Analysis of Variance and Design of Experiments MCQs 2026

Design of experiments emphasizes

1. A only post-hoc storytelling ✓
2. B only descriptive means without structure ✓
3. C only non-parametric ranks ✓
4. D deliberate layout to maximize information and validity ✓

Analysis of variance (ANOVA) partitions

1. A total variation into components attributable to sources of variation ✓
2. B only means without variation ✓
3. C only categorical labels ✓
4. D only time-series trend ✓

One-way ANOVA compares

1. A exactly two paired means only ✓
2. B only two correlated samples always ✓
3. C only proportions without means ✓
4. D means across three or more independent groups ✓

The null hypothesis in one-way ANOVA is

1. A all group variances are equal only ✓
2. B the grand mean is zero ✓
3. C each treatment effect is large ✓
4. D all group means are equal ✓

The F-ratio in one-way ANOVA equals

1. A SS_within / SS_between ✓
2. B df_between × df_within ✓
3. C MS_between / MS_within ✓
4. D the grand mean squared ✓

In one-way ANOVA, SS_between measures variation

1. A within each group only ✓
2. B among group means around the grand mean ✓
3. C of the error term only ✓
4. D of blocking units only ✓

In one-way ANOVA, SS_within measures variation

1. A among group means only ✓
2. B within groups around respective group means ✓
3. C only block effects ✓
4. D only seasonal indices ✓

Mean square equals

1. A sum of squares times df ✓
2. B only SS_total ✓
3. C only the F-ratio ✓
4. D sum of squares divided by its degrees of freedom ✓

A completely randomized design (CRD) assigns

1. A units to fixed blocks by convenience only ✓
2. B experimental units to treatments entirely at random ✓
3. C treatments in a Latin square always ✓
4. D only one replicate per treatment ✓

A randomized complete block design (RCBD) groups units into blocks to

1. A control a known source of extraneous variation ✓
2. B eliminate the need for replication ✓
3. C avoid randomization ✓
4. D increase treatment df only ✓

Blocking in experiments is useful when

1. A units are heterogeneous along a nuisance factor ✓
2. B all units are identical ✓
3. C error variance is zero ✓
4. D treatments are infinite ✓

Replication in experimental design means

1. A measuring one unit many times without new units ✓
2. B using only one block ✓
3. C dropping randomization ✓
4. D repeating each treatment on multiple experimental units ✓

Randomization in experiments primarily helps

1. A justify probabilistic inference and reduce bias ✓
2. B guarantee equal means ✓
3. C eliminate all error variance ✓
4. D replace replication ✓

Two-way ANOVA examines

1. A only one factor ✓
2. B only blocking without factors ✓
3. C two factors and their possible interaction on the response ✓
4. D only time-series seasonality ✓

A significant interaction in two-way ANOVA means

1. A main effects are always zero ✓
2. B the effect of one factor depends on the level of the other ✓
3. C blocks are unnecessary ✓
4. D F ratio equals one always ✓

Main effect of a factor refers to

1. A average effect across levels of the other factor ✓
2. B only the interaction ✓
3. C only error variation ✓
4. D only block sum of squares ✓

The least significant difference (LSD) procedure is

1. A a pre-experiment blocking rule ✓
2. B a non-parametric runs test ✓
3. C a post-hoc pairwise comparison method after significant ANOVA ✓
4. D an index-number formula ✓

LSD is most appropriate when

1. A many unplanned comparisons without adjustment ✓
2. B pairwise comparisons were planned and ANOVA is significant ✓
3. C sample sizes are zero ✓
4. D normality is grossly violated without remedy ✓

Experimental unit is

1. A always the plot subplot only ✓
2. B the entity to which a treatment is applied ✓
3. C the measured response only ✓
4. D the F-table ✓

Treatment in designed experiments is

1. A only the error term ✓
2. B only the block label ✓
3. C only the grand mean ✓
4. D a controlled condition applied to units ✓

Control treatment is

1. A always the largest mean ✓
2. B the error sum of squares ✓
3. C a baseline or standard condition for comparison ✓
4. D a post-hoc test ✓

Balanced design has

1. A equal number of observations per treatment (or cell) ✓
2. B no replication ✓
3. C zero error df ✓
4. D only one block ✓

Post-hoc tests are conducted

1. A before collecting data only ✓
2. B after a significant omnibus ANOVA to locate differences ✓
3. C without any F test ✓
4. D only in CRD without blocks ✓

Assumptions of ANOVA include

1. A only rank ordering ✓
2. B only seasonal adjustment ✓
3. C only geometric means ✓
4. D independence, normality and homogeneity of variances ✓

Homogeneity of variances means

1. A means are equal ✓
2. B sample sizes are equal always ✓
3. C population variances are equal across groups ✓
4. D F is less than 1 ✓

