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