Sample Numbers for Forage Production Determinations

Journal of the Arkansas Academy of Science Volume 7 Article 17 1955 Sample Numbers for Forage Production Determinations E. S. Ruby University of Arkansas, Fayetteville Follow this and additional works at: http://scholarworks.uark.edu/jaas Part of the Other Plant Sciences Commons, and the Plant Biology Commons Recommended Citation Ruby, E. S. (1955) "Sample Numbers for Forage Production Determinations," Journal of the Arkansas Academy of Science: Vol. 7 , Article 17. Available at: http://scholarworks.uark.edu/jaas/vol7/iss1/17 This article is available for use under the Creative Commons license: Attribution-NoDerivatives 4.0 International (CC BY-ND 4.0). Users are able to read, download, copy, print, distribute, search, link to the full texts of these articles, or use them for any other lawful purpose, without asking prior permission from the publisher or the author. This Article is brought to you for free and open access by ScholarWorks@UARK. It has been accepted for inclusion in Journal of the Arkansas Academy of Science by an authorized editor of ScholarWorks@UARK. For more information, please contact , . Journal of the Arkansas Academy of Science, Vol. 7 [1955], Art. 17 SAMPLE NUMBERS FOR FORAGE PRODUCTION DETERMINATIONS1 E. S. RUBY University of Arkansas and technicians constantly are confronted with the probof samples necessary to attain a given degree of This is due to the variability that iccuracy in forage production measurements. of changes in the soil, plant species, or physiooccurs in vegetation because slopes, exposure, etc. --and the habits of the anigraphic differences--such as mals grazing on the area. Literature on the variability of native vegetation is limited. Pechanec (1941) reported a coefficient of variation for forage production of 20 per cent ranges of Idaho. He also reported (1940) coefficients of for the sagebrush-grass variation of 64 per cent for arrowleaf balsamroot and 103 per cent for tapertip hawksbeard, with other species as high as 141 per cent. Davies (1931) in Australia reported forage yields of natural vegetation with a coefficient of variation of 32.5 per cent. Beruldsen and Morgan (1934), also working in Australia with pastures composed of ryegrass, Kentucky bluegrass, cocksfoot, and clovers, reported similar variations in forage production. Hanson (1934) reported a coefficient of variation of 27.8 per cent for the mixed prairie of North Dakota. Neven (1945) found a coefficient of variation of 23.7 per cent for bluegrass pastures of Illinois. Costello and Kipple (1939) state that no relationship exists betype and the number of samples needed for any tween the size of vegetational given degree of accuracy on the ranges of Colorado and Wyoming. Formulae for the determination of sample numbers are important to the investigator since no tables appear in the literature showing the number of samples necessary for a given degree of accuracy. Hanson (1934) and Neven (1945) have used the formula N = S 2 (px)2 to calculate the number of samples necessary to achieve the accuracy of p (percentage of the mean). The odds are 2 to 1 that the population mean lies within the desired limit (p) in the above formula. Any estimates calculated by the use of this formula would err in one- third of the cases. Pechanec (1941) states that the sampling error of the estimated forage yield of range was 18 per cent. He further states that the a section of sagebrush-grass odds are 2 to 1 that the actual forage yield of the section of land was within 18 per cent of the estimate. Experimental work in other fields has shown that odds of at least 19 to 1 or 99 to 1 should be used. Other formulae are available that permit the investigator to obtain estimated sample numbers that are more reliable than those used by Pechanec. Such formulae are shown by Snedecor (1946). Range scientists lem of determining the number -- 1. N ¦ 2. N 3. N 2 4. C = number of required samples t = the value of students s = the standard deviation x = sample mean t 2 s 2/(x I - m) 2 (100) 2 t2 s 2/p2 x2 t 2C2 /P 2 = (100) 2s 2/x2 N p = desired limits in per cent of the mean = coefficient of variation = one hundred per cent C 100 m = population mean In most range work these formulae provide an estimate of the number of samples required for a given degree of accuracy in the measurements made on any set °f values. These formulae are applicable to forage production and botanical composition data. Helpful conments and suggestions of Dr. R. E. Comstock of the Statistical Laboratory N. C., were appreciated. NOTE: Research Paper No. 1111, Journal Series, University of Arkansas. Published by Arkansas Academy of Science, 1955 I 55 at Raleigh 55 Journal of the Arkansas Academy of Science, Vol. 7 [1955], Art. 17 " ARKANSAS ACADEMY OF SCIENCE 56 The first formula lends itself readily to determinations of the number of samples necessary to set a desired limit around the sample mean. Suppose that an area of range land has been sampled to determine the forage yield and that 300 samples were used, and that the standard deviation was 100 pounds per acre, and the desired limits around the mean were 50 pounds per acre (x m) , and the mean was 400 pounds per acre. For a sample as large as 300, a t value of 2.6 is a approximation to the one per cent level of significance. Therefore, close enough N (2.6) 2 (100) 2/(50) 2 and N = 27.04 is an indication of the number of samples necessary to measure the production to within 50 pounds per acre of the mean when the standard deviation is 100 pounds per acre with odds of 99 to 1 that the population mean falls within the limits set around the sample mean. This formula can be used in terms of the coefficient of variation and the limits should then be expressed as a percentage of the mean. Thus the second formula becomes of - - value to the investigator. N = (100) 2 t2 s2/p 2x 2 N = 27.04 Under the conditions of the above problem, the limits of 50 pounds per acre were equal to 12.5 per cent of the mean. Substitution in the above formula gives the same value for N as in the first formula. Thus the statement may be made that 28 samples (any fraction must be counted as a v/hole) are necessary to determine the production within 12.5 per cent of the mean. The formula may be simplified if the coefficient of variation has been calculated. Therefore, N = t 2 C2/p 2 (Formula 3). Values of N required for a known size of the mean and standard deviation have been calculated. They are shown in Table I. Data calculated from Formula 2 indicate that 400 samples are necessary when the standard deviation is equal to the mean and that 100 samples are necessary to measure the forage production when the standard deviation is equal to one-half of the mean with an accuracy of 10 per cent at the .05 level of significance .Table II shows the calculated values for N at a limit of one per cent of the mean and at P .05. and IIpermit the investigator wh (...truncated)