Statistics in Food Science
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)
 Identify the following (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)
 R^{2}
 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 F_{α=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)