Effect of Fertilizer on Potato Yield under Integrated Soil Fertility Management

Authors

R.W. Waithera

Department of Mathematics and Statistics, Machakos University, Machakos (Kenya)

M. Mungau

Department of Mathematics and Statistics, Machakos University, Machakos (Kenya)

M.M. Kasina

Department of Mathematics and Statistics, Machakos University, Machakos (Kenya)

Thomas Kwambai

Kenya Agricultural and Livestock Research Organization (KALRO) FCRI – P.O. Box 450-30200, Kitale (Kenya)

Mary Kifuko-Koech

Kenya Agricultural and Livestock Research Organization (KALRO) FCRI – P.O. Box 450-30200, Kitale (Kenya)

Keziah Ndungu-Magiroi

KALRO FCRC ALUPE – P.O. Box 278-50400, Busia (Kenya)

Jane Mugwe

Kenyatta University, P.O. Box 43844-001000, Nairobi (Kenya)

Article Information

DOI: 10.47772/IJRISS.2026.100700301

Subject Category: Statistics

Volume/Issue: 10/7 | Page No: 4256-4272

Publication Timeline

Submitted: 2026-07-14

Accepted: 2026-07-20

Published: 2026-07-31

Abstract

To improve nutrient management in potato cropping, it is critical to grasp the nature of fertilizer response surfaces. In this study, Canonical Analysis was used to determine optimal operation conditions in the context of integrated soil fertility management systems. An experiment was conducted in two seasons of potato cropping in Western Kenya with the objective of assessing eight fertilizer treatments under randomized complete block design and five replications.
The treatments comprised: farmers’ practice, DAP recommendations, Baraka and Yara fertilisers programme, farmyard manure and integrated organic-inorganic. The treatment effects were evaluated by analysis of variance (ANOVA), fertilizer combinations were compared by Tukey’s HSD, Dunnett’s test, and response-surface canonical analysis was used to investigate the curvature of the fitted response surface. Replication/site effects were highly significant in both seasons, with no significant fertilizer treatment effects found in either Season One (𝐹7,28 = 1.255, 𝑝 = 0.307) or Season Two (𝐹7,28 = 1.913, 𝑝 = 0.105). The farm and season effects were also highly significant, and the overall treatment effect was not significant (𝐹7,64 = 1.152, 𝑝 = 0.343) in the combined analysis. Canonical analysis identified stationary points at mixture proportions (𝑥1, 𝑥2, 𝑥3) = (0.0584, 0.1017, 0.8399) in Season One and (0.0494, 0.0376, 0.9130) in Season Two. The stationary point was a saddle point in both seasons, as the eigenvalues of the response surface had opposite signs, and thus no statistically proven global maximum was found in the experimental area
When integrated organic–inorganic treatments are compared, ½ DAP + ½ CAN + FYM gave maximum numerical mean yield and hence, it is suggested as a viable option for further field testing rather than a proven universal optimum. The model diagnostics for the Season One model did not present problems of residual normality and homoscedasticity, while the Season Two model presented problems of non-normal residuals, suggesting for caution use and independent validation. The conclusions point to the usefulness of using both ANOVA and response-surface and canonical analysis to highlight the significance of the environmental variation in fertilizer response experiments.

Keywords

Potato yield, marketable number of tubers, Mixture experiments, ANOVA

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