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The Standardization of Poultry Experiments
POULTRY SCIENCE VOL. I I
August-September, 1923
No. 6
THE STANDARDIZATION OP POULTRY EXPERIMENTS H. C. K N A N D E L P e n n s y l v a n i a S t a t e College Downloaded from http://ps.oxfordjournals.org/ at Michigan State University on June 12, 2015
The subject of this paper was brought very forcibly to the writer's attention through a letter received from one of our poultry magazines of large circulation. To quote from the editor of this magazine: " W e would be very glad to be placed on the mailing list of the Pennsyh^ania State College Poultry Department. Bulletins issued by this department are conspicuous by their absence and we have often wondered why. We receive almost everything of this nature from nearby states but we get so little from Pennsylvania we have often wondered whether you were dead or only sleeping. Let's wake up for our mutual advantage. Give us all the material on poultry that comes out of Penn State and we will do our best to give it to our readers while it is yet news. " The writer's reply was as follows: " T o pick up any poultry magazine today, one is impressed with the great amount of material written primarily for what the writer can get out of it. This would-be-knowledge is disseminated to our rural population who do not have the time to investigate the facts or statements given. Too many of our Experiment Stations put out material on one year's test which is absolutely worth nothing to the poultry industry. The one year test on incubation, feeding, the use of electric lights, brooding or anything else connected with the poultry industry is of little practical value. Until our experiment stations and poultry magazines realize this and realize that this information should have at least several years of conscientious, thorough investigation behind it, we are doing a great injustice to the farmers and poultrymen. I am in thorough sympathy with all agricultural college work. It is how I make my living, etc."
174
POULTRY
SCIENCE
It is not until quite recently that mathematics has been employed in studying carefully the results of experiments. The formulas given later in this paper are those which are used by many of the mathematicians and biometrists of note today. It is by the use of these formulas that we are better able to study the
Downloaded from http://ps.oxfordjournals.org/ at Michigan State University on June 12, 2015
In reply to this letter, the editor wrote; " I had little idea when I made the comment about the absence of material from the Pennsylvania State College Poultry Department that it would lead you to give me so much time and such a very pleasant and satisfactory letter. You are absolutely right regarding the publication of much that might be better left out. This is probably due, in part, to the lack of real knowledge on the part of those editing our poultry journals or too high a regard on the part of these men for hasty opinions sent out from experiment stations. We hope the colleges Avill revise their methods and overcome their desire to rush into print knowledge that is ill founded and only partially substantiated. It is a pity that poultry journals are not endowed so that they could do and say what they felt best in such matters." Horace AtAvood in 1908 presented a paper to this association in which he said, ' ' Not only is the industry whose problems we are studying a large and important one but poultry husbandry as carried on at the present time, with its artificial methods and appliances is a development of recent years and there is behind this business no such accumulation of facts and experiences as in the ease of other branches of livestock industry that have been carried on for a much longer time." To quote further—"The problems which we may select for study are so numerous that there is some danger that we may spread our energies over too wide a range thus interfering with the quality of our work. The ideal is to concentrate effort on a few specific problems until final results are achieved and presented to the public." And finally he said : " L e t us be doubly careful and resist with all our power any pressure which may be brought to bear on us for quick results and when we do publish the results of an investigation let us be sure not only of the facts involved, but also that our interpretation of the facts is the most logical and consistent that can be given. Sometimes a set of facts resulting from an investigation can be explained in two or more ways. ' '
STANDARDIZATION
OF POULTRY
EXPERIMENTS
I'J^y
The results of experiments may be published giving the description of plants, animals, or other material used, how they were treated or fed, they may give all the conditions of the experiment and a statement of yields, increases in animals or plants, financial results and the like; yet according to one authority "while such a statement is in itself valuable and not void· of interest because it contains the description of a fact, so long as this fact is not connected with other facts its statement is not so much knowledge as the material for the future acquisition of knowledge." On this ground one cannot conclude that under similar conditions results will be obtained which resemble those of the first series of observations. It is impossible to produce exactly the same conditions and therefore it is necessary to have more repetitions. Hence it is important to express the results of several tests in the form of a mean or average. The mean annual eg^ production
Downloaded from http://ps.oxfordjournals.org/ at Michigan State University on June 12, 2015
