OCCUPATIONAL WAGE SURVEY SIXTH ROUND 2008 REPORT ON TEN

ENGINEERING  INDUSTRIES

ANNEXURE-IV

SAMPLING DESIGN AND ESTIMATION PROCEDURE

1.0  SAMPLING DESIGN

1.1    INTRODUCTION

The sampling design for the Sixth Round of Occupational Wage Survey (OWS) consisted of two stages.  The first stage sampling units were the registered factories, while the second stage sampling units were the workers employed in different occupations in the first stage units. The sampling design also stipulated that the estimates should not differ from the true values by more than 5 percent with 95 percent probability.

1.2  SELECTION OF ESTABLISHMENTS (FIRST STAGE)

The first step in the selection of sample establishment was the determination of sample size.  It was found desirable to determine the sample size in such a way that the permissible error in the average maximum wage rate would be 5 percent with 95 percent confidence coefficient.  For the purpose of statistical exercise, average maximum wage rate was derived as weighted average of maximum wage rate of all the occupations in each of the sample units covered during the Fifth Round.  The weights were the number of workers employed in the different occupations in the sample units. The formula used for the determination of the sample size is given below.

                 å W_i.S²_i                          n_o

        n_o  = -------------------   and      n  = ----------

                 [0.05 . Ÿ / 1.96]²                  1 + n_o/N

where,

As the sample size yielded by the above formula related to stratified random sampling with proportional allocation, the share of each stratum was allocated in proportion to its share in the frame at all India level.

For this purpose, the frame in each stratum was divided into two size classes, viz. Upper Size Class and Lower Size Class. The average daily employment at the national level for an industry was used as the cut-off point for classifying the units in an industry into these classes.  All the units with employment above the cut-off point were taken in the upper size class while the remaining were taken in the lower size class in each stratum. While allocating the sample size in the both the size classes in proportion of its frame size within a stratum, it was taken care that at least two units were selected in each size class.

In order to draw the required number of sample units determined in accordance with the procedure described above, the frame units in each size class within a stratum were arranged in the alphabetical order of states and within each state in the descending order of employment.

The required number of sample units in each of the two size classes of a stratum was then drawn on the basis of simple random sampling without replacement. Provision for the selection of substitute units was also made so that the required sample size in each industry was obtained.

1.3  SELECTION OF WORKERS (SECOND STAGE)

For the purpose of obtaining reliable estimates in respect of the pay roll earnings of workers in each occupation, it was decided to draw a sample of workers belonging to each category of sexage and system of payment in proportion to the number of workers in each such categories in the total work force in an occupation.  For this purpose, the following sample size was adopted.

The number of workers required for the study was drawn from each occupation in each establishment on the basis of random sampling in such a way as to ensure that each category (by sex/age and system of payment) was represented in the sample in proportion to the respective strength in the total workforce of the occupation.

2.0    ESTIMATION PROCEDURE

The estimation procedure for the Survey was, designed to obtain estimates for all the three important characteristics, namely, employment, wage rates and earnings by occupations. The estimation procedure adopted for each of these characteristics is given below.

2.1  EMPLOYMENT

Estimation of the number of workers was done for each sex/age group and each category of workers by system of payment of wages in each occupation in a stratum of an industry. The corresponding multiplicative inverse of the sampling fraction in each employment size class of a stratum was used as the multiplier for the estimation. For instance, the number of time-rated male workers in an occupation in a stratum was estimated by using the following formula:

                 N_u           N₁

           É =  ---- . E_u  + ---- . E₁

                 n_u           n₁

where,

The estimated total number of time-rated male workers for the industry as a whole was obtained by adding the corresponding estimates for all the occupations in each of the two employment size classes.  Addition of the estimates at the employment size class level, gives the stratum levels estimate, while addition of stratum level estimates gives all India estimates.

2.2    WAGE RATES

The formula for the estimation of wage rate of time rated male workers in an occupation in a stratum is as under:

                W_{u .} Ê_u + W₁ . Ê₁

          Ŵ = -----------------

                    Ê_u + Ê₁ 

where,

The formula for deriving W_u and W₁ are as under:

              n                              n

              Σ W^u_j . E^u_j                      Σ W^l_j . E^l_j

              ^{j=1                             j=1}

        W_u = -----------       and     W₁ = -------------

              n                              n

              Σ E^u_j                            Σ E^l_j

              ^{j=1                             j=1}

where,

The estimated wage rate of workers at the stratum level combined for all the occupations was obtained as the weighted average of the estimated wage rates in different occupations in a stratum, the weights being the estimated employment of workers in each occupation in the stratum.  In symbols:

                      k

å                   Ŵ_o . Ê_o

^o=1

               W = ------------------

                     k

å                    Ê_o

^o=1 

where,

All-India estimates of the wage rates of workers were obtained as the weighted average of the corresponding stratum level estimates, weights being the estimated number of workers in each stratum.

