TESTING ACROSS SAMPLES

In document Labor absorption in agriculture : case study of Pakistan Punjab (Page 143-153)

In order to decide whether or not different time periods or farm categories should be pooled for regression analysis, variance-covariance analysis could be used. In the main text (chapter3, section 6) the example of two farm categories is discussed. Here its generalised form will be used for 'N' time periods or farm categories and 'M' number of explanatory variables^.

1 See Maddala 1977, p. 322-3; Rao and Miller 1971, and Koutsoyianis 1977, p.402-8.

In this test actually 'N' number of regression equations each with (M + 1) parameters are compared against a pooled regression equation. For 'N' farm categories (or years) and 'M' number of explanatory variables the following hypothesis can be tested:

: H is not true

In order to test H 0 , 'F' statistic is calculated using the following formula:

£

RSS2' ) / ( KN - K ) F = ---

Where:

R S S p

R S S t

N K

= Regression sum of square for pooled data

= Regression sum of square for the ith farm category or year

= Number of farm categories = M + 1

T £ = Sample size in ith farm category or year

If calculated 'F' is greater than tabulated 'F ' at 1 or 5 per cent probability level for (KN-K) and ( T^- - KN ) degrees of freedom then the null hypothesis is rejected and the regressions are not the same.

In the following table calculated *F' significance are given for time series and

values and their levels farm categories.

TABLE IV.1

'F' VALUES FOR YEARS, CROP ZONES, AND TENURES ( 1966-72 DATA ) Items Total Labor Family labor Casual Labor Permanent Hired Labor Years 0.11 0.31 0. 1 1.34 Crop Zones 1.04 0 1.51 Tenures 0.49 1.61 1 . 19 Note :

'F' value significant at 5 per cent probability level 'F' value significant at 1 per cent probability level

TABLE IV.2

'F' VALUES FOR CROP ZONES, TENURES, AND FARM SIZES ( 1981-82 DATA ) Total Labor Family Labor Casual Permanent Labor Hired Labor Crop Zones 4.82** Tenures 2.18** Farm Sizes 3.22** 4.86** 80.52** 1.53 6.10** 1.99* 3.69** 5.50** 7.78** 1.58 Note

'F' value significant at 5 per cent probability level 'F' value significant at 1 per cent probability level

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