Abstract
STUDENTS' t may be standardized by expressing it in units of its own standard deviation; thus, t s = t√{(ν − 2)/ν}, where ν is the number of degrees of freedom. The procedure reduces the variability of the tails with ν for a given probability, P, and in particular, for P = 0.05 and ∞ ≥ ν ≥ 4, t s lies between 1.96 and 2.0 whereas t lies between 1.96 and 2.776. This finding extends the applicability of certain ‘large’ sample methods down to 4 degrees of freedom. The standardizing is extremely simple to apply—merely divide the error sum of squares by ν − 2 instead of by ν and use this value to calculate the appropriate standard error (SE). For example, if d is the difference between two means and d ≥ 2 SE, P ≤ 0.05, that is, the difference is significant at the 5 per cent level. If d < 1.96 SE, P > 0.05 and the difference is not significant. Between these two limits of d, P ≃ 0.05; actually 0.0535 > P > 0.0455. Again, ± 2SE will give a close approximation to 95 per cent confidence limits (actual value between 95 and 95.45 per cent). When the formula is applied to the correlation coefficient, r, we find that r is significant at the 5 per cent point if r ≥ 2/√(ν + 2).
Similar content being viewed by others
Article PDF
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
WEIR, J. Standardized t . Nature 185, 558 (1960). https://doi.org/10.1038/185558a0
Issue Date:
DOI: https://doi.org/10.1038/185558a0
This article is cited by
-
Effects of polychlorinated biphenyls (PCBs) onin vitro biosynthesis of testosterone and cell viability in mouse leydig cells
Bulletin of Environmental Contamination and Toxicology (1989)
-
Activity of liver catalase and its inhibitor in persons dying from acute leukemia
Bulletin of Experimental Biology and Medicine (1970)
-
Significance of the Difference between Two Means when the Population Variances may be Unequal
Nature (1960)
Comments
By submitting a comment you agree to abide by our Terms and Community Guidelines. If you find something abusive or that does not comply with our terms or guidelines please flag it as inappropriate.