results of our experiments in a true and fair light. According to Pearl, the ordinary methods of description fail when the attempt is made to deal with any group of individuals such as a population because they are fundamentally and necessarily incapable of giving a description of the group in terms of anything but the individuals which compose it. Lord Kelvin, the great physicist, has said, " I often say that when you can measure what you are speaking about and express it in numbers, you know something about it, but when you cannot measure it, when you cannot express it in numbers, your knowledge is of a meager and unsatisfactory kind. It may be the beginning of knowledge but you have scarcely in your thoughts advanced to the stage of science whatever the matter may be. ' ' Karl Pearson, who now occupies the Francis Galton Chair of Eugenics at the University of London has very well stated his views regarding the importance of statistical analysis. He says, "General theories of society are of no use, verbal discussions are of no use, philosophical reasoning is of no use. We need to observe, measure, record, to analyze by the methods of exact science before we can advance in our sociology, before we can aid our working classes to a true weight of the factors which make for or mar our national vigor. ' '
176
POULTRY
SCIENCE
P. E. M. = ± .6745 y
.D^
n(n-l)
Where 5D^ ^ the summation of the squares of differences between such individuals and the mean, and η = number of individuals. This can better be explained by using a concrete example. In Pennsylvania State College Bulletin 87 results are given of an experiment in which eggs from various breeds and varieties of fowls were weighed. These eggs were incubated and the chicks then weighed. One of the conclusions drawn was that the Light Brahmas laid a sinaller egg than the Black Minorca but the Light
Downloaded from http://ps.oxfordjournals.org/ at Michigan State University on June 12, 2015
is affected by differences in vitality, digestion, assimilation, and environmental factors with which one is dealing. Biometry is nothing more than a method of analysis. By the methods developed in this field we are much better able to study statistical material and to draAV more accurate conclusions as to the variation in the material used and the probable extent to which our treatments have influenced this variability. The biometrician 's usual means of studying variation are : 1. Probable error of the average or mean. 2. Probable error of the difference. 3. Standard deviation. 4. Coefficient of variability. The probable error is concerned with the fact that when a mean is determined this mean does not give the true value for all the possible individuals in the material under study but only for those observed. Due to variation, the mean of another group may be different. If 100 men are measured for height, a certain mean would be determined. If another 100 men be taken, another mean is found. Two groups give seldom the same average. The results therefore of a single experiment are often misleading. Hence the falsity of one-year experiments unless they have been perfqrmed with a very large number of in dividuals under various conditions. Practical recommendations should not be made to the farmer from the results of experiments conducted but one year. It is far better to make several tests before conclusions are published. The formula used in com puting the probable error of the mean is
STANDARDIZATION
OF POULTRY EXPERIMENTS
I77
The results of the steer feeding experiments carried on at State College and published in Bui. No. 64 of that Station show an average gain in 126 days in one lot of 267.7 pounds and in another lot a gain in the same length of time under different treatment was 247.7 pounds. The conclusions drawn were that the first lot was better by 20 pounds per steer. However, only 12 steers were used in each lot and the probable error was 11.5 pounds per steer. The difference is only 8 per cent and according to Wood and Stratton's formula 80 animals are needed to measure such a difference. Therefore the results are not significant and the difference in weight was not necessarily due to the different treatments which these lots received. An experiment was completed, so to speak, comparing the amount of edible meat on the dual purpose breeds with those of the Mediterraneans and Asiatics. This experiment was conducted at the Pennsylvania State, College and published in Bui. No. 87 of that station. The conclusions 4rawn from this experiment stated that the dual purpose breeds dressed out better than the egg or meat breeds and that the pullets among the Wyandottes and Rhode Island Reds dressed out better than the
Downloaded from http://ps.oxfordjournals.org/ at Michigan State University on June 12, 2015
Brahma chick was larger than that of the Black Minorca. Byapplying Bessel's formula, we find there is no significant difference and the conclusions drawn may not be entirely true. In other words the mean weight of the Light Brahma chicks was 39.7 grams, with a probable error of 1.1 grams. That is: the chances are even that the weight of a single chick would fall between 39.7 + 1.1 = 40.8 grams or 39.7 —1.1 = 38.6. The probable error of the difEerence is obtained by finding the difference between the mean of two lots which may be compared and extracting the square root of the sums of the probable errors squared. The difference then is divided by the probable error. The ratio of 3.8 to 1, which is equivalent to odds of 30 to 1, is considered quite significant. In the same bulletin the statement is made that eggs hatched better during the middle of April than they did the latter part of May. By applying Bessel's formula again, we find that there is no significant difference. The odds in this case are less than one to one and the conclusions drawn have no significance whatever.
