SAMAR Analysis Report

Statistical Analysis Machine for Agricultural Research
Dataset
wheat_nitrogen_rcbd.csv
Data size
30 rows × 5 columns
Generated
20 October 2026, 19:31

Methods

The experiment was laid out in a randomised complete block design with 6 levels of Treatment in 5 blocks, giving 30 observations. The design was balanced. GrainYield_tha, GrainsPerSpike and TGW_g were recorded as response variables. Data were analysed by 1-Factor ANOVA. Treatment means were separated by LSD at p < 0.05. All analyses were carried out in R 4.5.3, agricolae 1.3.7.

📐 1-Factor ANOVA (RBD)

📋 Analysis Results ▸ GrainYield_tha, GrainsPerSpike, TGW_g

📐 ANOVA Summary
Design
Block: Replication
RBD
Significant
3/3
Method
Fisher's LSD | α=0.05
Variable F value p-value CV% Sig?
GrainYield_tha 18.974 5.6e-07 5.66% Yes ✓
GrainsPerSpike 16.444 1.7e-06 4.79% Yes ✓
TGW_g 4.735 0.0051 2.04% Yes ✓
📊 Treatment & Error Mean Squares (ANOVA)
Hypotheses

Ho1: The means of all the replications are equal. Ho2: The means of all the levels of Treatment are equal.

Each effect is tested against the error mean square of its trait (Error, 20 df). A null hypothesis is rejected when p ≤ α = 0.05; the stars give the level reached.

SoV DF GrainYield_tha GrainsPerSpike TGW_g
Replication 4 0.156NS 6.077NS 0.521NS
Treatment 5 1.352*** 55.313*** 3.409**
Error 20 0.071 3.364 0.72

*** p<0.001 ** p<0.01 * p<0.05 NS p≥0.05 | Values are Mean Squares

Interpretation of the ANOVA results

For GrainYield_tha: Replication (MS = 0.156) was not significant (NS), so Ho1 is not rejected; Treatment (MS = 1.352) was significant at the 0.1% level (***), so Ho2 is rejected. The error mean square was 0.071. For GrainsPerSpike: Replication (MS = 6.077) was not significant (NS), so Ho1 is not rejected; Treatment (MS = 55.313) was significant at the 0.1% level (***), so Ho2 is rejected. The error mean square was 3.364. For TGW_g: Replication (MS = 0.521) was not significant (NS), so Ho1 is not rejected; Treatment (MS = 3.409) was significant at the 1% level (**), so Ho2 is rejected. The error mean square was 0.72.

📋 Means ± SD with Letter Groups & Statistics
📋 Means & Letter Groups
Treatment GrainYield_tha Grp (LSD) GrainsPerSpike Grp (LSD)​ TGW_g Grp (LSD)​​
N0 3.752 ± 0.311 c 32.98 ± 0.853 d 41.44 ± 0.695 b
N40 4.524 ± 0.209 b 35.56 ± 0.789 c 41.98 ± 0.867 ab
N80 4.852 ± 0.336 ab 38.56 ± 1.295 b 42.6 ± 0.711 a
N120 5 ± 0.418 a 41.26 ± 2.126 a 41.7 ± 0.424 ab
N160 5.162 ± 0.231 a 40.68 ± 2.611 ab 41.14 ± 1.178 bc
N200 5.012 ± 0.176 a 40.54 ± 2.921 ab 40.16 ± 0.902 c

Mean ± SD of the observations; letters from the chosen method.

For GrainYield_tha, the highest mean was recorded by N160 (5.162); N200, N120 and N80 were statistically at par with it (sharing a letter). The lowest mean was recorded by N0 (3.752).

For GrainsPerSpike, the highest mean was recorded by N120 (41.26); N160 and N200 were statistically at par with it (sharing a letter). The lowest mean was recorded by N0 (32.98).

For TGW_g, the highest mean was recorded by N80 (42.6); N40 and N120 were statistically at par with it (sharing a letter). The lowest mean was recorded by N200 (40.16).

📊 Statistics
Statistic GrainYield_tha GrainsPerSpike TGW_g
F stat 18.97*** 16.44*** 4.74**
p value 5.61e-07 1.74e-06 0.005
CD (LSD, 1%) 0.48 3.3 1.53
CD (LSD, 5%) 0.35 2.42 1.12
MSE 0.071 3.364 0.72
SE(m) 0.12 0.82 0.38
SE(d) 0.17 1.16 0.54
CV(%) 5.66 4.79 2.04
Cohen's F 2.18 2.03 1.09

CV = 5.66% for GrainYield_tha: Excellent experimental precision (CV < 10%).

CV = 4.79% for GrainsPerSpike: Excellent experimental precision (CV < 10%).

