No sqr!!! Your response should be (Editable(T|F), weight, color, ..) product.

Hi,

Variance always should be positive, I thing there is some thing wrong, could you show us the data and recheck it again

Hi Liz,

I agree with Hazhar because it is a sum of squares. Show us only one variable.

Regards

Variance can never be negative. Since genetic variance has been obtained negative, it is certain that some error has been committed either in selecting / applying the formula(s) correctly or in the computational steps.

Thorough verification is required in detecting the error(s) committed.

"mean squares of the analysis of variance" is already a variance. We can further discuss if you could provide which formula you are using for calculating genetic variance.

Thanks everyone for your help. The formula I´m using to calculate the genetic variance is Vg= (mean square of genotypes - mean square of genotypes x environment) / (number of environments x number of replications).

Thanks

Numerator of this formula is actually difference of two variances which can be negative. I think, we need to interpret the negative value of this formula. In this regards, some peer in the field of genetics can help. It is not the issue of negative variance.

Negative genetic variance could be due to sampling error and lack of non-random mating and are replaced by Zero during computing. The true values are small positive quantities (Comstock and Robinson, 1948).

@ John Charles Aru, I don't agree that the genetic variance could be negative due to sampling error and lack of non-random mating and are replaced by Zero during computing.

I already mentioned that variance can never be negative. Since genetic variance has been obtained negative, it is certain that some error has been committed either in selecting / applying the formula(s) correctly or in the computational steps. Therefore, thorough verification is required in detecting the error(s) committed whether in applying the formula or in computations.

@ Hafiz Arshad,

Numerator of this formula is the difference between two variances, however, it is the subtraction of a smaller variance from a larger variance. Hence, it can't be negative. I am sure that some error has been committed either in selecting / applying the formula(s) correctly or in the computational steps.

Dhritikesh Chakrabarty genetic variance is possible to negative due to many factors such sampling error, miscalculating, or the reality of the population itself. Based on Johnson et al., 1955 and Singh & Chaudhary, 1979 formula in calculating the value of genetic variance, it is obviously possible to be negative which is caused by the higher value of error variance than the treatment or genotype variance tested. Ms Liz Katherine Lagos santander , I recommend to refer to this article below. I am suffering the same problem as that of you.Article Probabilities of negative estimates of genetic variances

This extract from a paper I wrote with Atam Vetta on Demographic behaviour and genetic behaviour in 2003 may explain why you can find negative estimates for variances, which are not acceptable. You can get the whole paper in my ResearchGate website.

For a population mating at random Fisher (1918) found the genetic sib covariance and genetic parent-child covariance which in modern terminology are written as:

Cov (sibs) = 0.5 Var A + 0.25 Var D

and

Cov (parent-offspring) = 0.5 Var A.

Note that:

Cov (sibs) > genetic Cov (parent-offspring).

Fisher (1918) did not consider monozygotic (MZ) twins and did not find their covariance. As all of their genes are common,

Cov (MZ) = Var A + Var D.

In setting up these equations we ignored the contribution of environment. Assuming random environment, the phenotypic covariance between MZ twins reared together will be:

Cov (MZ) = Var A + Var D + Var Ce

where Var Ce is the variance due to common environment. It is not necessary to use covariances and sometimes a correlation matrix is used. Thus, a behaviour geneticist collects data, calculates covariances (correlations), equates them to theoretical correlations and solves these equations to find estimates of parameters like Var A and Var D. The amount of genetics used is minimal.

There is, however, a mathematical restriction on the number of equations required if a unique solution is to be found. This restriction is that the number of equations must equal the number of parameters to be estimated. This is known as the minimal set. In the absence of a minimal set, a unique solution is not possible. If estimates of only three parameters e.g. Var A, Var D, and Var Ce are required, a minimal set of three equations is needed. This set could have the format:

Cov (MZa) (phenotypic covariance between monozygotic twins reared apart) = Var A + Var D

Cov (DZt) (phenotypic covariance between dizygotic twins reared together) = 0.5Var A + 0.25Var D + Var Ce

and

Cov (Dza) (phenotypic covaraince between dizygotic twins reared apart) = 0.5Var A + 0.25Var D.

Given these three phenotypic covariances, unique values of the parameters can be found. As we are using correlations and not covariances, the values of the parameters will, in fact, be proportions of the phenotypic variance. Please note that behaviour geneticists use a statistical package, mostly LISREL, for model fitting.

For a trait, the mathematical uniqueness of the solution refers only to the set of equations used and has no other significance. Capron et. al. (1999) emphasise this point by estimating the values of behaviour genetic parameters using correlations used by Jinks & Fulker (1970) in two different minimal sets of three equations. Their sets had two common equations but differed in the third. One of the sets gave Var D = - 0.22. A negative value for a proportion of the variance is not acceptable The estimates of parameters obtained from fitting a behaviour genetic model should, therefore, be treated with caution as the results obtained using a different covariance or correlation matrices are likely to be different. It is not generally realised that an acceptable solution to a minimal set is available when numerical value of correlations differ and that the source of these correlations is immaterial.

@ Faizal Rezha Zulkarnain ,

The concept as well as the definition/formulation of variance is such that it can not be negative. This is the basic principle behind the the measure namely "variance" of dispersion of data.

However, estimate of variance, based on data from sample, may rarely be found to be negative in some situation and it is so due to some serious error or errors.

But, this does not mean that the corresponding population variance for which estimate is computed is negative.

In order to be more clear it is to be noted that there are two concepts on variance. One is population variance and the other is sample variance. sample variance is nothing but estimate of population variance. Population variance can never be negative. On the other hand, sample variance can usually not be negative but in some rare case, the computed value of sample variance may be found to be negative which is due to some serious error or errors.

When using random random parents, there can be cases of negative variance