Help me to decide which test to use - If each proportion belongs to the same population

#1
Hi all
Please see the attached table.
I'd like to test if each proportion belongs to the same population.
Can you please indicate which statistical test is the appropriate to use?
Regards
Loukas
 

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indubioush

Quite Involved in Discussions
#2
There is not enough information to understand your question or to answer it. It looks like the proportion is the percent of defects. You cannot determine similarities in population by looking at percent of defects. What is the defect? Is there more than one defect? What attributes were measured?
 

Bev D

Heretical Statistician
Staff member
Super Moderator
#3
What is the process? How were the samples collected.? Sequential? Over time?
There is a lot more to real analysis than some statistical test...
 
#4
Dear indubioush and Bev D,
thanks for your replies.
Let me clarify the table.
The process concerns surgical procedures. The data are operating room times. All data drawn on January 1st, 2015, from 08:00 to 15:00 hours, for the 14 clinics. For example the first row expresses that, from 5745 minutes of surgeries, it was found that the 872 minutes was dead time (e.g. delays). The proportion is the quotient of 872/5745.
I applied to P control chart and found out the the data is over-dispersed, so the Laney P prime chart explains better the process.
My thought is to perform a proportion hypothesis testing (or any other one like ANOVA for example), to find out if each proportion comes from the same population of 51570 minutes and the whole significance interval.
I hope the above are clear to you.
Regards
Loukas
 

Bev D

Heretical Statistician
Staff member
Super Moderator
#5
Nice to hear that you are aware of the Laney p prime chart...
Unfortunately no statistical test is appropriate for your data. There is not enough independence and replication in your data set. The issue is that your samples are all from a single day. Data from a single day will not be completely independent from each other.

A control chart from each individual hospital is the appropriate ‘test’ but there must be multiple days involved. Remember that each day will have it’s own common causes of delay (volumes, types of surgery, material delivery, nursing attendance, etc.). So you must collect data over many days (20 or so) to make any reliable conclusions. For cycle times I have found that the I, MR chart is usually best even for proportional data, although the p prime chart is a better choice than the p chart. The p chart requires homogeneity while the p prime chart adjusts for natural non-homogeneity that isn’t handled through rational subgrouping.

‘Hypothesis tests’ such as ANOVA or even the better ANOM for proportions are NOT appropriate when you have more than 3 or 4 comparisons. The probabaility of a ‘false’ positive is just too high once the number of comparisons becomes large. And since the effect of factors that are related to time are involved in this type of situation any point estimate comparison is simply not appropriate.
 
#6
Dear Bev D hi,
I have a large database of these data for three years, collected daily.
I can make a table collected data in different days.
Then do you think that hypothesis testing for proportion, is applicable for relating each defect with the population?

Regards
Loukas
 

Bev D

Heretical Statistician
Staff member
Super Moderator
#7
No. Under no circumstances is a hypothesis test of any kind appropriate for this data.
 

Bev D

Heretical Statistician
Staff member
Super Moderator
#8
You will find “Data Sanity” by Davis Balestracci very helpful.
I also suggest you think about waht you really want to know about these surgery functions...that is teh most important step...then what do you think you will do to improve things?
 
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