On-farm evaluation and determination of sources of variability of soybean response to Bradyrhizobium inoculation and phosphorus fertilizer in northern Ghana

•Inoculation increased grain yield over the control by 24%.•Combined application of P + I increased grain yield over the control by 37%.•Soil and environmental factors explained up to 79% of yield variation.•Agronomic index for responsiveness was robust than economic index.•About 53% of the farmers...

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