An Approach to Analyzing a Response Variable as Affected by its Additive Components: Example for Spring Barley Grain Yield


A problem of decomposing a response variable into a sum of other variables (so-called additive components) is presented in the paper. We propose how to analyze a relationship in which the response variable is affected by its additive components. The approach and interpretation proposed are based on and quite similar to path analysis. Therefore, the approach provides a commonly known view on inferring from causal systems. Its application is presented for grain yield of two spring barley cultivars, which is studied as an effect of grain yields from plants with different number of spikes.


  1. 1.

    Briggs, D. E. (1978). Barley. British School of Malting and Brewing, London, 1–75.

    Book  Google Scholar 

  2. 2.

    Dofing, S., Knight, C. (1994). Yield component compensation in uniculum barley lines. Agron. J. 86, 273–276.

    Article  Google Scholar 

  3. 3.

    Donald, M. C. (1979). A barley breeding programme based on an ideotype. J. Agric. Sci. Camb. 93, 261–269.

    Article  Google Scholar 

  4. 4.

    García del Moral, M., García del Moral, L. (1995). Tiller production and survival in relation to grain yield in winter and spring barley. Field Crops Res. 44(2–3), 85–93.

    Article  Google Scholar 

  5. 5.

    García del Moral, L., García del Moral, M., Molina-Cano, J., Slafer, G. (2003). Yield stability and development in two-and six-rowed winter barleys under Mediterranean conditions. Field Crops Res. 81, 109–119.

    Article  Google Scholar 

  6. 6.

    Jolliffe, P. A., Eaton, G. W., Lovett Doust, J. (1982). Sequential analysis of plant growth. New Phytol. 92, 287–296.

    Article  Google Scholar 

  7. 7.

    Kang, K. M., Seneta, E. (1980). Path analysis: An exposition. Developments in statistics, red. Krishnaiah P. R., 3, 217–245.

    Google Scholar 

  8. 8.

    Kirby, E., Jones, H. (1977). The relations between the main shoot and tillers in barley plants. J. Agric. Sci. Camb. 88, 381–389.

    Article  Google Scholar 

  9. 9.

    Kozak, M., Mądry, W., Wyszyński, Z. (2002). Method of analysis the influence of weight of roots from different fractions on sugar beet yield. Fragmenta Agronomica 2(74), 251–262 (in Polish).

    Google Scholar 

  10. 10.

    Pecio, A. (1995). Studies on the spring barley plant and canopy model. Institute of Soil Science and Plant Cultivation, Puławy, 1–75 (in Polish).

    Google Scholar 

  11. 11.

    Piepho, H. P. (1995). A simple procedure for yield component analysis. Euphytica 84, 43–48.

    Article  Google Scholar 

  12. 12.

    Shipley, B. (2002). Cause and Correlation in Biology. A User’s Guide to Path Analysis, Structural Equations and Causal Inference. Cambridge University Press, Cambridge.

    Google Scholar 

  13. 13.

    Webster, R. (1997). Regression and functional relations. Europ. J. Soil Sci. 48, 557–566.

    Article  Google Scholar 

  14. 14.

    Williams, W. A., Jones, M. B., Demment, M. W. (1990). A concise table for path analysis statistics. Agron. J. 82, 1022–1024.

    Article  Google Scholar 

Download references

Author information



Corresponding author

Correspondence to Marcin Kozak.

Rights and permissions

This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (, which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.

Reprints and Permissions

About this article

Cite this article

Kozak, M., Gozdowski, D. & Wyszyński, Z. An Approach to Analyzing a Response Variable as Affected by its Additive Components: Example for Spring Barley Grain Yield. CEREAL RESEARCH COMMUNICATIONS 34, 981–988 (2006).

Download citation

Key words

  • additive yield components
  • spring barley
  • number of spikes per plant