Statistics in Food Science

Attempt the following questions to check your understanding of the subject:

PART 1

1. A food scientist got the following output after running their data in SAS.
   1. Which SAS procedure was used to generate the following output?                                                                                                 (2 Marks)
   2. Which other SAS procedures can be used to generate these same outputs?                                                                                                 (2 Marks)
   3. Briefly explain the results in the Moments table (6 Marks)

Ash Content

Moments

Basic Measures of Location and Variability

Tests For Location

2. 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.
   1. Identify the following             (3 Marks)
      1. Experimental units
      2. Independent variables
      3. Response variables
   2. What is the most ideal statistical design for this study? Explain (2 Marks)
   3. What is the statistical model for this experiment?             (3 Marks)
   4. Draw the experimental layout for this study             (2 Marks)
   5. Show the statistical model for this experiment (3 Marks)
   6. Show the SAS Program that you would write to carry ANOVA for this data                                                                                                 (3 Marks)

PART 2

3. A researcher found the following results

1. Interpret the results (3 Marks)
2. Give the statistical model that was used in this study (3 Marks)
3. Which SAS program was used to obtain these results? (4 Marks)
4. Given the mean cooking loss was 14.22597, calculate the following (6 Marks)
   1. R²
   2. Coefficient of variation
   3. Standard deviation

4. 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.

1. Write down an appropriate statistical model and ensure that every symbol and notation used is given meaning (3 Marks)
2. 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)
3. If instead of a RCBD, aa CRD was used, calculate the relative efficiency and state whether it was necessary to use RCBD (2 Marks)