Attempt the following questions to check your understanding of the subject:
PART 1
A food scientist got the following output after running their data in SAS.
Which SAS procedure was used to generate the following output? (2 Marks)
Which other SAS procedures can be used to generate these same outputs? (2 Marks)
Briefly explain the results in the Moments table (6 Marks)
Ash Content
Moments
Moments
N
36
Sum Weights
36
Mean
3.10977778
Sum Observations
111.952
Std Deviation
0.64475285
Variance
0.41570623
Skewness
0.38531895
Kurtosis
-0.786359
Uncorrected SS
362.69556
Corrected SS
14.5497182
Coeff Variation
20.7330843
Std Error Mean
0.10745881
Basic Measures of Location and Variability
Basic Statistical Measures
Location
Variability
Mean
3.109778
Std Deviation
0.64475
Median
2.979500
Variance
0.41571
Mode
.
Range
2.44200
Interquartile Range
1.01400
Tests For Location
Tests for Location: Mu0=0
Test
Statistic
p Value
Student’s t
t
28.93925
Pr > |t|
<.0001
Sign
M
18
Pr >= |M|
<.0001
Signed Rank
S
333
Pr >= |S|
<.0001
In a study to determine the best training methods for student’s sensory panels, three panels of 30 students each were subjected to three different training methods and their ability to identify samples examined using 4 samples of juices with varied concentration of sugar (0%, 1%, 2% and 3%). The samples were presented in a random order to each panelist and the students awarded a score depending on the number of samples that they correctly identified.
Identify the following (3 Marks)
Experimental units
Independent variables
Response variables
What is the most ideal statistical design for this study? Explain (2 Marks)
What is the statistical model for this experiment? (3 Marks)
Draw the experimental layout for this study (2 Marks)
Show the statistical model for this experiment (3 Marks)
Show the SAS Program that you would write to carry ANOVA for this data (3 Marks)
PART 2
A researcher found the following results
Source
DF
Sum of Squares
Mean Square
F Value
Pr > F
Model
12
841.2299670
70.1024972
26.67
<.0001
Error
26
68.3540040
2.6290002
Corrected Total
38
909.5839710
Source
DF
Type I SS
Mean Square
F Value
Pr > F
Extender
6
642.8673361
107.1445560
40.75
<.0001
extension_Level
1
91.3585500
91.3585500
34.75
<.0001
Extender*extension_L
5
107.0040808
21.4008162
8.14
<.0001
Interpret the results (3 Marks)
Give the statistical model that was used in this study (3 Marks)
Which SAS program was used to obtain these results? (4 Marks)
Given the mean cooking loss was 14.22597, calculate the following (6 Marks)
R2
Coefficient of variation
Standard deviation
A RCBD experiment was conducted in which a chemical was used to increase the shelf life of ripe pawpaw fruit. Three treatments were used: C (no chemical added), L (low dose), H (high dose). The experimental unit is a shelve containing six fruits. Because of variation in ventilation within the green grocery store, the position of each shelf was thought to influence the outcome. Shelves were therefore blocked based on their position and the three treatments were randomly assigned to each block. The following data was obtained.
Block
Control (C)
Low dose (L)
High dose (H)
Block total
1
3.93
3.99
4.08
12.00
2
3.78
3.96
3.94
11.68
3
3.88
3.96
4.02
11.86
4
3.93
4.03
4.06
12.02
5
3.84
4.10
3.94
11.88
6
3.75
4.02
4.09
11.86
7
3.98
4.06
4.17
12.211
8
3.84
3.92
4.12
11.88
Treatment total
30.93
32.04
32.42
Grand total: 95.39
Write down an appropriate statistical model and ensure that every symbol and notation used is given meaning (3 Marks)
Construct the ANOVA table to test whether there is sufficient evidence of a difference between the three treatments (use Fα=0.05; 2,14 = 3.739) (5 Marks)
If instead of a RCBD, aa CRD was used, calculate the relative efficiency and state whether it was necessary to use RCBD (2 Marks)