Statistics in Food Science

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

PART 1

1. Discuss four types of research             (4 Marks)
2. As a requirement for the award of your degree, you are required to carry out a survey on consumption patterns for high fat foods amongst students. Briefly discuss the design process for your questionnaire                                                                         (4 Marks)
3. While testing relationships between variables, a researcher got the following results:

1. Explain the meaning of these results (3 Marks)
2. What SAS procedure was used to generate these results (3 Marks)

PART 2

4. A researcher noted that University students preferred street vended food than food sold from the licensed food businesses. Owing to the poor handling practices he had observed, he thought that this could be contributing to the student’s frequent visits to the university hospital. Show that the situation outlined meets the conditions for the existence of a research problem                   (4 Marks)
5. A researcher obtained the following data while studying student’s ability to rate food samples. In this research, the students were grouped into two and allowed to rate food samples on a scale of 1-7. The following were the results:

Can the researcher conclude that the two groups were different? (Use t-value = 2.365) (4 Marks)

6. A researcher studying the effect of extenders in meat found the following results.
   1. Complete the ANOVA table below and report the findings in regard to mean separation using the Student-Newman-Keuls Test             (6 Marks)
   2. Write the SAS program that yielded the results below             (2 Marks)

Student-Newman-Keuls Test for Moisture_Level

Note: This test controls the Type I experiment wise error rate under the complete null hypothesis but not under partial null hypotheses.

7. In a study to determine the ability of a student’s sensory panel to correctly identify samples’ sweetness, a panel of 30 students was presented with 4 samples of juices with varied concentration of sugar (0%, 1%, 2% and 3%). The same experiment was repeated again with a different panel of 30 students. In both, the first and second experiments, the samples were presented in a random order to each panelist. Students were awarded a score depending on the number of samples that they correctly identified.
   1. What test can be used to analyze the data? Explain. (2 Marks)
   2. Show the SAS Program that you would write to analyze the data (2 Marks)

8. The analysis of variance of Aflatoxin (AFs) and DON contamination in animal feeds from two dairy systems and type of the feeds is shown in the table below. The table represents the mean squares for all the sources of error.

1. Identify the experimental design and layout that was employed in this study (3 Marks)
2. Critically explain the results in the table (5 Marks)

9. A manufacturer requires data on sodium content in raw material vegetable supplies for product labelling purposes. Batches of each source of vegetables (two sources.1) are delivered and a random selection of sample units is drawn from each lot of vegetables. As this is a new raw material, 10 samples of 200–300 g containing approximately 10–15 individual units are selected from each consignment, are prepared in a similar manner to the form that they would be used in products, then blended to form a homogeneous mass. Duplicate subsamples are taken and analyzed for sodium content. Average values for each sample are reported.
   1. Explain the steps the manufacturer should follow in significance testing                                                                                                 (10 Marks)
   2. If the two-tail significance for the t statistic is 0.01, what conclusion would the manufacturer make? (2 Marks)
10. The table below is a mean squares table for four sensory attributes determined from a research which was carried out to determine the effect of adding four levels of gum arabic as a source of soluble fiber to mozzarella cheese.

1. Explain the significance of R² in this study             (2 Marks)
2. What was the experimental design for this study? Explain (2 Marks)
3. Calculate the standard deviation and the mean for each sensory attribute presented above (8 Marks)
4. Give a critical analysis of the data from this table and discuss what could have contributed to the experimental error in this study             (8 Marks)

11. A food scientist wanted to determine the effect of using meat extenders on the water holding capacity of brine injected hams. Gum Arabic was applied at four levels (1%, 2%, 3% and 4%). A sample with no extender was prepared for comparison. Hams were injected at three targeted brine injection levels (10%, 20 and 30%) with brines containing these extenders.
    1. Draw an experimental layout, give the statistical model explaining each term and set up an ANOVA table that is suitable for this experiment             (9 Marks)
    2. State the hypothesis of this experiment and explain the purpose of preparing the sample with no extender                         (4 Marks)
    3. What SAS program would you use to analyze the data to obtain the mean water holding capacity values for each extender at each extension level presented as Mean ± Standard deviation? (4 Marks)
12. In question 7, If the same panel of 30 students was used and the panel was trained on sensory evaluation so as to study the effect of training on the ability of panelist to identify similar samples, what statistical test would be ideal to analyze the data? Show the SAS program to support your answer                                        (3 Marks)
13. While carrying out extrusion of a breakfast cereals using the same machine at three temperatures, a researcher recorded the reduction in moisture content of the food sample as shown below. Since the extrusion process was long, the replications were carried out by different operators. Carryout analysis of variance and show the conclusion the researcher may have made (12 Marks)