POULTRY
178
SCIENCE
Egg Yield 7 5 - 89 90-104 105-119 120-134 135-149 150-164
Frequency 11 21 15 10 14 28
Egg Yield 165-179 180-194 195-209 210-224 225-239
Frequency 21 15 6 4 3
T O T A L . .148
In reviewing poultry experiments carried on by the many experiment stations, one is rather amused at the conclusions drawn from the number of individuals used. For instance, in the case of experimental work in feeding laying hens, or pullets, the number of individuals used varies from ten up to twenty, thirty and one hundred. In the case of growing stock, the range is just as striking. Some experiments have been carried on with nine chicks in each lot and with but one lot under each treatment. A bulletin was published giving these results. At other experiment stations twenty-five (25) chicks were used. Fifty (50) chicks were used by other stations while a few used one
Downloaded from http://ps.oxfordjournals.org/ at Michigan State University on June 12, 2015
cockerels, while among the Leghorns, Brahmas, and Cochins, the cockerels dressed out better. Applying Bessel's formula to these results, we find the difference in dressing percentage to be 4.5 ± 2.2. Therefore, in 100 trials the probable occurrence of a deviation as great or greater is 18 times, or the odds are 4.6 to 1. The standard deviation affords a basis of comparison of one variety with another or with itself at some future time. One standard deviation cannot always be compared directly Math another for two reasons. First, one mean may be very much larger than the other and second, the two may be of entirely different units. Therefore, an abstract expression is desired and is found in the term coefScient of variability which is expressed in per cent. In technical bulletins, it is important that the individual data be printed. For instance, in the case of feeding fowls for egg production, the number of eggs which each hen lays should be given. • This will allow another investigator to thoroughly analyze the data. In the case of 148 trapnested pedigreed pullets at the Pennsylvania State College during the year 1919-20, the mean production was 144.6 eggs per year. These birds were grouped as follows :
STANDARDIZATION
01' POULTRY EXPERIMENTS
^79
Τ
'^
L
100 e
J
L
10
J
Solving, η = 46. Therefore, if a 10% difference is required, there must be in the experiment at least 46 individuals. Similarly, if a 4% difference is expected, it will be necessary to have 287 individuals in the experiment in each pen. Witli growing stock, we have a very interesting condition. The results which are here given, I have worked from the data ob tained in Storrs' Bulletin No. 80. The coefficient of variability varied from 4.8 per cent at hatching time to '25 per cent at five weeks of age and then dropped to 21 per cent at six weeks of age. These results were computed from the weights in lots of (10) ten chicks because the individual weights per chick were not given in the bulletin. However, there was a sufficient number of individuals in each lot so that the results obtained were significant.
