# 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

 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

1. 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
1. 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

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

1. 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

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 Fα=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)