A Quick - But Accurate - Approximation to the Standard Deviation of a Distribution

Lathrop, Robert L.

doi:10.1080/00220973.1961.11010698

The Journal of Experimental Education

1961

DOI: 10.1080/00220973.1961.11010698

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A Quick - But Accurate - Approximation to the Standard Deviation of a Distribution

Robert L. Lathrop

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“…Formulae for approximations were proposed by Jenkins (1946; later unpublished manuscript), Diederich (1958), Saupe (1961), and Lord (1957, and a modification was proposed by Mason and Odeh (1968). While additional relationales for individual formulae have appeared (Swineford, 1959;Lathrop, 1961;Gardner, 1970), the number of empirical verifications remains limited. Recently Sabers (1970) and Jurs and Hopkins (197 I) provided findings supporting the use of short-cut approaches for the standard deviation.For the present paper, approximations for each of the three statistics were computed and compared with the corresponding standard statistics.…”

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EVIDENCE ON THE QUALITY OF SEVERAL APPROXIMATIONS FOR COMMONLY USED MEASUREMENT STATISTICS¹

McMorris

1972

J Educational Measurement

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What is the extent of error likely with each of several approximations for the standard deviation, internal consistency reliability, and the standard error of measurement? To help answer this question, approximations were compared with exact statistics obtained on 85 different classroom tests constructed and administered by professors in a variety of fields; means and standard deviations of the resulting differences supported the use of approximations in practical situations. Results of this analysis (1) suggest a greater number of alternative formulas that might be employed, and (2) provide additional information concerning the accuracy of approximations with non‐normal distributions.

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confidence: 99%

EVIDENCE ON THE QUALITY OF SEVERAL APPROXIMATIONS FOR COMMONLY USED MEASUREMENT STATISTICS¹

McMorris

1972

J Educational Measurement

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Accuracy of Short‐cut Estimates for Standard Deviation

Sabers

Klausmeier

1971

J Educational Measurement

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The accuracy of short‐cut estimates of standard deviation was investigated for distributions of raw scores on classroom tests and computer generated samples. Estimates proposed by Mason and Odeh, Jenkins, Diederich, Ebel, and Davenport were compared for relative accuracy in three studies. The loss in accuracy due to short‐cut methods versus the conventional statistic ranged from 0 to 7,8%. Based on the findings of these studies, it is recommended that a shortcut method for computing standard deviations he included in courses where the conventional formula is taught.

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Metodologia simplificada para a estimativa em campo da uniformidade de sistemas de irrigação por gotejamento superficial

Levien

Figueirêdo

2013

RBAI

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Na agricultura irrigada, a avaliação dos parâmetros que afetam a qualidade da irrigação é de fundamental importância, especialmente aqueles relacionados à uniformidade de distribuição de água. Objetivou-se com esse trabalho propor uma metodologia para a estimativa da uniformidade de distribuição de vazão de sistemas de irrigação por gotejamento superficial em condições de campo. O procedimento de avaliação consiste de uma técnica gráfica simplificada que usa aproximadamente a metade dos dados coletados, em uma avaliação de um sistema de irrigação por gotejamento superficial, e também pode ser usada para uma avaliação rápida no campo. Neste procedimento, o tempo para encher um recipiente é usado no lugar da vazão do emissor para determinar a uniformidade. Usando esta técnica, os tempos coletados para preencher o recipiente instalado em suas posições predeterminadas na subunidade, Tmax e Tmin, podem ser calculados como a soma dos quatro maiores e a soma dos quatro menores tempos de descarga dos emissores avaliados, respectivamente. Os exemplos de aplicação mostraram que o coeficiente de uniformidade pode ser determinado usando um gráfico ou uma equação simples, e observou-se, também, que à medida que o valor do coeficiente de uniformidade diminuiu, o erro aumentou, corroborando com a prerrogativa de que se deve analisar eventuais causas da diminuição da uniformidade do sistema quando os valores de CU forem menores que 80%.

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A Quick - But Accurate - Approximation to the Standard Deviation of a Distribution

Cited by 3 publications

References 1 publication

EVIDENCE ON THE QUALITY OF SEVERAL APPROXIMATIONS FOR COMMONLY USED MEASUREMENT STATISTICS¹

EVIDENCE ON THE QUALITY OF SEVERAL APPROXIMATIONS FOR COMMONLY USED MEASUREMENT STATISTICS¹

Accuracy of Short‐cut Estimates for Standard Deviation

Metodologia simplificada para a estimativa em campo da uniformidade de sistemas de irrigação por gotejamento superficial

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A Quick - But Accurate - Approximation to the Standard Deviation of a Distribution

Cited by 3 publications

References 1 publication

EVIDENCE ON THE QUALITY OF SEVERAL APPROXIMATIONS FOR COMMONLY USED MEASUREMENT STATISTICS1

EVIDENCE ON THE QUALITY OF SEVERAL APPROXIMATIONS FOR COMMONLY USED MEASUREMENT STATISTICS1

Accuracy of Short‐cut Estimates for Standard Deviation

Metodologia simplificada para a estimativa em campo da uniformidade de sistemas de irrigação por gotejamento superficial

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Product

Resources

About

EVIDENCE ON THE QUALITY OF SEVERAL APPROXIMATIONS FOR COMMONLY USED MEASUREMENT STATISTICS¹

EVIDENCE ON THE QUALITY OF SEVERAL APPROXIMATIONS FOR COMMONLY USED MEASUREMENT STATISTICS¹