Downloaded from http://ps.oxfordjournals.org/ at Michigan State University on June 12, 2015
hundred (100) and one used three hundred and seventy-flve (375) chicks in each lot. Should there be a certain number of individuals in a lot ? Or should we just guess at the number and say ' ' well for this experiment we have a few chicks upon which we can experiment just as well as not and we Avill use what we have." Most assuredly we should have a sufficient number of individuals in each lot. The number of individuals in an experiment will depend entirely upon the amount of dilïerence one expects to get. For instance, if a ten per cent difference in egg production between two lots is to be measured, according to the pedigree records of our hens at State College for the year 1919-20, there will have to be at least 46 individuals in each pen. If a four per cent difference in egg production between two lots is claimed sufficient, there Λνϋΐ have to be at least 287 individuals in each lot to dem onstrate this difference. These results are found by the use of the following formulae recommended by Mitchell & Grindley. η = number of individuals necessary C == coefficient of variability c ^^ difference between lots expressed in per cent 1.849 X C V2 + 1/2 c^ 100 c _ r 1.849 X 26 V2 -f y2 a^V ^ Γ1.849 X 2.6 V2 + .00251='
180
POULTRY
SCIENCE
Downloaded from http://ps.oxfordjournals.org/ at Michigan State University on June 12, 2015
Probably 25 per cent is too low a coefficient of variability to use but nevertheless with this low coefficient if 4 per cent difference in weight is to be expected betAveen two flocks, the results will not be significant unless at least 262 individuals are used. There have been many poultry bulletins published which contain experimental data that show an increase of but four per cent In weight of growing stock between lots and onlj^ nine to fifty or one hundred chicks have been used in each lot. This kind of experimental work is of no use. If we can't carry on experiments thoroughly, let us omit them altogether. At any rate let us not publish the results. I have presented but a few examples where the results of the experiments did not Avarrant the conclusions which were drawn when the probable error Avas taken into consideration. Any one of you may apply these formulae to your own experimental data or to the experiments from other institutions provided you have the necessary individual data and I can assure you that many interesting facts will be brought to your attention. Some of you may wish to stop the publication of some bulletin now in the hands of the printer. In conclusion, let me plead that we as investigators, extension specialists and instructors insist that our future experiments be so organized that the conclusions drawn from them may be reasonably reliable. It is important first to haA^e a sufficient number of individuals in each lot, but it should also be borne in mind that a large lot of animals offers no excuse for poor selection. Second, it is important that these animals be uniform in so far as possible. They should be of the same age, breed and type and should have been before the experiment under similar conditions both as to feeding and environment. Third, the individuality and unequal conditions should be eliminated so far as possible. Fourth, the data should be subjected to mathematical study, by which we may ascertain the true meaning of the results of the experiment. If we neglect this important duty, our results and conclusions are bound to be attacked and we may discover that the conclusions drawn from a certain experiment can not stand the test.
August-September, 1923
No. 6
THE STANDARDIZATION OP POULTRY EXPERIMENTS H. C. K N A N D E L P e n n s y l v a n i a S t a t e College Downloaded from http://ps.oxfordjournals.org/ at Michigan State University on June 12, 2015
The subject of this paper was brought very forcibly to the writer's attention through a letter received from one of our poultry magazines of large circulation. To quote from the editor of this magazine: " W e would be very glad to be placed on the mailing list of the Pennsyh^ania State College Poultry Department. Bulletins issued by this department are conspicuous by their absence and we have often wondered why. We receive almost everything of this nature from nearby states but we get so little from Pennsylvania we have often wondered whether you were dead or only sleeping. Let's wake up for our mutual advantage. Give us all the material on poultry that comes out of Penn State and we will do our best to give it to our readers while it is yet news. " The writer's reply was as follows: " T o pick up any poultry magazine today, one is impressed with the great amount of material written primarily for what the writer can get out of it. This would-be-knowledge is disseminated to our rural population who do not have the time to investigate the facts or statements given. Too many of our Experiment Stations put out material on one year's test which is absolutely worth nothing to the poultry industry. The one year test on incubation, feeding, the use of electric lights, brooding or anything else connected with the poultry industry is of little practical value. Until our experiment stations and poultry magazines realize this and realize that this information should have at least several years of conscientious, thorough investigation behind it, we are doing a great injustice to the farmers and poultrymen. I am in thorough sympathy with all agricultural college work. It is how I make my living, etc."
