1. To study the variability (CV%) of mango crop experiments conducted at South Gujarat region
2. To develop yardstick of CV% for accepting or rejecting the results of the filed experiments of Mango crop at South Gujarat region

The secondary data on yield of 158 mango experiments collected from Regional Horticulture Research Stattion and Agriculture Experimental Station, paria of last 15 years. These data were utilized for the variability study and for develop yardstick of CV% for accepting or rejecting the results of the filed experiments of mango crop at South Gujarat region. Information on design of experiment, number of treatments, replication, SEm± and CD, plot size and CV% were subjected to statistical analysis. CV is a ratio of standard deviation (σ) and general mean (X) and formula is as below:

CV = σX     .....(1)

The distribution of X and σ have simple forms and student’s t-distribution provides complete solution for testing the hypothesis or estimating fiducial limits relating to either X or σ, singly,  But t distribution cannot be used for CV = σX . Instead of this, non-central t-distribution providing fiducial limits of CV.

Let z be a quantity distributed normally about zero mean with unit standard deviation and let w be a quantity distributed independently as χ2 with degrees of freedom of χ2. Then, t is defined by the following equation:

t = Z+ δW     …..(2)

Where, δ is some constant, then t is distributed in a manner depending only on δ and f.

This is a non-central t distribution. When δ equals to zero, the distribution is the familiar to Student’s t-distribution.

Let an estimate of sample coefficient of variation V

v =s/

Now one may write,

nv = nXS =n(X-µ)σ + nµσ +Sσ       .....(3)

It appears from comparison with eq. (2) that n/V is distributed as non-central t with f=(n–1) and σn/V. This distribution can be used for test of significance and for providing fiducial limits of V (i.e. CV), as is done for µ.

Since the objective was to work out the yardstick based on CV, the upper fiducial limit of CV using non-central t-distribution was estimated following the procedure given by Johnson and Welch (1939). The procedure is as below:

1. CV = Error Means SquareGeneral Mean

Now the upper fiducial limit of CV is:

CVUL = nδ (f, t0, ε)   where, t0 = nCV

1. y = (1+ t022f)-1/2                 or

y’ = t02f (1+ t022f)-1/2

Consider Y and Y’according to value of t0/2f is greater than or less than 0.75.

Consider Y’, if t0/2f lies s between – 0.75 and 0.75, otherwise consider Y.

1. If f > 9, calculate
2. Select desired probability level of confidence, i.e. ε and obtain λ (f, to, ε) from the table in (Johnson and Welch, 1939) interpolating with respect to the quantities obtained in (ii) and (iii).
3. Calculate δ (f, to, ε) = t0- λ (1+ t022f)-1/2