SAMAR Analysis Report

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

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

🎨 Advanced Plots

GrainsPerSpike ▸ GrainYield_tha, GrainsPerSpike, TGW_g

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

🎨 Advanced Plots

TGW_g ▸ GrainYield_tha, GrainsPerSpike, TGW_g

📊 Basic Plots ▸ GrainYield_tha, GrainsPerSpike, TGW_g

📊 Plot

📐 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.