174
POULTRY
SCIENCE
It is not until quite recently that mathematics has been employed in studying carefully the results of experiments. The formulas given later in this paper are those which are used by many of the mathematicians and biometrists of note today. It is by the use of these formulas that we are better able to study the
Downloaded from http://ps.oxfordjournals.org/ at Michigan State University on June 12, 2015
In reply to this letter, the editor wrote; " I had little idea when I made the comment about the absence of material from the Pennsylvania State College Poultry Department that it would lead you to give me so much time and such a very pleasant and satisfactory letter. You are absolutely right regarding the publication of much that might be better left out. This is probably due, in part, to the lack of real knowledge on the part of those editing our poultry journals or too high a regard on the part of these men for hasty opinions sent out from experiment stations. We hope the colleges Avill revise their methods and overcome their desire to rush into print knowledge that is ill founded and only partially substantiated. It is a pity that poultry journals are not endowed so that they could do and say what they felt best in such matters." Horace AtAvood in 1908 presented a paper to this association in which he said, ' ' Not only is the industry whose problems we are studying a large and important one but poultry husbandry as carried on at the present time, with its artificial methods and appliances is a development of recent years and there is behind this business no such accumulation of facts and experiences as in the ease of other branches of livestock industry that have been carried on for a much longer time." To quote further—"The problems which we may select for study are so numerous that there is some danger that we may spread our energies over too wide a range thus interfering with the quality of our work. The ideal is to concentrate effort on a few specific problems until final results are achieved and presented to the public." And finally he said : " L e t us be doubly careful and resist with all our power any pressure which may be brought to bear on us for quick results and when we do publish the results of an investigation let us be sure not only of the facts involved, but also that our interpretation of the facts is the most logical and consistent that can be given. Sometimes a set of facts resulting from an investigation can be explained in two or more ways. ' '
STANDARDIZATION
OF POULTRY
EXPERIMENTS
I'J^y
The results of experiments may be published giving the description of plants, animals, or other material used, how they were treated or fed, they may give all the conditions of the experiment and a statement of yields, increases in animals or plants, financial results and the like; yet according to one authority "while such a statement is in itself valuable and not void· of interest because it contains the description of a fact, so long as this fact is not connected with other facts its statement is not so much knowledge as the material for the future acquisition of knowledge." On this ground one cannot conclude that under similar conditions results will be obtained which resemble those of the first series of observations. It is impossible to produce exactly the same conditions and therefore it is necessary to have more repetitions. Hence it is important to express the results of several tests in the form of a mean or average. The mean annual eg^ production
Downloaded from http://ps.oxfordjournals.org/ at Michigan State University on June 12, 2015
results of our experiments in a true and fair light. According to Pearl, the ordinary methods of description fail when the attempt is made to deal with any group of individuals such as a population because they are fundamentally and necessarily incapable of giving a description of the group in terms of anything but the individuals which compose it. Lord Kelvin, the great physicist, has said, " I often say that when you can measure what you are speaking about and express it in numbers, you know something about it, but when you cannot measure it, when you cannot express it in numbers, your knowledge is of a meager and unsatisfactory kind. It may be the beginning of knowledge but you have scarcely in your thoughts advanced to the stage of science whatever the matter may be. ' ' Karl Pearson, who now occupies the Francis Galton Chair of Eugenics at the University of London has very well stated his views regarding the importance of statistical analysis. He says, "General theories of society are of no use, verbal discussions are of no use, philosophical reasoning is of no use. We need to observe, measure, record, to analyze by the methods of exact science before we can advance in our sociology, before we can aid our working classes to a true weight of the factors which make for or mar our national vigor. ' '
176
POULTRY
SCIENCE
P. E. M. = ± .6745 y
.D^
n(n-l)
Where 5D^ ^ the summation of the squares of differences between such individuals and the mean, and η = number of individuals. This can better be explained by using a concrete example. In Pennsylvania State College Bulletin 87 results are given of an experiment in which eggs from various breeds and varieties of fowls were weighed. These eggs were incubated and the chicks then weighed. One of the conclusions drawn was that the Light Brahmas laid a sinaller egg than the Black Minorca but the Light