Bartlett test is used to test

1. A normality only ✓
2. B homogeneity of variances ✓
3. C interaction only ✓
4. D trend in time series ✓

Levene test is often preferred for homogeneity because it is

1. A more robust to departures from normality than Bartlett ✓
2. B always exact with tiny samples ✓
3. C unrelated to variances ✓
4. D only for two groups ✓

If ANOVA assumptions are violated mildly, alternatives include

1. A data transformation or non-parametric methods ✓
2. B ignoring all assumptions always ✓
3. C setting F to zero ✓
4. D using only index numbers ✓

In RCBD, SS_blocks captures variation

1. A only treatment effects ✓
2. B only within-unit noise unrelated to blocks ✓
3. C among blocks around the grand mean ✓
4. D only interaction SS ✓

Error df in one-way ANOVA with k groups and n total observations is

1. A k − 1 only ✓
2. B n − 1 only ✓
3. C n − k ✓
4. D n × k ✓

Treatment df in one-way ANOVA with k groups is

1. A n − k ✓
2. B k − 1 ✓
3. C n − 1 ✓
4. D k + 1 ✓

A large F statistic in ANOVA suggests

1. A groups are identical ✓
2. B between-group variation exceeds what is expected from within-group variation ✓
3. C MS_within exceeds MS_between ✓
4. D error df is zero ✓

Multiple comparisons inflate

1. A Type I error if unadjusted ✓
2. B Type II error only always ✓
3. C sample size ✓
4. D block SS only ✓

Tukey HSD differs from LSD by

1. A controlling family-wise error rate for all pairwise comparisons ✓
2. B ignoring significance ✓
3. C using only two groups ✓
4. D replacing randomization ✓

Latin square design controls

1. A no blocking ✓
2. B only one nuisance variable ✓
3. C two blocking factors with equal number of levels ✓
4. D only continuous covariates without factors ✓

Factorial experiment crosses levels of

1. A only one factor ✓
2. B only blocks without treatments ✓
3. C only time index ✓
4. D two or more factors simultaneously ✓

Split-plot design is used when

1. A some factors are harder to randomize than others ✓
2. B all factors are equally easy to randomize ✓
3. C no replication exists ✓
4. D only CRD is valid ✓

Confounding occurs when

1. A treatment effects cannot be separated from block or other effects ✓
2. B randomization is perfect ✓
3. C replication is ample ✓
4. D F is small ✓

Orthogonal contrasts allow

1. A only one mean to be tested ✓
2. B partitioning treatment SS into independent components ✓
3. C error SS to vanish ✓
4. D blocking to be ignored ✓

Grand mean in ANOVA is

1. A the largest treatment mean ✓
2. B MS_within ✓
3. C the mean of all observations combined ✓
4. D only block average ✓

RCBD is preferred over CRD when

1. A units are perfectly homogeneous ✓
2. B randomization is impossible ✓
3. C known heterogeneity among units can be grouped into blocks ✓
4. D only two treatments exist ✓

Efficiency of blocking is higher when

1. A blocks are unrelated to response ✓
2. B blocks explain substantial variation relative to error ✓
3. C replication is absent ✓
4. D treatment df is zero ✓

Missing values in RCBD analysis require

1. A no change in formulas always ✓
2. B careful handling because balance may be lost ✓
3. C deletion of all blocks ✓
4. D ignoring treatment effects ✓

Expected mean squares logic helps determine

1. A only sample means ✓
2. B only index relatives ✓
3. C which effects are tested against which error terms ✓
4. D only runs in sequences ✓

In two-way ANOVA, interaction df equals

1. A a + b − 2 only ✓
2. B ab − 1 ✓
3. C n − ab ✓
4. D (a − 1)(b − 1) for a levels of A and b levels of B ✓

Residual plots after ANOVA help check

1. A only treatment means ordering ✓
2. B only Laspeyres weights ✓
3. C only rank sums ✓
4. D normality and homogeneity assumptions ✓

A non-significant ANOVA F does not prove

1. A all pairwise mean differences are zero with certainty ✓
2. B that H₀ is true with 100% probability ✓
3. C that data were balanced ✓
4. D that blocks existed ✓

Increasing replication generally

1. A decreases error df to zero ✓
2. B eliminates need for randomization ✓
3. C guarantees significant F ✓
4. D improves power to detect treatment differences ✓

In CRD with k treatments and r replicates each, total df is

1. A k − 1 only ✓
2. B r − 1 only ✓
3. C kr − 1 ✓
4. D kr ✓

Treatment sum of squares in one-way ANOVA increases when

1. A all means equal the grand mean ✓
2. B within-group variation alone rises ✓
3. C sample size falls to one ✓
4. D group means spread farther from the grand mean ✓