Standard Deviation, Individual Eggs

The standard deviation (SD) for individual eggs is very slightly different from theory, and the three egg types have detectably different characteristics from each other. These differences are so small that it takes an analysis of several months' data to show them as reliable or statistically significant. Mike Meyer wrote programs to do this, and the results are presented here.

Date: Sat, 15 Sep 2001 23:19:15 -0400
From: Mike Meyer 
To: rdnelson@Princeton.EDU
Subject: sd values for 12 more months

Roger

I have attached a csv file to this document that has the sd statistics
and number of valid data items for 18 months of data.  The data has been
broken down into three groups, with six month in each group.

first group  - jan 2000 to june 2000

second group - july 2000 to dec 2000

third group  - jan 2001 to june 2001

The first line of the file is the egg id#, next three lines are for the
sd totals, and the final three contain the number of data elements each
egg generated.  

The program also checked for, and rejected all values of 0 and 200.  It
displayed the egg number and the date and time of the event.  The
results show that the zero's found have the same pattern surrounding
them.  The pattern for all 4 days is:

-random number
-1
-1
-1
-184
-0
-a few other numbers
-then the generators produce no data for an unknown length of time


Here are the dates and times of the events:

June 22, 2000  21:43:16   egg id# 111

Dec 09, 2000   13:57:48   egg id# 115

Feb 27, 2001   01:33:04   egg id# 118

Mar 16, 2001   21:43:16   egg id# 106


Note that the June and March times are the same. 

Although the zero values were not included in the data used for the
attached file, the values around it were.  This may effect the sd of
its six month period.

Later, mike sent another version of the analysis, which he describes as follows.

This is three groups of six month totals, but I have removed the errors from 
the days that I had previously identified, along with a couple of new errors.  
Comparing the values of the sd before and after removal of the errors shows 
only a small drop in the sd of the corrected period.  For example, with the
error in egg#111 the first six months of 2000 is 7.071832, without the error 
it is 7.071607.  The data from July to Dec of 2000, egg 1000, and Jan to 
June 2001, egg 28 has not been included due to the errors in the periods.

I have tested the entire period from Jan 2000 to June 2001 for values
<50, and >150.  I have only found three days with data in this range. 
These times are:

Sept. 29, 2000 egg#1 - 00:14:04 - has value of 6, then ends

Oct. 09, 2000 egg#1024 - 08:18:11 - has value of 159, then ends

May 16, 2001 egg#118 - 04:39:19 - has values 1,1,1,184 then ends

In the following table, I have only included egg values for six month 
periods that contain more than 10 million trials.  This will keep the 
chart as simple to read as possible, and will still allow comparisons 
across the three time periods.  When the data from the last six months 
of 2001 is available, I will add it to the chart, and email it to you.

This table lists the values of each eggs standard deviation during three 
periods of six months. Only periods with eggs that have reported over 10 
million trials have been entered, with most of the eggs reporting about 
15 million trials in a six month period.

Mike Meyer