ICAR AIEEA-PG / PGS Statistics, Experimental Design & Chemometrics for Food Science: practice questions

ICAR AIEEA-PG / PGS — Code 18 Food Science Technology · India · ICAR through the National Testing Agency

Original practice questions written to the published syllabus · not past papers

10worked here, free

64written to this exam in this subject

6syllabus units

What this subject covers

Probability, inference and the designs used in food research and quality work: factorial and response-surface designs for formulation and process optimisation, mixture designs, the statistics of sensory panels, and multivariate methods (PCA, PLS) used with spectra and chromatograms. Goes further than the general statistics subjects in Agricultural Engineering (probability-statistics-data) and Agribusiness (business-statistics) by focusing on food formulation, sensory and analytical data.

In the exams: Applied throughout ICAR AICE-JRF/SRF research units and every PG thesis; probability and statistics also appear in GATE XE-A

Descriptive statistics and probability distributions: binomial, Poisson and normal
Sampling distributions, confidence intervals and hypothesis tests: z, t, chi-square and F
Correlation and linear and multiple regression
Analysis of variance: one-way, two-way and multiple comparisons
Completely randomised, randomised block and Latin square designs
Factorial and fractional factorial designs
Response surface methodology: central composite and Box-Behnken designs
Mixture designs for formulation
Non-parametric tests used with sensory data
Multivariate methods: principal component analysis, cluster analysis and partial least squares
Calibration, limit of detection and measurement uncertainty basics
Statistical software and reproducible data analysis

Where the 64 questions fall

How our questions for ICAR AIEEA-PG / PGS spread across the units of Statistics, Experimental Design & Chemometrics for Food Science. Difficulty: 24 easy, 28 medium, 12 hard.

Descriptive statistics and probability distributions: binomial, Poisson and normal	12
Sampling distributions, confidence intervals and hypothesis tests: z, t, chi-square and F	12
Correlation and linear and multiple regression	10
Analysis of variance: one-way, two-way and multiple comparisons	10
Completely randomised, randomised block and Latin square designs	10
Non-parametric tests used with sensory data	10

10 practice questions, worked

Choose an answer, then open the working. Each explanation says why the right answer is right and why the others are not.

1 · Descriptive statistics and probability distributions: binomial, Poisson and normal · easy

Why are aerobic plate counts usually converted to log10 values before means are calculated and tests are run?

Log values are required by law for every microbiological result reported by a food laboratory worldwide
Taking logs removes the dilution factor, so the count no longer depends on the volume that was plated
Counts are right-skewed and close to log-normal, so logs give near-symmetric data with steadier variance
Counts are left-skewed with a long lower tail, and logs stretch that tail so the outliers become visible

Answer and working

C. Counts are right-skewed and close to log-normal, so logs give near-symmetric data with steadier variance

Microbial counts vary multiplicatively and follow an approximately log-normal distribution; on the log scale they are near-symmetric and their variance is more stable, which suits means, t tests and ANOVA. Logs do not remove dilution factors, and counts are right-skewed, not left-skewed.

Further reading: Montgomery, Design and Analysis of Experiments; Box, Hunter and Hunter, Statistics for Experimenters

2 · Correlation and linear and multiple regression · easy

A fitted shelf-life model gives colour score y = 0.5 + 0.2x, where x is storage weeks. What colour score does it predict at 12 weeks?

Answer and working

D. 2.9

y = 0.5 + 0.2 × 12 = 0.5 + 2.4 = 2.9. 2.4 forgets the intercept; 8.4 multiplies (0.5 + 0.2) by 12; 3.4 adds 0.5 twice.

Further reading: Montgomery, Design and Analysis of Experiments; Box, Hunter and Hunter, Statistics for Experimenters

3 · Correlation and linear and multiple regression · easy

Across 20 biscuit recipes, hardness and sweetness are strongly correlated. Both rise with sugar content. What does this show?

Hardness causes sweetness, because a strong correlation demonstrates a direct causal effect
Sugar, a shared cause, explains the correlation; hardness does not cause sweetness
Sweetness causes hardness, because the sensory attribute must drive the instrumental one
The correlation is spurious and must be zero once a larger number of recipes is tested

Answer and working

B. Sugar, a shared cause, explains the correlation; hardness does not cause sweetness

Correlation is not causation. Both attributes depend on sugar, a confounding variable, so they move together without either causing the other. Nothing suggests the correlation would vanish with more recipes.