2.3    PAY ROLL EARNINGS

On the basis of the data on pay roll earnings collected for the sample workers in each occupation in each sample unit, average daily earnings per day paid for were estimated for men, women, adolescents and children.  The formula for estimation of average daily earnings of workers in an occupation in a stratum is given below:

                Y_u . Ê_u  +  Y₁ . Ê₁

    Ŷ  =  --------------------

                Ê_u  + Ê₁

where,

The formula for deriving Y_u and Y₁ are as under:

            n                                 n

         Σ Y^u_j . E^u_j                        Σ Y^l_j . E^l_j

           ^{j=1                                 j=1}

     Y_u = -------------         and   Y_l = -------------

            n                                  n

            Σ  E^u_j                             Σ  E^l_j

            ^{j=1                                 j=1} 

where,

The stratum level estimates of average daily earnings of workers in each occupation is combined in proportion to their estimated employment in the occupation in each stratum so as to obtain the corresponding All India estimates for each occupation.

The estimated average daily earnings of workers in a stratum combined for all the occupations is obtained as a weighted average of the estimated average daily earnings in all the occupations, the weights being the estimated employment of workers in each occupation.

In symbol:

k

å                   Ŷ_o . Ê_o

^o=1

           Y   =   -----------------

                     k

å                    Ê_o

^o=1

where,

All-India estimates of average daily earnings of workers are obtained as the weighted average of the corresponding stratum level estimates, weights being the estimated number of workers in each stratum.

Average daily earnings of workers were separately estimated for basic wage, dearness allowance, house rent allowance, etc. These figures were estimated without any reference to either sexage or the system of payment. The procedure involved in the estimation of these figures was the same as that described earlier.

The distribution of workers by different groups of earnings, are also estimated without reference to either agesex or the system of payment of wages.  For this, in the first instance, the average daily earnings for each sample worker in each of the sample units, having the given occupation in an employment size class, in a stratum, in an industry, is calculated.  This is turn is obtained by dividing the total earnings of sample workers in each unit having the given occupation by the corresponding number of days paid for.  On the basis of these figures, the sample workers of a given occupation in each sample unit are distributed among the different (predetermined) size classes of earnings.  The number of sample workers in each earnings size classes is then expressed as a percentage of the total number of sample workers in the unit.  The percentage for each earnings size class is thus multiplied by the total number of sample workers in the occupation in the unit.  The products obtained thus for all the units in a size class of a stratum are then added and the sum divided by the total number of sample workers in the size class.  The quotient gives the estimated percentage of workers in the given occupation in each earnings size class at employment size class level. In symbol:

                         n

å                   E_kj . Y_kj

j=1

           Ŷ_k  =  -----------------------

                     n

å                    E_kj

j=1

where,

The stratum level estimates for a given earnings size class in a given occupation is obtained by taking the weighted average of the percentage of workers for the given earnings class in the upper and lower employment size group, weights being the estimated employment in the two size classes.  In order to obtain all India estimates for the given earnings size class in the given occupation, the stratum level estimates are combined in proportion to the estimated employment in each stratum in an industry.

The estimated percentage of the workers, combined for all the occupations, in a given earnings class at size class level is obtained by combining the percentage of the workers in the given earnings class in all the occupations in proportion to the total employment in each occupation. The stratum level estimate, combined for all the occupations, is obtained by adding the estimated percentage of workers at upper and lower employment size classes in proportion to the estimated employment in each size class.  All India estimates are obtained by further adding the stratum level estimates in proportion to the estimated employment in different strata.

2.4    COEFFICIENT OF VARIANCE OF AVERAGE DAILY EARNINGS

The coefficient of variance was calculated for each stratum in an industry after obtaining the estimates of mean square for the population S² and mean per unit of the population Ÿ separately for the stratum. The mean square for the population of a stratum in an industry was estimated by the sample mean square of the stratum, whereas, the mean per unit of the population of a stratum in an industry was estimated by the sample mean of the stratum. In symbol, the sample mean square and sample mean of average daily earnings in j^th stratum in the i^th industry are defined, respectively, by:

                      1      n_ij

           Ŝ²_ij  =  -------- . Σ (y_ijk - ŷ_ij)²

                   (n_ij -1)    ^k=1

and

                     1    n_ij

            ŷ_ij  =  ----- . Σ y_ijk

                     n_ij   ^k=1

where,

Sample mean square and sample mean of average daily earnings for an industry were calculated as the weighted average of sample mean squares and sample means respectively, of different strata in an industry, weights being the proportion of number of units in the frame in different strata in an industry. In symbol,

                              1          

                Ŝ²_i   =    ---------- . Σ (N_ij - 1) . Ŝ²_ij

                            (N_i - 1)    ^j=1

and

                             1 

ŷ_i    =    ----- . Σ N_ij . ŷ_ij

                             N_i    ^j=1

where,

Sample mean square and sample mean of average daily earnings combined for all the Plantations and Tea Processing Industries were also calculated as the weighted average of sample mean squares and sample means respectively, of different industries, weights being the proportion of number of units in the frame in different industries.

The coefficient of variance was calculated for each occupation in an industry using the same method described above.