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Statistics 601, Fall 2005
Lab 2 Notes
In this lab we will describe several studies. Our objective will be, for each study, to
achieve the initial modeling step of defining appropriate random variables.
Study 1
A problem considered by Dr. Dixon in the past year was the topic of a seminar
he recently presented to the department. This problem involved the capture of
insects by a predatory plant species, a member of the family of pitcher plants Sarraceniaceae. These plants have a long central tube with a hood-shaped part at the
upper end. The tube has hair-like structures that point downward. Insects that
enter the tube are not able to move back up because of these hairs, and eventually
are digested by enzymes in the plant. Insects that do not enter the tube may obtain
nectar from the plant without becoming plant food. A primary prey species of the
pitcher plant species involved in this study are a certain type of small wasp. The
study was designed to determine how effective these plants are at capturing wasps.
The study consisted of two parts. The first part involved direct observation of
the plants for several hundred hours. The data recorded were the number of wasps
visiting the plants and the number of these that were captured by the plants. There
were a total of about 376 “plant-hours” of observation, 157 visits, and 2 captures.
The second part of the study involved cleaning out a number of plants, leaving the
study site, and returning about 2 weeks later (it takes the plants longer than 2 weeks
to totally digest a wasp that is captured). The data recorded in this part of the
study were the number of wasps captured by the plants over a period of 2 weeks,
which was equivalent to about 1416 “plant-hours”. There were a total of 6 wasps
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captured in this indirect observation portion of the study.
Our concern here is not with the actual numbers that resulted from this study,
but rather with the model formulated and the behavior of possible estimators from
this model. To this end, note that what has been described is a situation involving
rather rare events (capture of a wasp). The focus of the seminar by Dr. Dixon was
how information from the indirect observation part of the study could be combined
with information from the direct observation part of the study to improve estimation
of the rate of visits by wasps and the probability of capture given a visit.
Study 2
A set of data given by R.G. Jarrett (1979), Biometrika 66, 191-193, consists of
times at which explosions occurred in British coal mines that resulted in the deaths
of ten or more men, from 15 March 1851 to 22 March 1962. The data were compiled
from the Colliery Year Book and Coal Trades Directory, published by the National
Coal Board in London. The “observational operation” here consisted of recording
the time interval (in days) between the occurrence of such disasters. The objective of
most analyses of these data has been to determine whether or not there is a change
in frequency of such events over time.
Study 3
A major pest of soybeans is the Soybean Cyst Nematode (SCN). As the name implies, the eggs of these (unsegmented) worms are found in cysts, distributed in the
topsoil layers of fields. The spatial distribution of SCN are of interest to agronomists
and plant pathologists. To sample for SCN, soil samples are collected, and then the
number of cysts are extracted from the soil. It is suspected that soil characteristics,
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such as soil type, and soil moisture level may affect the efficiency of extraction. That
is, characteristics of the soil sample may affect the measurement operation. It is also
suspected that the overall level of infestation of SCN in a soil sample may effect the
efficiency of the extraction procedure. The overall goal of this study, then, is to
investigate the effects of soil types, soil moisture levels, and infestation levels on the
performance of an extraction method.
The extraction procedure we will be concerned with here is called wet sieving.
In this procedure, 100 cm3 of soil is added to 1.89 liters of water, any soil clumps
broken by mixing for 15 seconds. The soil suspension is then poured through a
20cm diameter, 850µm pore sieve, nested over a slimilarly sized 250µm pore sieve.
Sediment that is trapped in the 850µm sieve (and anything left in the original
suspension) is used to repeat the procedure 4 times. For each of the 4 repetitions,
the number of cysts left in the 250µm sieve are counted. It is a basic assumption
of the study that the cumulative number of cysts removed by the end of the 4t h
extraction is the total number present (based on previous studies).
The design of the study is that 4 soil texture classes (soil types) are stored at
3 soil moisture levels. For each soil type and moisture level combination, cysts are
artificially added to the soil at 3 levels of infestation,10, 50, and 200 cysts per 100g
of soil; I do not know if this means 100g wet weight or dry weight. For each of these
36 combinations of soil type, moisture, and infestation, 5 replicate soil samples are
taken and processed using the above extraction procedure. To give you some feel for
the data, the maximum numbers of cysts resulting from the 4 extractions (overall all
soil types, moisture levels, and replicates) were 318, 102, 27, and 14 (for extractions
1,2,3, and 4 respectively) while the minimum numbers of cysts were 9, 2, 0, and 0.