Further reading: Montgomery, Design and Analysis of Experiments; Box, Hunter and Hunter, Statistics for Experimenters

4 · Analysis of variance: one-way, two-way and multiple comparisons · medium

A one-way ANOVA has a treatment sum of squares of 60 on 3 df and an error sum of squares of 80 on 16 df. What is the F statistic?

0.75
1.33
0.25
4.00

Answer and working

D. 4.00

MS treatment = 60/3 = 20; MS error = 80/16 = 5; F = 20/5 = 4.00. 0.75 is SS treatment / SS error without df; 1.33 inverts that; 0.25 inverts the correct F.

Further reading: Montgomery, Design and Analysis of Experiments; Gomez and Gomez, Statistical Procedures for Agricultural Research

5 · Analysis of variance: one-way, two-way and multiple comparisons · easy

Five new formulations are each compared with the current product, not with one another. Which procedure fits this aim?

Tukey's HSD
Scheffé's contrast test
Kruskal-Wallis test
Dunnett's test

Answer and working

D. Dunnett's test

Dunnett's test compares each treatment with a single control and is more powerful than all-pairs methods for that purpose. Tukey's covers every pair; Scheffé's covers all contrasts; Kruskal-Wallis is a rank-based overall test.

Further reading: Montgomery, Design and Analysis of Experiments; Gomez and Gomez, Statistical Procedures for Agricultural Research

6 · Analysis of variance: one-way, two-way and multiple comparisons · easy

Which is an assumption of the standard ANOVA F test?

Equal treatment means in the population
Correlated errors within each group
Equal variances among the treatment groups
Exactly normal raw data before any fitting

Answer and working

C. Equal variances among the treatment groups

ANOVA assumes independent errors, approximately normal residuals and equal variances. Equal means is the null hypothesis being tested, not an assumption; correlated errors violate independence; normality refers to residuals, approximately.

Further reading: Montgomery, Design and Analysis of Experiments; Gomez and Gomez, Statistical Procedures for Agricultural Research

7 · Completely randomised, randomised block and Latin square designs · medium

An assessor can taste only three of seven samples in a session without fatigue. Which design family handles this?

Randomised complete block design
Completely randomised design
Full 2^7 factorial design
Balanced incomplete block design

Answer and working

D. Balanced incomplete block design

When a block (session) cannot hold all treatments, incomplete block designs allocate subsets so that every pair appears together equally often. A complete block would need all seven samples per session.

Further reading: Gomez and Gomez, Statistical Procedures for Agricultural Research; Montgomery, Design and Analysis of Experiments

8 · Non-parametric tests used with sensory data · easy

Liking scores for one product come from two separate consumer groups that are not normally distributed. Which test compares the groups?

Wilcoxon signed-rank test
Friedman test
McNemar test
Mann-Whitney U test

Answer and working

D. Mann-Whitney U test

Two independent groups with non-normal data call for the Mann-Whitney U (Wilcoxon rank-sum) test. The signed-rank and McNemar tests are for paired data; Friedman for three or more related samples.

Further reading: Næs, Brockhoff and Tomic, Statistics for Sensory and Consumer Science

9 · Non-parametric tests used with sensory data · medium

Which statistic measures agreement among several assessors' rankings of the same products?

Pearson's correlation between the first two assessors only
The coefficient of variation of each assessor's ranks
Kendall's coefficient of concordance, W, across all assessors
The chi-square goodness-of-fit statistic of the rank totals

Answer and working

C. Kendall's coefficient of concordance, W, across all assessors

Kendall's W ranges from 0 (no agreement) to 1 (complete agreement) among all assessors and is used to check panel consistency.

Further reading: Næs, Brockhoff and Tomic, Statistics for Sensory and Consumer Science

10 · Non-parametric tests used with sensory data · hard

Ten assessors rank three products; rank sums are 15, 20 and 25. Using the Friedman statistic 12/[bt(t + 1)] ΣR² − 3b(t + 1), and a critical chi-square of 5.99 (2 df, α = 0.05), what is the result?

5.0; significant
5.0; not significant
125.0; significant
2.5; not significant

Answer and working

B. 5.0; not significant

12/(10 × 3 × 4) = 0.1; ΣR² = 225 + 400 + 625 = 1,250; 0.1 × 1,250 = 125; minus 3 × 10 × 4 = 120 gives 5.0, below 5.99, so not significant. 125.0 forgets to subtract 120; 2.5 halves the statistic.

Further reading: Næs, Brockhoff and Tomic, Statistics for Sensory and Consumer Science

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