animal genetics and breeding AGB-Unit-I.pptx

animal genetics and breeding

1. ANIMAL GENETICS & BREEDING UNIT – I Principles of Animal & Population Genetics Lecture – 2 Standard Error & Coefficient of Variation % Dr K G Mandal Department of Animal Genetics & Breeding Bihar Veterinary College, Patna Bihar Animal Sciences University, Patna

2. Standard Error Standard Error: It is the ratio of Standard Deviation (SD) and the square root of total number of observation. It is also called as the S.D. of the mean. The standard error (S.E.) together with mean (X ± SE) describes the true mean of the population. SE tells about the reliability of the mean of that sample from which it was estimated. The SE of the mean is a measure of spread of the means estimated from a number of samples drawn from a large population.

3. It is logical to think over reliability of the sample mean as a true representative of the population mean. However, the reliability of the mean depends on: i ) amount of variation in the population & ii) sample size i.e., no. of observations taken The sample mean has a certain error depending upon the : i ) no. of individuals included in a sample & ii) sampling procedure

4. If the entire population is divided into a large number of samples with N number of observation per sample and standard deviation, 6, then mean of the population is obtained with its standard deviation 6/√N. This expression is a measure of error with which a sample estimates the population mean. This is called the standard error of the mean or simply standard error and it is given with the mean value. As for example, (X ± SE).

5. The standard error is thus obtained by dividing the 6 (SD) of the distribution by square root of the number of observation in the sample. Hence, SE = SD = + variance Variance = [∑x 2 – (∑x) 2 / N] / (N – 1)  

6. Use of Standard Error: 1. To measure the precision of sample statistic i.e., the sample mean. Higher the standard error lower is the precision of statistic. It indicates that the data are not consistent. 2. The S.E. indicates the reliability of the mean . However, the reliability of the mean depends on the sample size.

7. 3. To fix confidence limit for the population parameters. 95% confidence limit: Mean ± 1.96 SE should include 95% of the means. Lower limit = mean – 1.96 SE of mean Upper limit = mean + 1.96 SE of mean It means that if a large number of samples are drawn from a population , about 95% of them will have a value in the range between the sample mean ± 1.96 SE of mean .

8. 99% confidence limit: Mean ± 2.58 SE should include 99% of the means. Lower limit = mean – 2.58 SE of mean Upper limit = mean + 2.58 SE of mean It means that if a large number of samples are drawn from a population, about 99% of them will have a value in the range between the sample mean ± 2.58 SE of mean . Example: at 95% confidence limit Mean body wt. of chicken at 12 weeks 1500 ± 50g Lower limit 1500 – 1.96x50 = 1402g Upper limit 1500 + 1.96x50 = 1598g

9. 4. To determine the size of the sample required to achieve the desired precision. 5. To compute test of significance for significant difference between two means . The standard errors of two independent means can be used to determine the test of significance of the difference between the two means. If the difference between the two means is about twice than the SD or SE of difference, it is then taken as a significant difference between the two means at 5% level of probability.

10. Coefficient of Variation Percentage Coefficient of variation (CV): It is the ratio of standard deviation (SD) to the mean. It is always expressed in percentage (%). CV% = x 100 % & SD = + variance If in a particular group the CV % is less, then it is suggestive that the data are more consistent and reliable. The concept of CV% was given by Karl Pearson.  

11. Merit of CV% Independent of unit i.e., no unit but expressed in % Used to compare the variability of two or more than two sets of data Used to compare the variability when different sets of data have different units. Based on each and every item of the of the set of data. Less affected by sampling fluctuation.

12. THANK YOU