Post on 27-Apr-2015
transcript
02Smeth1
• Completely Randomized Design with
subsampling
02Smeth2
• Subsampling experiments promote efficient use of space and materials, and measures variability among observational units.
• They are most efficient when there is much variation in response among explants and little outside variation.
02Smeth3
• The design is not efficient when there is little variation among explants or when there is a high degree of variability from some other identifiable source.
• This is because it reduces the df for experimental error which means that a higher F-value is required to detect significant differences among treatments.
• If there is a little variation among experiments, a CRD without subsampling should be used.
• If variation from an identifiable source exists, a RCBD with subsampling should be used.
02Smeth4
Subsampling
• Often multiple observations are collected on an experimental unit.
• For example, you may have four plants in a single pot each receiving the same treatment. The experimental unit for treatment comparisons being the pot of four plants.
• However, if you are interested in plant height you may measure the height of each of the plants within the pot. You would then have four sampling units per experimental unit.
02Smeth5
• The main reason for having multiple sampling units per experimental unit is cost. That is the cost for measuring all four plants in each pot is small compared to the cost of measuring a single plant in four times as many pots.
02Smeth6
• It is very important to note that subsampling does
not increase the number of replications.
• That is in terms of treatment comparisons you
might as well analyze the average height of the
four plants.
• The number of replications is still the number of
EXPERIMENTAL UNITS per TREATMENT, not the
number of observations per treatment.
02Smeth7
• Replications of treatments are assigned completely at random to independent groups of experimental subjects, such as adjacent trees, plants within the same pot or leaves on the same tree.
• Adjacent groups could potentially have the same treatment.
• A group of experimental subjects is considered a single independent experimental unit.
02Smeth8
• Large EU make subsampling a necessity.
• In other experiments, the researcher may
introduce subsampling in order to study the
within variability. Knowledge of this variation
may be of value in future research experiments.
02Smeth9
Sample layout:
There are 4 replications (1-4) of 3 treatments (A-C)
with 3 subsamples (a-c) per replication. Different
colors represent different treatments.
A1a A1b A1c B2a B2b B2c C3a C3b C3c B4a B4b B4cB1a
B1b B1c A2a A2b A2c C2a C2b C2c A4a A4b A4cC1a C1b
C1c B3a B3b B3c A3a A3b A3c C4a C4b C4c
02Smeth10
Examples on Subsampling
Example Trt E.U. Sampling Unit
Agronomy Fertilizer Rate Plot Plot has 6 rows and only
harvest 2 rows
Row is Sampling Unit
Animal
Science
Diet Pen of 4
calves
Measure 2 calves
Calf = Sampling Unit
Lab Science Growth media Beaker Measure 2 samples from
beaker,
Sample = Sampling Unit
02Smeth11
ANOVA with Sampling (Equal Number of
Samples Per Experimental Unit)
02Smeth12
Model
02Smeth13
ANOVA
02Smeth14
ANOVA Fixed Effect
SOV df SS MS F-Value
Treat t-1 SST MST MST/MSE
Exp. Error t(r-1) SSE MSE
Sampling
Error
tr(s-1) SSS MSS
Total trs-1 SSY
02Smeth15
02Smeth16
Example
02Smeth17
Hypothesis
02Smeth18
02Smeth19
02Smeth20
02Smeth21
02Smeth22
02Smeth23
02Smeth24
02Smeth25
ANOVA Fixed Effect
SOV df SS MS F-Value
Treat t-1 SST MST MST/MSE
Exp. Error t(r-1) SSE MSE
Sampling
Error
tr(s-1) SSS MSS
Total trs-1 SSY
02Smeth26
02Smeth27
02Smeth28
Example
02Smeth29
Data
02Smeth30
ANOVA
02Smeth31
02Smeth32
Trt
Plot 1 2 3 4
1 - - - - - - - -
2 - - - - - - - -
3 - - - - - - - -
4 - - - - - - - -
5 - - - - - - - -
6 - - - - - -
7 - - - -
8 - -
02Smeth33
ANOVA
Sov df
Trt t - 1
Exp. Error r.- t
Sample. Error n.. – r.
Total n.. - 1
t = # of treatment. r. = # E.U n.. = sample number
02Smeth34
ANOVA
Sov df
Trt t – 1 = (4-1) = 3
Exp. Error r.- t = 26 – 4 = 22
Sample. Error n.. – r. 52 – 26 = 26
Total n.. - 1 52 – 1 = 51