Completely Randomized Design (CRD)
Also known as: CRD, completely randomised design, one-way experimental design, Tam Tesadüf Deneme Deseni (CRD)
The completely randomized design is the most fundamental experimental design, in which experimental units are assigned to treatments entirely at random with no restrictions. Analysed by one-way ANOVA, it was formalised by R. A. Fisher in the 1930s and remains the reference starting point for experimental research whenever the experimental material is homogeneous and nuisance variation is absent or negligible.
Key highlights
- Simplest experimental design — straightforward layout, analysis, and interpretation.
- Flexible sample sizes: treatments do not need equal replication, though equal groups improve power.
- Maximum degrees of freedom assigned to the error term compared with blocked designs, which increases statistical power when homogeneity holds.
- Directly extends to factorial and response-surface designs by adding treatment structure.
Intuition
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How it works
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When to use it
Use the completely randomized design when experimental units are homogeneous enough that unrestricted random assignment creates comparable groups. The design suits laboratory and controlled-environment studies where extraneous sources of variability are absent. Four assumptions must hold: (1) errors are independent, (2) errors are normally distributed — check with Shapiro-Wilk, (3) error variances are equal across treatments — check with Levene's or Bartlett's test, and (4) the minimum recommended group size is around ten observations per treatment. If the experimental material is heterogeneous, block that variability using a randomized complete block design instead. If normality or variance homogeneity fail, use the Kruskal-Wallis test.
Strengths & limitations
- Simplest experimental design — straightforward layout, analysis, and interpretation.
- Flexible sample sizes: treatments do not need equal replication, though equal groups improve power.
- Maximum degrees of freedom assigned to the error term compared with blocked designs, which increases statistical power when homogeneity holds.
- Directly extends to factorial and response-surface designs by adding treatment structure.
- Requires homogeneous experimental material; heterogeneity inflates the error term and reduces sensitivity.
- No built-in mechanism for blocking or controlling known sources of nuisance variation.
- The overall F test only signals that some difference exists; post-hoc tests are always needed to pinpoint which pairs differ.
- Sensitive to outliers and violations of normality in small samples.
Common pitfalls
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Applications
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Frequently asked
When should I prefer a randomized complete block design over CRD?
When you can identify a source of nuisance variation — such as location in a greenhouse, litter of animals, or day of measurement — that is unrelated to the treatments, grouping experimental units into blocks and using RCBD removes that variability from the error term and increases precision. CRD is appropriate only when no such blocking factor exists or when experimental units are genuinely homogeneous.
Do all treatment groups need the same number of observations?
No. CRD accommodates unequal group sizes, and the ANOVA calculations remain valid. Equal replication per treatment is nonetheless recommended because it maximises statistical power and simplifies post-hoc comparisons.
The overall F is significant — what do I do next?
Run a post-hoc multiple comparison procedure. Tukey's HSD controls the familywise error rate when comparing all pairs and is the most common choice. Bonferroni correction is more conservative but straightforward. Dunnett's test is appropriate when each treatment is compared only against a control. Always report the mean difference, its confidence interval, and an effect size such as eta-squared.
What is the nonparametric alternative?
When normality or variance homogeneity assumptions fail, and especially with small samples (fewer than ten per group), the Kruskal-Wallis test is the rank-based nonparametric equivalent. It tests whether the distributions of the groups are stochastically equal, without assuming a specific distributional form.
Sources
- 1.Montgomery, D.C. (2017). Design and Analysis of Experiments. Wiley.ISBN 978-1119320937
- 2.Cochran, W.G. & Cox, G.M. (1957). Experimental Designs. Wiley.
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Cite this page
ScholarGate. (2026, June 1). Completely Randomized Design. ScholarGate. https://scholargate.app/experimental-design/completely-randomized-design