would expect such variables to be positively skewed since there is an obvious floor (0) but no apparent ceiling. Therefore, the variability in total sales is likely to be quite large. Your sample size might be large enough to overcome the potential distributional problems but if the groups differed in sample size and variance, this could e a problem. Perhaps we need to see the sample sizes and standard deviations in addition to the means.

Paul R. Swank, Ph.D. Professor, Developmental Pediatrics Medical School UT Health Science Center at Houston

-----Original Message----- From: Lu Liu [mailto:Lu.Liu@talbots.com] Sent: Tuesday, June 07, 2005 11:15 AM To: Swank, Paul R; SAS-L@LISTSERV.UGA.EDU Subject: RE: A stat question

Hi Dr. Swank,

Thank you for your reply. I did have a dataset with all the customers from both groups and each of their orders, sales and average order size. I ran t-test on that dataset to see whether 2 groups' order, AOS and sales are significantly different. And p-value shows that group A's order is significantly different group B, but AOS and sales are not.

Lu

-----Original Message----- From: Swank, Paul R [mailto:Paul.R.Swank@uth.tmc.edu] Sent: Tuesday, June 07, 2005 12:06 PM To: Lu Liu; SAS-L@LISTSERV.UGA.EDU Subject: RE: A stat question

How did you do a t test on total sales when there are only two values, one for each group?

Paul R. Swank, Ph.D. Professor, Developmental Pediatrics Medical School UT Health Science Center at Houston

-----Original Message----- From: SAS(r) Discussion [mailto:SAS-L@LISTSERV.UGA.EDU] On Behalf Of Lu Liu Sent: Tuesday, June 07, 2005 9:54 AM To: SAS-L@LISTSERV.UGA.EDU Subject: A stat question

I have a stats rather than SAS question, but I think many SAS experts can help on this. Thank you very much in advance. We did an A/B test to test effectiveness of 2 e-mail creatives. The results are below:

Group Order AOS Sales A 62 $243 $15,000 B 92 $239 $22,000

* AOS stands for average order size ** Sales = AOS x Order

After I applied t-test, it shows that Group B placed significantly more orders than Group B, but the average order size (total sales divided by total orders) and total sales are not significantly different. I have 2 questions,

1) Is the total sales not significantly different because average order size between the 2 groups is not significantly different?

2) Is it correct to conclude that group B has generated (92 - 62) * $239 = $ 7,170 incremental sales since Group B's total orders are significantly different from Group A?

Your help is greatly appreciated.

Thank you, Lu


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