Downloaded from http://ps.oxfordjournals.org/ at Michigan State University on June 12, 2015
is affected by differences in vitality, digestion, assimilation, and environmental factors with which one is dealing. Biometry is nothing more than a method of analysis. By the methods developed in this field we are much better able to study statistical material and to draAV more accurate conclusions as to the variation in the material used and the probable extent to which our treatments have influenced this variability. The biometrician 's usual means of studying variation are : 1. Probable error of the average or mean. 2. Probable error of the difference. 3. Standard deviation. 4. Coefficient of variability. The probable error is concerned with the fact that when a mean is determined this mean does not give the true value for all the possible individuals in the material under study but only for those observed. Due to variation, the mean of another group may be different. If 100 men are measured for height, a certain mean would be determined. If another 100 men be taken, another mean is found. Two groups give seldom the same average. The results therefore of a single experiment are often misleading. Hence the falsity of one-year experiments unless they have been perfqrmed with a very large number of in dividuals under various conditions. Practical recommendations should not be made to the farmer from the results of experiments conducted but one year. It is far better to make several tests before conclusions are published. The formula used in com puting the probable error of the mean is
STANDARDIZATION
OF POULTRY EXPERIMENTS
I77
The results of the steer feeding experiments carried on at State College and published in Bui. No. 64 of that Station show an average gain in 126 days in one lot of 267.7 pounds and in another lot a gain in the same length of time under different treatment was 247.7 pounds. The conclusions drawn were that the first lot was better by 20 pounds per steer. However, only 12 steers were used in each lot and the probable error was 11.5 pounds per steer. The difference is only 8 per cent and according to Wood and Stratton's formula 80 animals are needed to measure such a difference. Therefore the results are not significant and the difference in weight was not necessarily due to the different treatments which these lots received. An experiment was completed, so to speak, comparing the amount of edible meat on the dual purpose breeds with those of the Mediterraneans and Asiatics. This experiment was conducted at the Pennsylvania State, College and published in Bui. No. 87 of that station. The conclusions 4rawn from this experiment stated that the dual purpose breeds dressed out better than the egg or meat breeds and that the pullets among the Wyandottes and Rhode Island Reds dressed out better than the
Downloaded from http://ps.oxfordjournals.org/ at Michigan State University on June 12, 2015
Brahma chick was larger than that of the Black Minorca. Byapplying Bessel's formula, we find there is no significant difference and the conclusions drawn may not be entirely true. In other words the mean weight of the Light Brahma chicks was 39.7 grams, with a probable error of 1.1 grams. That is: the chances are even that the weight of a single chick would fall between 39.7 + 1.1 = 40.8 grams or 39.7 —1.1 = 38.6. The probable error of the difEerence is obtained by finding the difference between the mean of two lots which may be compared and extracting the square root of the sums of the probable errors squared. The difference then is divided by the probable error. The ratio of 3.8 to 1, which is equivalent to odds of 30 to 1, is considered quite significant. In the same bulletin the statement is made that eggs hatched better during the middle of April than they did the latter part of May. By applying Bessel's formula again, we find that there is no significant difference. The odds in this case are less than one to one and the conclusions drawn have no significance whatever.
POULTRY
178
SCIENCE
Egg Yield 7 5 - 89 90-104 105-119 120-134 135-149 150-164
Frequency 11 21 15 10 14 28
Egg Yield 165-179 180-194 195-209 210-224 225-239
Frequency 21 15 6 4 3
T O T A L . .148
In reviewing poultry experiments carried on by the many experiment stations, one is rather amused at the conclusions drawn from the number of individuals used. For instance, in the case of experimental work in feeding laying hens, or pullets, the number of individuals used varies from ten up to twenty, thirty and one hundred. In the case of growing stock, the range is just as striking. Some experiments have been carried on with nine chicks in each lot and with but one lot under each treatment. A bulletin was published giving these results. At other experiment stations twenty-five (25) chicks were used. Fifty (50) chicks were used by other stations while a few used one
Downloaded from http://ps.oxfordjournals.org/ at Michigan State University on June 12, 2015
