Weighting

5.1 Estimation Procedure (General Underlying Estimation Concepts)

For any survey, estimates for total of a variable is computed using the general equation:

^ n

X = ?wixi ,where w is the weight of each ultimate sampling unit, x is the

I=1 observation, and n is the number of samples.

The general equation used to compute the total of any variable x in the 2007 Census of Agriculture is given below:

^ n m n

X = ?? (N/n)[Hproj/(?(N/n)Mi)](Mi'/mi')(mi'/mi)xij eq. (1)

I=1 j=1 i=1

Where:

^

X - the estimated total for variable x

N - total number of EAs in the stratum, i.e., group of islands

n - number of sample EAs in the stratum

Mi - total number of households in EA i from 2006 listing of households (frame)

Mi' - total number of households engaged in agriculture in EA i

mi' - total number of households listed in listing form (with 10 or more trees,

etc.) in EA i.

mi - total number of sample households in EA i.

Hproj - projected number of households in the stratum (see section for the

estimation of projected households)

The weight of each household or questionnaire in sample EA i is:

wi = (N/ni)[Hproj/(?(N/ni)Mi)](Mi'/mi')(mi'/mi) eq. (2)

5.2 Derivation of the Weights used in this Survey

Since the enumeration procedure is to list all households in each target EA - target EA means all EAs in small island group, 1/3 of all EAs in medium and large island groups, the weight should be:

wi = (N/n)(Mi/mi)[Hproj/(?(N/n)(Mi/mi)Mi)] eq. (3)

Where N/n is the inverse of the probability that the EA would be selected and M/m is the inverse of the probability that the household would be selected. But since Mi = mi, then these two numbers cancel each other out hence the equation can be written as:

wi = (N/n)[Hproj/(?(N/n)Mi)] eq. (4)

The equation term Hproj/(?(N/n)Mi is the adjustment factor due to non-coverage or adjustment to the projected number of households in the stratum. This factor can be excluded if the variability in the size of all EAs is low, but for the sampling design employed in this survey, the factor cannot be removed because the resulting estimate of the number of households without the adjustment factor is much less compared to the 2006 census of agriculture. This is due to high variability in the size of sample EAs in each stratum.

For Small Island Group, all EAs were enumerated, i.e., N = n, hence the equation could be reduced to just the adjustment factor.

wi = Hproj/(?Mi) è Hproj / M, where M is the total number of households in

the Stratum.

This adjustment factor should no longer be needed for this stratum had the listing and enumeration been done correctly. Even though the instruction is to list all households, i.e., each household must have Form 1 or listing form, the actual procedure done was that, only those households engaged in agriculture with 10 or more trees and/or with cattle were listed. Hence, there is no way that the total number of households could be known in this stratum. This is the reason for including the adjustment factor in the weight of the households in this stratum. Another adjustment factor is added in the weight due to reason that will be discussed in the succeeding paragraph, i.e., weights of Medium Island Group. The actual weight used for small island group is:

wi = (Hproj / M) (Mi'/mi')

Note that this is just a special case of equation (2) where N = n, and mi' = mi.

In case of Medium Island Group where all households in sample EAs were supposedly listed, the weight should be the same as equation (4) had all households in the EA have their respective questionnaire. Unfortunately, after analyzing the frequency distribution of households by sample EAs, the numbers were found to be much less than the counts of household in the 2006 Census of Agriculture or the 2006 Listing of Households. The reason is that only those households with 10 trees or more and, etc. were enumerated. When equation (4) was applied to generate the total number of households, the result gives only approximately 60% of the projected number of households. The reason is that the resulting count is the number of households with 10 trees or more and, etc. and not the total number of households in the stratum. These figures would definitely be very difficult to explain to data users - considering that this is supposed to be a census of all households and not a census of those with 10 trees or more … To solve the problem, another adjustment factor is included in the weight, that is, M'/m' where M' is the total number of households engaged in agriculture from the 2006 listing of households and m' is the number of households with 10 trees or more and etc. In layman terms, the total number of households found to be engaged in agriculture in 2006 listing of households in the EA is distributed proportionately to each questionnaire in the file. The effect of this technique is higher estimates since those households engaged with less than 10 trees, etc. (that is, households excluded in the frame) have been included in the estimation. The weight used for medium island group is:

wi = (N/n)[Hproj/(?(N/n)Mi)] (Mi'/mi') eq. (5)

Note that this is a special case of equation (2) where mi' = mi.

Estimation procedure for Large Island Group used weight similar to the above equation but another factor is included. The adjustment factor is mi' / m, where m is the number of sample households. Since mi' will cancel out, the simplified equation is given below:

wi = (N/n)[Hproj/(?(N/n)Mi)] (Mi'/mi) eq. (6)

The weight derived using the above equation (equation 6) is attached to all sample households only while weight derived using equation (5) is attached to all questionnaires (set of forms or cases) in the file. As mentioned above, sample households are those questionnaires with household form, i.e., all questionnaires in small and medium island groups and sample household questionnaires in large island group. The data item name of sample household weight is SWEIGHT, while all forms weight is DWEIGHT. Hence DWEIGHT is computed using equation (5) while equation (6) is used to compute SWEIGHT.

5.3 Using the Weights

As described above, SWEIGHT should be applied to all households (questionnaires) with household forms. In addition, this should be applied when generating totals for Kava and Coconut sub-holdings characteristics.

On the other hand, DWEIGHT should be used when tabulating Cocoa, Vanilla, Pepper, and Cattle sub-holdings characteristics.

Note that when cross tabulation is to be done for variables from these two different weighting groups (mixed), the sample weight SWEIGHT should be used.

5.4 Computation of the projected number of households

As described in the previous section, the number of households as of the first day of the enumeration (1st day of August, 2007) is needed in the weighting procedure. The practice in other countries is that official population projection is used, but since Vanuatu does not have this projection, and since required data are not available to be able to generate the population projection using internationally accepted procedure, an estimate was generated. The procedure for the estimation of the number of households is enumerated below.

1. Projected total population in the country for August, 2007 was computed using the growth rate between the last census of population conducted in November, 1999 and the listing of households which was conducted in May, 2006. The growth rate is 2.63 percent.

2. The total population counts for Urban and Rural areas were estimated using ratio and proportion, which resulted to 52,366 and 176,458 respectively. The main rationale for these prorated estimates is that it is more accurate to use the growth rate for the total population compared to estimates based on individual (i.e., provincial) growth rates.

3. Using the same rationale above, these estimates were distributed to their respective provincial areas using ratio and proportion.

4. The number of households in each province (urban/rural) was computed by dividing the population estimate with the average household size. The household size used is the one generated from the census of agriculture where the weights used is the basic weight, i.e., N/n*M/m. The rationale for using the average household size from the survey is that, when compared to the household size from the 1996 listing of households, it was found out that the figures are very different. If the average household size from 1996 listing of households would be used, the result to the weighted (final) population count would be unpredictable. Other reasons are: a) the sample is large enough to provide statistically accurate means and percentages, b) the definition of household membership used in the 1996 listing of households is not the same as in the 2007 census.

5. These numbers of households in all provinces (Urban / Rural) were added to come up with the final estimates for the total number of households in urban and rural areas in Vanuatu.

6. The final estimate for the number of households in each province was computed by prorating the final estimate for Vanuatu into all provinces using ratio and proportion.

7. In the same manner, the projected number of households in each stratum, i.e., small-island, medium-island, and large-island groups, was computed using ratio and proportion.