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Reply to comments on “An application of nonparametric statistics to the sampling in solids mixing”
Powder Technology, 12 (1975) @ Elsevier Sequois S.A.,
95 Lausanne -
Printed in The Netherlands
Letter to the Editor -
_ ____-___---
-
Reply to comments on “An application of nonparametric statistics to the sampling in solids mixing”
First of all, we appreciate the interest shown in our paper “An application of nonparametric statistics to the sampling in solids mixing” [l] by many readers including Drs. Kristensen and Holst [ 21. We are particularly appreciative of their concern with regard to the uncritical use of statistical tests. However, we are in disagreement with their comments on some specific aspects of our paper.
A sample from a finite population is a
random sample if each of the possible samples was equally likely to be obtained [3]. Therefore, even if a mixture itself is segregated or “non-random”, we can still carry out random sampling so that all of the samples from the mixture are equally likely to be obtained. Random sampling guarantees that the observations are independent and the distributions of samples are identicai as long as the samples are taken from the same lot of a mixture (the same population). Thus, the validity of the two assumptions mentioned in Kristensen and Holst’s letter cannot be tested by ‘;he outcome of sampling, and, furthermore, these assumptions are fulfilled by sampling methods usuahy employed in investigating solids mixing.
The sampling method employed in obtaining data used in Example 4 i; not the total sampling method; instead, it is a spot sampling method. Consequently, variations exist among the concentrations of the samples. Thus, the use of the Mann-Whitney test is appropriate for this example. F.S. LAI,
R.H. WANG
and L.T. FAN
Department of Chemical Engineering, Kansas State Universify, Manhattan, Kan. 66506, a-.S.A. Received
December
12, 1974
REFERENCES F.S. Lai, R.H. Wang and L.T. Fan, An application of nonparametric statistics to the sampling in solids mixing, Powder Technol., 10 (1974) 13. H.G. Kristensen and E. Hoist, Powder Tec’lnol., 12 (1975) 93. W.J. Conover, Practical Nonparametric Statistics, Wiley, New York, 1971.
95 Lausanne -
Printed in The Netherlands
Letter to the Editor -
_ ____-___---
-
Reply to comments on “An application of nonparametric statistics to the sampling in solids mixing”
First of all, we appreciate the interest shown in our paper “An application of nonparametric statistics to the sampling in solids mixing” [l] by many readers including Drs. Kristensen and Holst [ 21. We are particularly appreciative of their concern with regard to the uncritical use of statistical tests. However, we are in disagreement with their comments on some specific aspects of our paper.
A sample from a finite population is a
random sample if each of the possible samples was equally likely to be obtained [3]. Therefore, even if a mixture itself is segregated or “non-random”, we can still carry out random sampling so that all of the samples from the mixture are equally likely to be obtained. Random sampling guarantees that the observations are independent and the distributions of samples are identicai as long as the samples are taken from the same lot of a mixture (the same population). Thus, the validity of the two assumptions mentioned in Kristensen and Holst’s letter cannot be tested by ‘;he outcome of sampling, and, furthermore, these assumptions are fulfilled by sampling methods usuahy employed in investigating solids mixing.
The sampling method employed in obtaining data used in Example 4 i; not the total sampling method; instead, it is a spot sampling method. Consequently, variations exist among the concentrations of the samples. Thus, the use of the Mann-Whitney test is appropriate for this example. F.S. LAI,
R.H. WANG
and L.T. FAN
Department of Chemical Engineering, Kansas State Universify, Manhattan, Kan. 66506, a-.S.A. Received
December
12, 1974
REFERENCES F.S. Lai, R.H. Wang and L.T. Fan, An application of nonparametric statistics to the sampling in solids mixing, Powder Technol., 10 (1974) 13. H.G. Kristensen and E. Hoist, Powder Tec’lnol., 12 (1975) 93. W.J. Conover, Practical Nonparametric Statistics, Wiley, New York, 1971.