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STAT 4204/5204G: Experimental Design Homework 1
发布时间:2022-09-15
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STAT 4204/5204G: Experimental Design
The scenarios below illustrate the use of experimental and observational units (from notes of J. P. Morgan):
Fisheries researchers are investigating the use of various supplements in growth rate of farmed fish. The growth rate is measured for each fish. There are five supplements to be compared over a period of one month beginning with 50 fingerlings (tilapia) of similar age and size. Several designs are being considered, with varying costs and difficulties of implementation, and also with different implications for the statistical precision of the results. For each of the scenarios considered, identify the treatments, the replicates, the experimental units, the observational units, the blocking factor, if any, and the subsamples.
The scenarios are below.
1. Fifty standard tanks are set up, each with one fish. Ten tanks are randomly selected for each supplement. Feed pellets are produced with the supplements included, and poured into the tank twice a day for a month.
2. Ten standard tanks are set up, each with 5 fish. Two tanks are randomly selected for each supplement. Feed pellets are produced with the supplements included, and poured into the tank twice a day for a month.
3. Ten standard tanks are set up, each with 5 fish. But so only five tanks need be purchased and maintained, the experiment will be run over two months, five tanks each
month. One tank is randomly selected for each supplement each month. Feed pellets are produced with the supplements included, and poured into the tank twice a day for a month.
4. A large tank is partitioned into ten sections using a screen. The screen allows water circulation among sections but does not allow feed pellets to pass from one section to another. Five fish are placed in each section, and two sections are randomly selected for each supplement. Feed pellets are produced with the supplements included, and poured into the tank twice a day for a month.
5. Ten standard tanks are set up like in (b), but the supplements are given differently. The
5 fish in a tank have identification tags. The supplement is provided by individual injection to each fish, twice each day. One fish is randomly selected from each tank at the start of the experiment to receive each supplement. The fish still receive the feed
pellets twice a day, but they do not include the supplement.
The rest of the homework takes you through each scenario to answer the questions that you need to complete on Canvas for Homework 1.
Problem 1
Fifty standard tanks are set up, each with one fish. Ten tanks are randomly selected for each supplement. Feed pellets are produced with the supplements included, and poured into the tank twice a day for a month.
Question 1
Identify the treatments.
6. 5 supplements
7. 50 tanks
8. 10 tanks
9. 10 sections of the tank
10. 50 fish
11. 2 months
12. None
13. Growth rate
Question 2
Identify the Experimental Units.
a. 5 supplements
b. 50 tanks
c. 10 tanks
d. 10 sections of the tank
e. 50 fish
f. 2 months
g. None
h. Growth rate
Question 3
Identify the Observational Units.
a. 5 supplements
b. 50 tanks
c. 10 tanks
d. 10 sections of the tank
e. 50 fish
f. 2 months
g. None
h. Growth rate
Question 4
Identify the Blocks.
a. 5 supplements
b. 50 tanks
c. 10 tanks
d. 10 sections of the tank
e. 50 fish
f. 2 months
g. None
h. Growth rate
Question 5
State the number of replications. The replications are the number of experimental units per treatment.
Question 6
State the number of subsamples. The subsamples are the number of observational units per experimental unit. If there is only one observation per experimental unit, then answer 1, not 0. The number 0 is not a correct answer for this question.
Problem 2
Ten standard tanks are set up, each with 5 fish. Two tanks are randomly selected for each supplement. Feed pellets are produced with the supplements included, and poured into the tank twice a day for a month.
Question 7
Identify the treatments.
a. 5 supplements
b. 50 tanks
c. 10 tanks
d. 10 sections of the tank
e. 50 fish
f. 2 months
g. None
h. Growth rate
Question 8
Identify the Experimental Units.
a. 5 supplements
b. 50 tanks
c. 10 tanks
d. 10 sections of the tank
e. 50 fish
f. 2 months
g. None
h. Growth rate
Question 9
Identify the Observational Units.
i. 5 supplements
a. 50 tanks
b. 10 tanks
c. 10 sections of the tank
d. 50 fish
e. 2 months
f. None
g. Growth rate
Question 10
Identify the Blocks.
a. 5 supplements
b. 50 tanks
c. 10 tanks
d. 10 sections of the tank
e. 50 fish
f. 2 months
g. None
h. Growth rate
Question 11
State the number of replications. The replications are the number of experimental units per treatment.
