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Statistical analysis of two point pH-bicarbonate diagrams

  • K. Subrahmaniam
Article
  • 11 Downloads

Summary

In the present paper, the author deals with slightly altered problem of estimating the common slope of a number of lines which are parallel but where the following conditions obtain:
  1. 1)

    There are only two points for the estimation of each line.

     
  2. 2)

    There are two distinct groups of lines, every line in the first group having a corresponding line in the second group. Errors for corresponding pairs of observations between groups are correlated.

     
  3. 3)

    All lines have a separate intercepted on they-axis.

     
  4. 4)

    The errors all have the same zero mean and common variance σ2.

     
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The reasons for the assumptions and conditions that give rise to then are explained in the discussion of the biological aspects of the problem of the quantity of carbon dioxide displaced from hemoglobin by oxigen when adult and fetal blood was used.

Keywords

Oxygen Saturation Fetal Blood Ellas Common Slope Dissolve Carbon Dioxide 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Resumen

En el presente trabajo se estudia el problema ligeramente modificado de estimar la pendiente común de un krupo de lineas paralelas sometidas a las siguientes restricciones:
  1. 1)

    Sólo existen dos puntos para la estimación de cada linea.

     
  2. 2)

    Existen dos grupos distintos de líneas, teniendo cada línea del primer grupo una linea correspondiente en el segundo. Los errores correspondientes a los pares de observaciones entre los grupos están correlacionados.

     
  3. 3)

    Las intersecciones de las rectas con el ejey son todas diferentes.

     
  4. 4)

    Todos los errores tienen media cero y varianza común σ2.

     

Las razones para las suposiciones y para las condiciones que dan lugar a ellas se exponen al tratar los aspectos biológicos del problema de la cantidad de dióxido de carbono desplazado de la hemoglobina por el oxígeno cuando se emplea sangre fetal y de adulto.

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References

  1. Anderson, T. W. (1958):An Introduction to Multivariate Statistical Analysis, New York, John Wiley and Sons.MATHGoogle Scholar
  2. Berkson, J. (1950): “Are There Two Regressions?”,J. Am. Stat. Assoc., vol. 45, pp. 164–180.MATHCrossRefGoogle Scholar
  3. Henderson, C. R.;O. Kempthorne, S. R. Searle, and C. M. vonKrosigk (1959): “The Estimation of Environmental and Genetic Trends from Records Subject to Culling”,Biometrics, vol. 15, pp. 192–218.MATHCrossRefGoogle Scholar
  4. Wright, Samson (1961):Applied Physology, 10th ed., Oxford University Press, pp. 179–188.Google Scholar

Copyright information

© Springer 1965

Authors and Affiliations

  • K. Subrahmaniam
    • 1
  1. 1.Dept. MathematicsUniversity of W. OntarioLondonCanadá

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