CV = 2.04% for TGW_g: Excellent experimental precision (CV < 10%).

🔲 Block / Replication Means
Variable Block n mean sd se
GrainYield_tha R1 6 4.79 0.516 0.211
GrainYield_tha R2 6 4.863 0.657 0.268
GrainYield_tha R3 6 4.443 0.548 0.224
GrainYield_tha R4 6 4.723 0.649 0.265
GrainYield_tha R5 6 4.765 0.466 0.19
GrainsPerSpike R1 6 37.983 3.927 1.603
GrainsPerSpike R2 6 39.7 4.865 1.986
GrainsPerSpike R3 6 36.933 2.419 0.987
GrainsPerSpike R4 6 38.6 3.771 1.54
GrainsPerSpike R5 6 38.1 3.099 1.265
TGW_g R1 6 41.35 0.916 0.374
TGW_g R2 6 41.983 0.331 0.135
TGW_g R3 6 41.517 1.458 0.595
TGW_g R4 6 41.2 1.092 0.446
TGW_g R5 6 41.467 1.422 0.581
💡 Interpretation

Significant treatment effects (p ≤ α): GrainYield_tha, GrainsPerSpike, TGW_g — Treatments differ significantly. Use letter groups to identify which groups differ.

CV% = 5.66 % ( GrainYield_tha ): Excellent experimental precision (CV < 10%).

Mean Separation: Fisher's LSD — Treatments sharing the same letter are not significantly different.

Block Efficiency (GrainYield_tha) = 116.4%: the RCB design was 16.4% more precise than a CRD of the same plots would have been (Gomez & Gomez relative efficiency). Blocks are effective.

Design: RBD · Block: Replication | α = 0.05

📊 Summary Stats ▸ GrainYield_tha, GrainsPerSpike, TGW_g

📊 Full Descriptive Statistics Table
Variable Treatment n mean median sd se cv min max
GrainYield_tha N0 5 3.752 3.71 0.311 0.139 8.285 3.45 4.24
GrainYield_tha N40 5 4.524 4.63 0.209 0.094 4.622 4.28 4.74
GrainYield_tha N80 5 4.852 4.82 0.336 0.15 6.918 4.56 5.38
GrainYield_tha N120 5 5 5.08 0.418 0.187 8.363 4.47 5.57
GrainYield_tha N160 5 5.162 5.29 0.231 0.103 4.471 4.83 5.34
GrainYield_tha N200 5 5.012 5.02 0.176 0.079 3.517 4.82 5.21
GrainsPerSpike N0 5 32.98 32.9 0.853 0.381 2.585 32.1 34.3
GrainsPerSpike N40 5 35.56 35.8 0.789 0.353 2.22 34.6 36.5
GrainsPerSpike N80 5 38.56 38.7 1.295 0.579 3.359 37.1 40.5
GrainsPerSpike N120 5 41.26 41.4 2.126 0.951 5.152 38.8 44.4
GrainsPerSpike N160 5 40.68 40.1 2.611 1.168 6.418 37.8 44
GrainsPerSpike N200 5 40.54 41.1 2.921 1.306 7.206 37.1 44.6
TGW_g N0 5 41.44 41.7 0.695 0.311 1.677 40.2 41.8
TGW_g N40 5 41.98 42 0.867 0.388 2.066 40.8 43.2
TGW_g N80 5 42.6 42.5 0.711 0.318 1.668 41.6 43.5
TGW_g N120 5 41.7 41.8 0.424 0.19 1.017 41.2 42.3
TGW_g N160 5 41.14 41.7 1.178 0.527 2.864 39.5 42.1
TGW_g N200 5 40.16 40.2 0.902 0.403 2.245 39.3 41.6
📈 Normality & Variance Tests

GrainYield_tha SW (ANOVA residuals) W=0.937, p=0.075

GrainsPerSpike SW (ANOVA residuals) W=0.984, p=0.926

TGW_g SW (ANOVA residuals) W=0.969, p=0.505

🎨 Advanced Plots ▸ GrainYield_tha, GrainsPerSpike, TGW_g

🎨 Advanced Plot
🎨 Advanced Plots

GrainYield_tha ▸ GrainYield_tha, GrainsPerSpike, TGW_g

🎨 Advanced Plot — GrainYield_tha — Raincloud Plot
Figure 1. 🎨 Advanced Plot — GrainYield_tha — Raincloud Plot
🎨 Advanced Plots

GrainsPerSpike ▸ GrainYield_tha, GrainsPerSpike, TGW_g

🎨 Advanced Plot — GrainsPerSpike — Raincloud Plot
Figure 2. 🎨 Advanced Plot — GrainsPerSpike — Raincloud Plot
🎨 Advanced Plots

