STATISTICAL ANALYSIS OF NITROPHOSPHATE AND POTASSIUM LEVEL ON THE YIELD OF ONION (ALLIUM CEPA)
Abstract
This study investigated the effects of varying application rates of Nitrogen (N), Phosphorus (P),
and Potassium (K) fertilizers on crop yield using a factorial experimental design and Response
Surface Methodology (RSM). The experiment consisted of 54 observations, with each nutrient
applied at three levels: Nitrogen (50, 100, 150 kg/ha), Phosphorus (40, 80, 120 kg/ha), and
Potassium (30, 60, 90 kg/ha). Data were analyzed using descriptive statistics, Analysis of Variance
(ANOVA), Tukey post hoc tests, and regression-based RSM modelling. Descriptive analysis
revealed a general trend of yield improvement with increasing nutrient levels, particularly for
Nitrogen and Phosphorus. However, quadratic terms for both nutrients were negative and
significant, indicating diminishing returns at very high application levels. Potassium showed a
positive but statistically insignificant quadratic effect, suggesting a more linear relationship with
yield. The ANOVA results confirmed that all main effects (N, P, and K) were statistically
significant (p < 0.001), with Nitrogen having the strongest influence, followed by Phosphorus and
Potassium. The interaction between Nitrogen and Phosphorus was significant, demonstrating a
synergistic effect, whereas interactions involving Potassium were generally insignificant. Tukey
post hoc comparisons further highlighted significant differences in yield between all nutrient
levels, with the largest gains occurring between the lowest and highest application rates. The RSM
model achieved an R² of 0.994 and Adjusted R² of 0.993, indicating an excellent fit. Model
adequacy tests confirmed the assumptions of normality and independence of residuals. The
regression equation and surface plots identified optimal nutrient combinations for maximum yield,
vi
emphasizing the importance of balanced fertilization strategies. This study concludes that
strategic, optimized application of N, P, and K particularly Nitrogen and Phosphorus in
combination—can significantly enhance crop productivity. The findings demonstrate the value of
RSM as a decision support tool for agricultural nutrient management and provide actionable
recommendations for farmers and extension services.
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