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The analysis of variance and covariance techniques in relation to the conventional formulas for the standard error of a difference

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Abstract

In this paper it is demonstrated that the analysis of variance techniques yield results equivalent to the calculation oft by means of expressions based on the short or the long formula. It is also shown that the covariance technique gives results equivalent to those obtained by means of the formula fort which should be used with matched groups. The conditions necessary for equivalent results are such that the conventional formulas fort would normally be used rather than the variance or covariance techniques. However, a knowledge of the relationships described in this paper should contribute to one's understanding of the variance and covariance techniques.

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Bibliography

  1. Deemer, Walter L. A numerical example illustrating the generalized formula for testing significance of experimental treatments.Harvard educ. Review, 1940,10, 75–81.

    Google Scholar 

  2. Engelhart, Max D. Classroom experimentation.Review educ. Research, 1939,9, 555–563.

    Google Scholar 

  3. Fisher, R. A. Statistical methods for research workers. Edinburgh: Oliver and Boyd, 1938. 7th ed.

    Google Scholar 

  4. Lindquist, E. F. The significance of a difference between matched groups.J. educ. Psychol., 1931,22, 197–204.

    Google Scholar 

  5. Lindquist, E. F. Statistical analysis in educational research. Boston: Houghton Mifflin Company, 1940.

    Google Scholar 

  6. Rider, P. R. An introduction to modern statistical methods. New York: John Wiley and Sons, 1939.

    Google Scholar 

  7. Shen, Eugene. A generalized formula for testing the significance of experimental treatments.Harvard educ. Review, 1940,10, 70–74.

    Google Scholar 

  8. Shen, Eugene. Experimental design and statistical treatment in educational research,J. exper. Educ., 1940,8, 346–353.

    Google Scholar 

  9. Snedecor, G. W. Statistical methods. Ames, Iowa: Collegiate Press, 1938.

    Google Scholar 

  10. Walker, Helen M. Degrees of freedom.J. educ. Psychol., 1940,31, 253–269.

    Google Scholar 

  11. Wilks, Samuel S. The standard error of the means of matched samples.J. educ. Psychol., 1931,22, 205–208.

    Google Scholar 

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Authors and Affiliations

  1. Department of Examinations, Chicago City Junior Colleges, USA

    Max D. Engelhart

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  1. Max D. Engelhart
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Additional information

The relationships described in this paper were brought to the attention of the author by the excellent article of Eugene Shen (8). The proofs given here and the examples are the work of the present author.

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Engelhart, M.D. The analysis of variance and covariance techniques in relation to the conventional formulas for the standard error of a difference. Psychometrika 6, 221–233 (1941). https://doi.org/10.1007/BF02288055

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  • DOI: https://doi.org/10.1007/BF02288055

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