Design of experiments - principles of experimentation, analysis of variance, completely randomized design, randomized block design, Latin square design - One Line Questions

1. In an RBD with 'r' blocks and 'a' treatments, the degrees of freedom for error are: — (r-1)(a-1)
2. Degrees of freedom for treatments in a CRD with 'a' treatments is: — a - 1
3. Degrees of freedom for error in a CRD with N total observations and 'a' treatments is: — N - a
4. A 'treatment' in the context of experimental design refers to: — A condition or factor applied to the experimental units whose effect is being studied.
5. In the context of DOE, 'factor' refers to: — A variable whose level is manipulated or set by the experimenter.
6. The 'experimental unit' is defined as: — The smallest unit to which a treatment is applied independently.
7. In a CRD, if the F-calculated value is greater than the F-critical value (at a given significance level), we: — Reject the null hypothesis.
8. In ANOVA, the null hypothesis ($H_0$) typically states that: — All group means are equal.
9. If the F-test for treatments in an RBD is not significant, what can be concluded? — There is no statistically significant difference between the treatment means, after accounting for block effects.
10. Which test is used to check the assumption of homogeneity of variances (homoscedasticity) in ANOVA? — Levene's test
11. Which design is most efficient when the experimental units are expected to be homogeneous? — Completely Randomized Design (CRD)
12. If an experiment involves studying the effect of fertilizer type (Factor A) and watering frequency (Factor B) on plant growth, which design would be most suitable if you also want to control for variations due to different soil types? — Factorial design within an RBD or LSD framework
13. Consider an experiment to test 5 different oven temperatures (treatments) for baking cakes. If you suspect variations due to the day of the week and the baker, which design would be most appropriate? — LSD (rows=day, columns=baker, cells=temperature)
14. The assumption of 'no interaction' between treatments and blocking factors is crucial for which design? — LSD
15. The purpose of post-hoc tests in ANOVA is to: — Identify which specific group means differ significantly from each other.
16. Analysis of Variance (ANOVA) is a statistical technique used to: — Compare the means of three or more groups by analyzing variances.
17. In a Completely Randomized Design (CRD), what is the primary source of variation considered? — Differences between treatments and random error.
18. What statistical test is commonly used to check the assumption of normality of residuals in ANOVA? — Shapiro-Wilk test
19. The purpose of Randomization in experimental design is to: — Minimize the effect of unknown or uncontrolled variables and avoid bias.
20. A 'block' in experimental design is used to: — Group experimental units that are similar in characteristics that might affect the response.
21. The purpose of blocking in RBD is to: — Reduce the experimental error by accounting for variability within blocks.
22. What is a key characteristic of the Latin Square Design (LSD)? — It controls for variation in two different directions simultaneously.
23. What is the primary limitation of CRD when there's heterogeneity in experimental units? — It may lead to higher experimental error and reduced power to detect treatment differences.
24. A potential drawback of the Latin Square Design is: — It assumes no interaction between the blocking factors and the treatments.
25. What is the main advantage of using a factorial experiment within a designed structure like CRD, RBD, or LSD? — It allows for the study of main effects and interaction effects between factors.
26. The F-statistic in ANOVA is calculated as the ratio of: — Mean Square Treatment (MST) to Mean Square Error (MSE).
27. Which type of error is controlled by blocking? — Systematic error due to known sources of variation.
28. Which experimental design is the simplest and most basic, involving the random assignment of treatments to experimental units without any grouping? — Completely Randomized Design (CRD)
29. Which of the following is NOT a fundamental principle of experimentation? — Extrapolation
30. The Mean Square Error (MSE) in ANOVA is calculated as: — SSE / (N - a)
31. In ANOVA, the Mean Square Treatment (MST) is calculated as: — SSTr / (a - 1)
32. The 'grand mean' in ANOVA is: — The average of all observations in the experiment.
33. In a Latin Square Design, the number of treatment levels must equal: — The number of rows or the number of columns.
34. In an RBD, if the blocking factor is highly effective, we expect: — The Sum of Squares for Blocks (SSB) to be large and the error variance to be small.
35. The Sum of Squares Treatment (SSTr) in ANOVA measures: — The variation among the treatment means.
36. In ANOVA, the Sum of Squares Total (SST) represents: — The total variation in the data around the grand mean.
37. The Sum of Squares Error (SSE) represents: — The variation that cannot be explained by treatments or blocks, representing random error.
38. What is the primary assumption of ANOVA regarding the error terms? — They are independent, normally distributed with mean zero and equal variances.
39. What are the two sources of variation, besides treatments, that LSD attempts to control? — Both B and C
40. What is the primary goal of the Design of Experiments (DOE)? — To systematically plan and conduct experiments to efficiently obtain valid and objective answers to the questions being asked.
41. What is the main advantage of using Blocking in experimental design? — To reduce the variability within blocks, making it easier to detect treatment differences.
42. What is the purpose of 'random error' or 'residual' in ANOVA? — To represent the unexplained variation in the response variable after accounting for treatment and blocking effects.
43. In an RBD, the total variation is partitioned into variation due to: — Treatments, blocks, and error.
44. Which of the following is a method for post-hoc analysis after a significant ANOVA result? — Tukey's HSD (Honestly Significant Difference)
45. If the assumption of equal variances is violated, which alternative approach might be considered? — Performing Welch's ANOVA or using transformations.
46. What does the principle of Replication in experimental design refer to? — Repeating an experiment under identical conditions to assess variability.
47. When is a Latin Square Design particularly useful? — When there are three or more potential sources of variation to control.
48. When would a Randomized Block Design (RBD) be more appropriate than a CRD? — When there is a known source of variability (e.g., location, time) that can be used to form blocks.
All One Line Questions
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