More examples:
1. A researcher wants to investigate whether there is a genetic component that contributes to the
susceptibility to a particular debilitating virus in domestic sheep. He wants to test whether there is an
association between the inheritance of a particular allele in the genome (AA, AG, or GG) and the viral
load of the virus (any non-0 number indicates presence of virus, with higher numbers indicating
increased severity) in an experimental flock consisting of 200 sheep from 3 breeds ranging in age from 36 years. Past studies of this virus have determined that age and breed both are significant factors in the
susceptibility to this virus and so must be taken into account when determining the statistical model. In
addition, the breeding structure of the flock must be accounted for as well.
ID# - Individual ID number of sheep in flock
Breed – Breed of sheep – 3 - Polypay, Rambouillet, or Columbia
SireID – Individual ID number of the Sire (dad) of the sheep
Age – Age of sheep – ranges from 3-6 years
Genotype – genotype at genetic loci – 3 - AA, AG, or GG
Viral Load – non-0 numbers indicate presence of virus, higher numbers = increased severity
IID
Breed
SireID
20060019
Polypay
1999046501
20060020
Polypay
1997044528
20060021 Rambouillet 1997108008
20060022
Polypay
1997044528
Age
3
5
5
5
Genotype at genetic loci
GG
AG
GG
GG
Viral Load
0
1.2
0
0
2. Grain protein is an important quality standard in small grains such as wheat and barley. In wheat it is
an important factor in determining baking quality. In barley it is an indicator of malting quality as well as
food value. Traditionally grain protein was measured by combustion, however Near Infra Red (NIR)
technology has been developed as a rapid, non-destructive means of measuring grain protein and is now
the standard method for breeding programs, variety testing and grain quality inspection. NIR estimates
protein content based on reflectance from the grain at a specific wavelength, by taking repeated
readings of a bulk sample (approximately 600 grams). Because the result is based on a correlation (not
an absolute measure of protein) it is essential that analyzers are calibrated correctly.
In this experiment I grew 4 barley varieties in a Complete Randomized Block Design field experiment
with three replicates of each variety. A subsample of the harvested grain was cleaned and used to
estimate percent protein from each plot. Every subsample was tested on both analyzers (Protein 1 and
Protein 2). The two protein analyzers are located in the same room of the WSU-Pullman Seed House
and are routinely used by breeding programs and the WSU variety testing program. Protein 1 is from a:
Infratec 1241 grain analyzer (Foss); Protein 2 is from a: Infratec 1226 grain analyzer (Tecator).
I am interested in determining:
1.
Does variety have a significant effect on grain protein?
2.
Does protein analyzer have a significant effect on grain protein?
The answer to question 1 is a simple ANOVA if I only include the results from one analyzer. However, I
am not sure how to best compare Protein 1 and Protein 2.
Assumptions:
Because grain samples are relatively stable, NIR is non destructive and all measurements were taken
within an hour, I assumed that the order of analysis did not influence the results. (Ideally protein
measurements would be taken in a completely randomized order).
Data:
Variety
Block
1
1
1
2
2
2
3
3
3
4
4
4
1
2
3
1
2
3
1
2
3
1
2
3
Protein 1
9.8
11.8
12.1
10.2
11.2
12.2
9.1
9.2
10.7
8.8
10
11
Protein 2
10.2
11.9
12.3
10.4
11.5
12.3
9.4
9.7
10.8
9.2
10.2
11.1
3. A researcher was interested in studying the effect of Bovine Respiratory Disease (BRD) on feed
intake between two breeds of beef cattle ( Angus and Hereford) for different age groups (<6 months, 612 months, 12-20 months, >20 months). Four farms were chosen across Washington State. During
higher disease prevalent period (first week of September), from each farm daily feed intake was
measured in 20 diseased animals for 7 consecutive days. 10 healthy animals in each group were used as
control (to take account of breed differences).
4. Under such conditions, we have only five dairy cows that their body conditions are similar and they
are equipped with cannula. In order to evaluate the effect of four (1,2,3,4) kinds of fat supplement
production to the rumen fermentation, we chose these five cows to do this experiment.
Before the addition of these fat products, rumen samples were taken at five time points and analyzed
the concentration of ammonia nitrogen; then one fat product was added to the ration at four levels,
100, 200, 400, 800g/d; and at the same time points after feeding, rumen liquid samples were taken and
analyzed the concentration of ammonia nitrogen; after finishing this, we added another product, there
are 10 days diet adaption for these cows; and do the same things.
Table Collection data for the concentration of ammonia nitrogen concentration of rumen liquid
(mg/100mL)
adding
conc.
time0
time2
time4
time6
t8
0 17.64215
19.281
14.54 6.267788 10.08054
0 15.88132
23.72
14.02 5.983784 6.210986
0 16.73334 20.49638 10.92545 9.058128 7.062998
0 23.47134 22.16492 15.90262
14.1702 6.807396
0 15.80322
13.2 10.49945 10.26514 11.71356
10011
9.28
27.774
20.94
1.16
20.9
1001
12.08
14.8
12
2.26
10.62
1001
14.56
31.96
25.58
9.58
10.7
1001
20.36
28.64
15.64
8.06
10.32
5. The Rocky Mountain wood tick (RMWT), Dermacentor andersoni, has been collected from several
USDA ranges and differ in average mass. Ticks from Dubois ID, a site characterized by sagebrush and
only small potential hosts have on average, a smaller mass than ticks from the other sites. Reynold’s
Creek ID is an agricultural area and the ticks feed primarily upon cattle and are on average very large.
Lake Como MT is biologically very diverse, containing potential hosts of multiple species and sizes. Ticks
collected from this site range in size from smaller than Dubois ticks to larger than Reynold’s Creek ticks.
Ticks will be collected from the Lake Como site will be weighed and host type will be determined by PCR
analysis. Data will be analyzed for a correlation between tick body mass/egg mass and host type.
Preliminary weight data is provided. (some data)
females males
3.37
2.8
3.82
2.82
4.14
2.96
4.42
2.99
4.91
3.03
4.95
3.17
4.95
3.22
5.02
3.3
5.04
3.34
5.19
3.38
Dubois
3.24
3.31
3.32
3.55
3.61
3.66
3.92
3.96
3.98
4.02
Lake
Reynlds
Como
Ck.
2.21
1.99
2.49
3.52
3.39
3.88
3.63
4.16
3.96
4.17
4.05
4.36
4.14
5.03
4.35
5.05
4.55
5.05
4.85
5.06