TGW_g ▸ GrainYield_tha, GrainsPerSpike, TGW_g

🎨 Advanced Plot — TGW_g — Raincloud Plot
Figure 3. 🎨 Advanced Plot — TGW_g — Raincloud Plot

📊 Basic Plots ▸ GrainYield_tha, GrainsPerSpike, TGW_g

📊 Plot
📊 Plot — Boxplot
Figure 4. 📊 Plot — Boxplot

📐 1-Factor ANOVA (LSD)

🔤 Mean Separation ▸ GrainYield_tha

GrainYield_tha — Treatment · 6 means · error df = 20 · SE(d) = 0.169 · Fisher's LSD at α = 0.05
ⓘ 6 means = 15 pairwise comparisons, each tested by LSD at α = 0.05, so some "significant" pairs are expected by chance alone. With more than 5 means, Tukey HSD (which IRRI STAR uses above 5 levels) controls this — choose it under Mean separation method on the left.
📐 Critical difference by rank span
Rank span (p) Means in range Critical difference Note
every pair 2 to 6 0.352 flat test — one critical difference for every comparison

p is how many means the compared range CONTAINS, endpoints included — two neighbours give p = 2, the largest against the smallest gives p = k. A step-wise test raises the bar as p grows, because a wider range gives a large gap more chances to appear by luck alone. Fisher's LSD is flat — one value for every pair — which is why it separates the most. Two consequences worth knowing: at p = 2 Duncan and SNK equal Fisher's LSD exactly, and at p = k SNK equals Tukey HSD exactly. Both are identities, not coincidences.

⚖️ Every pairwise comparison
Comparison Mean 1 Mean 2 Difference Rank span (p) Critical difference Significant
N160 vs N0 5.162 3.752 1.41 6 0.352 Yes
N200 vs N0 5.012 3.752 1.26 5 0.352 Yes
N120 vs N0 5 3.752 1.248 4 0.352 Yes
N80 vs N0 4.852 3.752 1.1 3 0.352 Yes
N40 vs N0 4.524 3.752 0.772 2 0.352 Yes
N160 vs N40 5.162 4.524 0.638 5 0.352 Yes
N200 vs N40 5.012 4.524 0.488 4 0.352 Yes
N120 vs N40 5 4.524 0.476 3 0.352 Yes
N80 vs N40 4.852 4.524 0.328 2 0.352 No
N160 vs N80 5.162 4.852 0.31 4 0.352 No
N160 vs N120 5.162 5 0.162 3 0.352 No
N200 vs N80 5.012 4.852 0.16 3 0.352 No
N160 vs N200 5.162 5.012 0.15 2 0.352 No
N120 vs N80 5 4.852 0.148 2 0.352 No
N200 vs N120 5.012 5 0.012 2 0.352 No
🔤 Letter groups from this method
Group Mean Letter group
N160 5.162 a
N200 5.012 a
N120 5 a
N80 4.852 ab
N40 4.524 b
N0 3.752 c

For GrainYield_tha, the highest mean was recorded by N160 (5.162); N200, N120 and N80 were statistically at par with it (sharing a letter). The lowest mean was recorded by N0 (3.752).

Statistical notes

Mean separation. Means sharing a letter do not differ significantly at the stated α. Letters are computed from the error term of the design stratum appropriate to that comparison — the same error term as the CD (critical difference) reported with the table. In pooled multi-environment, split-plot, strip-plot and split-split-plot analyses this is the relevant interaction or whole-plot error, not the residual mean square, so letters and CD always refer to the same test.
Critical difference. A CD is specific to the comparison it was computed for. A split-plot reports four (main-plot means, sub-plot means, and each at a fixed level of the other); quoting one CD for a different comparison is not valid.
p-values. A p-value is never rounded to the number of decimal places chosen for the means: a small p is shown in scientific notation, and any value below double precision is reported as “< 2.2e-16” rather than as 0. A displayed p of 0 would mean “impossible”, which no test can conclude.
Significance codes. Stars and significance labels are assigned from the unrounded p-value, not from the rounded value shown in the table, so a marginal result cannot change class through display rounding.

References

Duncan DB (1955) Multiple range and multiple F tests. Biometrics 11: 1-42.

Fisher RA (1925) Statistical Methods for Research Workers. Oliver and Boyd, Edinburgh.

Gomez KA, Gomez AA (1984) Statistical Procedures for Agricultural Research, 2nd edn. John Wiley & Sons, New York.

Keuls M (1952) The use of the 'studentized range' in connection with an analysis of variance. Euphytica 1: 112-122.

R Core Team (2026) R: A Language and Environment for Statistical Computing, version 4.5.3. R Foundation for Statistical Computing, Vienna, Austria.

Tukey JW (1949) Comparing individual means in the analysis of variance. Biometrics 5: 99-114.