European Journal of Scientific Research - EuroJournals
European Journal of Scientific Research - EuroJournals European Journal of Scientific Research - EuroJournals
Nutritive Evaluation of Some Trees and Browse Species from Scotland 318 References [1] Adugna, T., Khazaal, K., and Ørskov, E.R. (1997). Nutritive evaluation of some browse species. Animal Feed Science and Technology 67: 181-195. [2] Apori, S.O., Castro, F.B., Shand, W.J., and Ørskov, E.R. (1998). Chemical composition, in sacco degradation and in vitro gas production of some Ghanaian browse plants. Animal Feed Science and Technology 76: 129-137. [3] Badran, A.M. and Jones, D.E. (1965). Polyethylene glycol- tannin interaction in extracting enzyme. Nature, 206: 622-623 [4] Blummel, M., Makkar, H.P.S., and Becker, K. (1990). In vitro gas production: a technique revisited. J. Anim. Physiol and Anim. Nutr. 77: 24-34 [5] Blummel, M. and Ørskov, E. R. (1993). Comparison of in vitro gas production and nylon bag degradability of roughages in prediction of feed intake in cattle. Animal Feed Science and Technology 40, 109-119. [6] Devendra, C; (1990). The use of shrubs and tree fodders by ruminants. In: Shrubs and Tree fodders for Farm Animals, proceedings of a workshop in Denpasar, Indonesia 24-29 July, IDRC, Ottawa, Canada, pp. 42-60. [7] Jones, W.T. and Mangan, J.L. (1977). Complexes of the condensed tannins of sainfoin with fraction 1 leaf protein and with submaxillary mucoproteins and their reversal by polyethylene glycol and p H J . Sci Food Agric., 28: 126-136. [8] Khazaal, K., Markantonatos, X., Nastis, A. and Orskov, E.R. (1993). Changes with maturity in fibre composition and levels of extractable poly phenols in Greek browse: Effects on in vitro gas production and in sacco DM degradation. J. Sci. Food Agric., 63: 237-244 [9] Kibbon, A. and Ørskov, E.R. (1993). The use of degradation characteristics of browse plants to predict intake and digestibility by goats. Anim. Prod. 57: 247- 251. [10] Kumar, R. and Vaithiyanathan, S. (1990). Occurrence, nutritional significance and effect on animal productivity of tannins in tree leaves. Anim. Feed Sci. Tech., 30: 21-38. [11] Menke, K., Raab, L., Salewski, A., Steingass, H., Fritz, D. and Schneider, W. (1979). The estimation of digestibility and metabolizable energy content of ruminant feedstuffs from the gas production when they are incubated with rumen liquor in vitro. J. Agric. Sci., Camb. 3: 217- 222. [12] Odeyinka, S.M., Hector, B.L., Ørskov, E.R. (2003). Evaluation of the nutritive value of the browse species Gliricidia sepium (Jacq). Walp, Leucaena leucocephala (Lam.) de Wit. and Cajanus cajan (L.) Millsp from Nigeria. Journal of Animal and Feed Sciences, 12: 341-349 [13] Ørskov, E. R. (2000). New concepts of feed evaluation for Ruminants with Emphasis on Roughages and Feed intake. Asian - Australian J. Anim. Sci 13: 128-136 [14] Ørskov , E.R and McDonald, I., (1979). The estimation of protein degradability in the rumen from incubation measurements weighted according to the rate of passage. J. Agric. Sci., Camb. 92: 499-503. [15] Ørskov E.R., Hovell F.D.DeB., Mould F., 1980. The use of the nylon bag technique for the evaluation of feedstuffs. Trop. Anim. Prod. 5, 195-213 [16] Ørskov, E. R., Reid, G.W., and Kay, M.M. (1988). Prediction of intake by cattle from degradation characteristics of roughages. Animal Production 46: 29-34 [17] Ørskov E.R., Ryle M., (1990). Energy Nutrition in Ruminants. Elsevier Applied Science, London, UK pp 133-144 [18] Sundstoøl, F., Homb, T., Ekern, A. and Breirem, K (1986). Sammensetning og Naeringsverdi av Norske Formidler. K.K. Heje Lommehandbok, P. F. Steensballes Forlag. [19] Van Soest, P.J. (1983). Nutritional Ecology of the Ruminant O and B Books, Corvalis [20] Woodword, A. and Reed, J.D. (1989). The influence of polyphenolics on the nutritive value of browse: a summary of research conducted at ILCA. ILCA Bull. 35: 2-11
European Journal of Scientific Research ISSN 1450-216X Vol.14 No.3 (2006), pp. 319-325 © EuroJournals Publishing, Inc. 2006 http://www.eurojournals.com/ejsr.htm Determination of Sample Size Nadia Saeed Department of Statistics, GC University (GCU) Lahore (Pakistan) E-mail: nadia_gcu@yahoo.com Muhammad Khalid Pervaiz Chairperson, Department of Statistics GC University (GCU), Lahore (Pakistan) E-mail: drkhalidpervaiz@hotmail.com Muhammad Qaiser Shahbaz Department of Statistics, GC University (GCU) Lahore (Pakistan) E-mail: drshahbaz@gcu.edu.pk Abstract The sample size determination is one of the most frequent problems in the discipline of Statistics. Although standard formulae are available for determining sample size in many situations, yet specific methodology is lacking. The purpose of the paper is to highlight the factors involved in determining a desirable sample size for a research project. The paper offers the brief review of determining the sample size under varying situations. Some new formulae are also developed with special reference of cost function and degree of affordable error. Key Words: Sample size, error, clinical trials, power analysis and cost function. 