ICAR AICE-JRF/SRF Statistics, Experimental Design & Chemometrics for Food Science: practice questions

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

Which is an assumption of the standard ANOVA F test?

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

2 · 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?

1. Randomised complete block design
2. Completely randomised design
3. Full 2^7 factorial design
4. Balanced incomplete block design

3 · Response surface methodology: central composite and Box-Behnken designs · medium

How many runs has a central composite design for three factors with six centre points?

1. 20
2. 14
3. 26
4. 15

4 · Response surface methodology: central composite and Box-Behnken designs · hard

In response surface analysis, what does the lack-of-fit test compare?

1. The R² of the model against the adjusted R² of a model with fewer terms in it
2. The predicted optimum against the verification run made at the optimum settings
3. The variance of the factorial points against the variance of the axial points
4. Residual error not explained by the model against pure error from replicated runs

5 · Mixture designs for formulation · medium

Why does a Scheffé mixture model have no intercept term?

1. The proportions sum to one, so an intercept is redundant with the linear terms
2. Because mixtures always give a zero response when all components are present
3. Because the intercept is replaced by the pure-error term from the centroid run
4. Because an intercept would make the model rotatable, which mixtures must avoid

6 · Mixture designs for formulation · easy

For a four-component mixture, what shape is the experimental region when every component may range from 0 to 1?

1. A triangle
2. A cube
3. A square
4. A tetrahedron

7 · 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?

1. Wilcoxon signed-rank test
2. Friedman test
3. McNemar test
4. Mann-Whitney U test

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

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

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

9 · 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?

1. 5.0; significant
2. 5.0; not significant
3. 125.0; significant
4. 2.5; not significant

10 · Statistical software and reproducible data analysis · easy

What is the purpose of version control for analysis scripts?

1. To compress data files so they occupy less storage on the server
2. To speed up statistical calculations on large data sets
3. To record every change, so earlier versions are recoverable
4. To translate scripts between programming languages automatically