Question 12
State the number of subsamples. The subsamples are the number of observational units per experimental unit. If there is only one observation per experimental unit, then answer 1, not 0. The number 0 is not a correct answer for this question.
Problem 3
Ten standard tanks are set up, each with 5 fish. But so only five tanks need be purchased and maintained, the experiment will be run over two months, five tanks each month. One tank is randomly selected for each supplement each month. Feed pellets are produced with the supplements included, and poured into the tank twice a day for a month.
Question 13
Identify the treatments.
a. 5 supplements
b. 50 tanks
c. 10 tanks
d. 10 sections of the tank
e. 50 fish
f. 2 months
g. None
h. Growth rate
Question 14
Identify the Experimental Units.
a. 5 supplements
b. 50 tanks
c. 10 tanks
d. 10 sections of the tank
e. 50 fish
f. 2 months
g. None
h. Growth rate
Question 15
Identify the Observational Units.
a. 5 supplements
b. 50 tanks
c. 10 tanks
d. 10 sections of the tank
e. 50 fish
f. 2 months
g. None
h. Growth rate
Question 16
Identify the Blocks.
a. 5 supplements
b. 50 tanks
c. 10 tanks
d. 10 sections of the tank
e. 50 fish
f. 2 months
g. None
h. Growth rate
Question 17
State the number of replications. The replications are the number of experimental units per treatment.
Question 18
State the number of subsamples. The subsamples are the number of observational units per experimental unit. If there is only one observation per experimental unit, then answer 1, not 0. The number 0 is not a correct answer for this question.
Problem 4
A large tank is partitioned into ten sections using a screen. The screen allows water circulation among sections but does not allow feed pellets to pass from one section to another. Five fish are placed in each section, and two sections are randomly selected for each supplement. Feed pellets are produced with the supplements included, and poured into the tank twice a day for a month.
Question 19
Identify the treatments.
a. 5 supplements
b. 50 tanks
c. 10 tanks
d. 10 sections of the tank
e. 50 fish
f. 2 months
g. None
h. Growth rate
Question 20
Identify the Experimental Units.
a. 5 supplements
b. 50 tanks
c. 10 tanks
d. 10 sections of the tank
e. 50 fish
f. 2 months
g. None
h. Growth rate
Question 21
Identify the Observational Units.
a. 5 supplements
b. 50 tanks
c. 10 tanks
d. 10 sections of the tank
e. 50 fish
f. 2 months
g. None
h. Growth rate
Question 22
Identify the Blocks.
a. 5 supplements
b. 50 tanks
c. 10 tanks
d. 10 sections of the tank
e. 50 fish
f. 2 months
g. None
h. Growth rate
Question 23
State the number of replications. The replications are the number of experimental units per treatment.
Question 24
State the number of subsamples. The subsamples are the number of observational units per experimental unit. If there is only one observation per experimental unit, then answer 1, not 0. The number 0 is not a correct answer for this question.
Problem 5
Ten standard tanks are set up like in Problem 2, but the supplements are given differently. The 5 fish in a tank have identification tags. The supplement is provided by individual injection to each fish, twice each day. One fish is randomly selected from each tank at the start of the experiment to receive each supplement. The fish still receive the feed pellets twice a day, but they do not include the supplement.
Question 25
Identify the treatments.
a. 5 supplements
b. 50 tanks
c. 10 tanks
d. 10 sections of the tank
e. 50 fish
f. 2 months
g. None
h. Growth rate
Question 26
Identify the Experimental Units.
a. 5 supplements
b. 50 tanks
c. 10 tanks
d. 10 sections of the tank
e. 50 fish
f. 2 months
g. None
h. Growth rate
Question 27
Identify the Observational Units.
a. 5 supplements
b. 50 tanks
c. 10 tanks
d. 10 sections of the tank
e. 50 fish
f. 2 months
g. None
h. Growth rate
Question 28
Identify the Blocks.
a. 5 supplements
b. 50 tanks
c. 10 tanks
d. 10 sections of the tank
e. 50 fish
f. 2 months
g. None
h. Growth rate
Question 29
State the number of replications. The replications are the number of experimental units per treatment.
Question 30
State the number of subsamples. The subsamples are the number of observational units per experimental unit. If there is only one observation per experimental unit, then answer 1, not 0. The number 0 is not a correct answer for this question.