1. Introduction The size of the sample is not only an essential element in every statistical procedure but it is also an item of great economic importance. In a sample survey, a statistician must determine the sample size. Statistical studies (surveys, experiments, observational studies, etc.) are always better when they are carefully planned. Good planning has many aspects. The study must be of adequate size, relative to the goals of the study. Sample size is important for economic reasons: An under-sized study can be a waste of resources for not having the capability to produce useful results, while an over-sized one uses more resources than are necessary (Mace, 1964; Kraemer & Thiemann, 1987; Cohen, 1988; Desu & Raghavarao, 1990; Lipsey, 1990; Shuster, 1990; and Odeh & Fox, 1991). The points to be considered while selecting a sample size are: i) Parameter: The population parameters to be estimated like mean the difference between means or proportion. ii) Variance: The samples are taken to form estimates of some characteristics of interest, like determination of mean in simple random sampling, stratified random sampling and cluster sampling. Most of the work has been done to determine the sample size based on precision to
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<strong>European</strong> <strong>Journal</strong> <strong>of</strong> <strong>Scientific</strong> <strong>Research</strong><br />
ISSN 1450-216X Vol.14 No.3 (2006), pp. 319-325<br />
© Euro<strong>Journal</strong>s Publishing, Inc. 2006<br />
http://www.eurojournals.com/ejsr.htm<br />
Determination <strong>of</strong> Sample Size<br />
Nadia Saeed<br />
Department <strong>of</strong> Statistics, GC University (GCU)<br />
Lahore (Pakistan)<br />
E-mail: nadia_gcu@yahoo.com<br />
Muhammad Khalid Pervaiz<br />
Chairperson, Department <strong>of</strong> Statistics<br />
GC University (GCU), Lahore (Pakistan)<br />
E-mail: drkhalidpervaiz@hotmail.com<br />
Muhammad Qaiser Shahbaz<br />
Department <strong>of</strong> Statistics, GC University (GCU)<br />
Lahore (Pakistan)<br />
E-mail: drshahbaz@gcu.edu.pk<br />
Abstract<br />
The sample size determination is one <strong>of</strong> the most frequent problems in the<br />
discipline <strong>of</strong> Statistics. Although standard formulae are available for determining sample<br />
size in many situations, yet specific methodology is lacking. The purpose <strong>of</strong> the paper is to<br />
highlight the factors involved in determining a desirable sample size for a research project.<br />
The paper <strong>of</strong>fers the brief review <strong>of</strong> determining the sample size under varying situations.<br />
Some new formulae are also developed with special reference <strong>of</strong> cost function and degree<br />
<strong>of</strong> affordable error.<br />
Key Words: Sample size, error, clinical trials, power analysis and cost function.<br />
1. Introduction<br />
The size <strong>of</strong> the sample is not only an essential element in every statistical procedure but it is also an<br />
item <strong>of</strong> great economic importance. In a sample survey, a statistician must determine the sample size.<br />
Statistical studies (surveys, experiments, observational studies, etc.) are always better when they are<br />
carefully planned. Good planning has many aspects. The study must be <strong>of</strong> adequate size, relative to the<br />
goals <strong>of</strong> the study. Sample size is important for economic reasons: An under-sized study can be a waste<br />
<strong>of</strong> resources for not having the capability to produce useful results, while an over-sized one uses more<br />
resources than are necessary (Mace, 1964; Kraemer & Thiemann, 1987; Cohen, 1988; Desu &<br />
Raghavarao, 1990; Lipsey, 1990; Shuster, 1990; and Odeh & Fox, 1991).<br />
The points to be considered while selecting a sample size are:<br />
i) Parameter: The population parameters to be estimated like mean the difference between<br />
means or proportion.<br />
ii) Variance: The samples are taken to form estimates <strong>of</strong> some characteristics <strong>of</strong> interest, like<br />
determination <strong>of</strong> mean in simple random sampling, stratified random sampling and cluster<br />
sampling. Most <strong>of</strong> the work has been done to determine the sample size based on precision to
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