cockerels, while among the Leghorns, Brahmas, and Cochins, the cockerels dressed out better. Applying Bessel's formula to these results, we find the difference in dressing percentage to be 4.5 ± 2.2. Therefore, in 100 trials the probable occurrence of a deviation as great or greater is 18 times, or the odds are 4.6 to 1. The standard deviation affords a basis of comparison of one variety with another or with itself at some future time. One standard deviation cannot always be compared directly Math another for two reasons. First, one mean may be very much larger than the other and second, the two may be of entirely different units. Therefore, an abstract expression is desired and is found in the term coefScient of variability which is expressed in per cent. In technical bulletins, it is important that the individual data be printed. For instance, in the case of feeding fowls for egg production, the number of eggs which each hen lays should be given. • This will allow another investigator to thoroughly analyze the data. In the case of 148 trapnested pedigreed pullets at the Pennsylvania State College during the year 1919-20, the mean production was 144.6 eggs per year. These birds were grouped as follows :
STANDARDIZATION
01' POULTRY EXPERIMENTS
^79
Τ
'^
L
100 e
J
L
10
J
Solving, η = 46. Therefore, if a 10% difference is required, there must be in the experiment at least 46 individuals. Similarly, if a 4% difference is expected, it will be necessary to have 287 individuals in the experiment in each pen. Witli growing stock, we have a very interesting condition. The results which are here given, I have worked from the data ob tained in Storrs' Bulletin No. 80. The coefficient of variability varied from 4.8 per cent at hatching time to '25 per cent at five weeks of age and then dropped to 21 per cent at six weeks of age. These results were computed from the weights in lots of (10) ten chicks because the individual weights per chick were not given in the bulletin. However, there was a sufficient number of individuals in each lot so that the results obtained were significant.
Downloaded from http://ps.oxfordjournals.org/ at Michigan State University on June 12, 2015
hundred (100) and one used three hundred and seventy-flve (375) chicks in each lot. Should there be a certain number of individuals in a lot ? Or should we just guess at the number and say ' ' well for this experiment we have a few chicks upon which we can experiment just as well as not and we Avill use what we have." Most assuredly we should have a sufficient number of individuals in each lot. The number of individuals in an experiment will depend entirely upon the amount of dilïerence one expects to get. For instance, if a ten per cent difference in egg production between two lots is to be measured, according to the pedigree records of our hens at State College for the year 1919-20, there will have to be at least 46 individuals in each pen. If a four per cent difference in egg production between two lots is claimed sufficient, there Λνϋΐ have to be at least 287 individuals in each lot to dem onstrate this difference. These results are found by the use of the following formulae recommended by Mitchell & Grindley. η = number of individuals necessary C == coefficient of variability c ^^ difference between lots expressed in per cent 1.849 X C V2 + 1/2 c^ 100 c _ r 1.849 X 26 V2 -f y2 a^V ^ Γ1.849 X 2.6 V2 + .00251='
180
POULTRY
SCIENCE
Downloaded from http://ps.oxfordjournals.org/ at Michigan State University on June 12, 2015
Probably 25 per cent is too low a coefficient of variability to use but nevertheless with this low coefficient if 4 per cent difference in weight is to be expected betAveen two flocks, the results will not be significant unless at least 262 individuals are used. There have been many poultry bulletins published which contain experimental data that show an increase of but four per cent In weight of growing stock between lots and onlj^ nine to fifty or one hundred chicks have been used in each lot. This kind of experimental work is of no use. If we can't carry on experiments thoroughly, let us omit them altogether. At any rate let us not publish the results. I have presented but a few examples where the results of the experiments did not Avarrant the conclusions which were drawn when the probable error Avas taken into consideration. Any one of you may apply these formulae to your own experimental data or to the experiments from other institutions provided you have the necessary individual data and I can assure you that many interesting facts will be brought to your attention. Some of you may wish to stop the publication of some bulletin now in the hands of the printer. In conclusion, let me plead that we as investigators, extension specialists and instructors insist that our future experiments be so organized that the conclusions drawn from them may be reasonably reliable. It is important first to haA^e a sufficient number of individuals in each lot, but it should also be borne in mind that a large lot of animals offers no excuse for poor selection. Second, it is important that these animals be uniform in so far as possible. They should be of the same age, breed and type and should have been before the experiment under similar conditions both as to feeding and environment. Third, the individuality and unequal conditions should be eliminated so far as possible. Fourth, the data should be subjected to mathematical study, by which we may ascertain the true meaning of the results of the experiment. If we neglect this important duty, our results and conclusions are bound to be attacked and we may discover that the conclusions drawn from a certain experiment can not stand the test.