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This article in AJ

  1. Vol. 73 No. 2, p. 379-382
    Received: May 27, 1980

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Treatment of Heterogeneity of Variances in Hydrocyanic Acid Data1

  1. Elmer Gray,
  2. Valina K. Hurt and
  3. Diana L. Duckworth2



Homogeneity of variance is a basic assumption of the analysis of variance. Hydrocyanic acid potential (HCN-p) of samples of sorghum (Sorghum bicolor (L.) Moench) plants may vary from nil to the maximum produced by the genotype-treatment combination, resulting in heterogeneous variances. The purpose of the present study was to further elucidate heterogeneity of variance in HCN-p data and to employ appropriate treatment of the heterogeneity.

‘Greenleaf’ and ‘Piper’ sudangrass (Sorghum sudarnese (Piper) Stapf.) and ‘Suhi-l’, a sorghum ✕ sudangrass hybrid were subjected to five N treatments: (a) no N applied, (b) 67.2 kg/ha at planting, (c) 33.6 kg/ha at planting and 33.6 kg/ha after second harvest, (d) 134.4 kg/ha at planting, and (e) 33.6 kg/ha at planting and 33.6 kg/ha after first, second, and third harvests. When the plants reached a height of 75 cm, they were cut at a height of 20 cm, resulting in four harvests. The cultivar, N, and harvest treatments were analyzed for heterogeneity of variances.

For the natural data the treatment means and variances were positively associated and the variances for several treatment comparisons were heterogeneous. Transforming the natural data to common logarithms failed to eliminate the evidence of heterogeneity of variances. Since the data did not meet the assumption of homogeneity of variance, an approximate test of equality of means based upon the assumption of heterogeneity of variance was recommended for the HCN-p data.

Heterogeneity of variances decreases the accuracy of statistical comparisons of means. Since HCN-p is converted to highly toxic hydrocyanic acid by ruminant animals, accuracy of statistical decisions is critical. Researchers should examine HCN-p data for evidence of heterogeneity of variances and, if present, employ the approximate test which includes provisions for heterogeneity of variances.

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