Statistical test for difference between2 time series plots among 3 groups

Primavera — Thu, 12 Jan 2023 21:35:51 GMT

Hi all,

I am preparing a report about the interactions of a bunch of users with an online reporting tool. I have broken the users down into 3 groups (G1, G2, and G3). I am comparing them over about 20 metrics. The data collection period covers from 2019 to 2022 but not every participant has data in all the data collection intervals in this period. It seems like each subject has reporting periods that are unique to them and were not the same as other subjects! I have used Tableau and a date scaffold to create the following plots on three of the metrics that I have to report on. The date scaffold is very similar to the idea presented here: https://tarsolutions.co.uk/blog/tableau-scaffolding-dates-calculating-deferred-revenue/

Some plots are clearly different between the 3 groups (like the green plots). Some are not really that different between the 3 groups (like the yellow line plots). I have attached a sample of my data containing a few users to this post. The original data file included Reporting_Period_Start_Date and Reporting_Period_End_Date and the "Value" was being compared which was "Numerator"/"Denominator". I have created the Date_scaf and corresponding Daily_Numerator and Daily_Denominator and AVGs based on the original data.

So my question is; I can see that the green line plots are much different between the 3 groups but is there a statistical test for this difference?

I tried using ANOVA:

proc ANOVA data=SAS_Stat_Q;                                                                                                                                                                                                  
      class Group;                                                                                                              
      model AVGs = Group;                                                                                                       
      means Groups /hovtest welch;                                                                                                 
      run;

But this is incorrect. What the test interprets as means is that AVGs for each group are added together and then divided by the number of records in that group (a classic mean). What I need is a test that considers each date in the date_scaf for example 11/26/2020 which makes for the following table:

Date_scaf	Reporting_Period_End_Date	Reporting_Period_Start_Date	AVGs	Daily_Denominator	Daily_Numerator	Denominator	Numerator	Value	personID	Group
11/26/2020	11/28/2020	11/1/2020	10.54166	0.285714	3.011903	8	84.3333	10.54166	person009	G3
11/26/2020	11/28/2020	11/1/2020	12.73263	0.857143	10.91369	24	305.5832	12.73263	person004	G3
11/26/2020	11/28/2020	11/1/2020	20.76333	0.714286	14.83095	20	415.2666	20.76333	person007	G3
11/26/2020	11/28/2020	11/1/2020	1.356139	0.678571	0.920237	19	25.76664	1.356139	person011	G2
11/26/2020	11/28/2020	11/1/2020	2.133332	0.071429	0.152381	2	4.266664	2.133332	person021	G2
11/26/2020	11/28/2020	11/1/2020	11.18214	0.5	5.59107	14	156.5499	11.18214	person010	G1
11/26/2020	11/28/2020	11/1/2020	7.892497	0.714286	5.637498	20	157.8499	7.892497	person055	G1
11/26/2020	11/28/2020	11/1/2020	6.466663	0.321429	2.07857	9	58.19996	6.466663	person047	G1

so now for G1 the average that I want for this date is sum(Daily_Numerator for persons 010, 055, 047)/sum(Daily_Denominator for persons 010, 055, 047). This would be (13.30713/1.5357)=8.6652

Similar averages should be calculated for groups G2 and G3 and the results of all three to be compared.

Does anyone know what statistical test should be used here?

(view in My Videos)

Re: Statistical test for difference between2 time series plots among 3 groups

sbxkoenk — Fri, 13 Jan 2023 12:11:14 GMT

Hello,

Do you have SAS/ETS (part of SAS Econometrics in SAS VIYA)??

You could use PROC SIMILARITY to compare time series.
proc similarity has dynamic time warping (DTW) so time series can have :

different frequencies,
irregular intervals ,
different scale and
different length.

SAS/ETS 15.2 User's Guide
The SIMILARITY Procedure
https://go.documentation.sas.com/doc/en/pgmsascdc/9.4_3.5/etsug/etsug_similarity_syntax02.htm

See also here :
Fundamentals of Statistical Consulting
Week 10 Comparison of two time series

https://www.maths.usyd.edu.au/u/jchan/Consult/W10_CompareTwoTimeSeries.pdf

BR,

Koen

topic Statistical test for difference between2 time series plots among 3 groups in SAS Data Science

Statistical test for difference between2 time series plots among 3 groups

Re: Statistical test for difference between2 time series plots among 3 groups