If a population from which a sample is to be drawn does notconstitute a homogeneous group, stratified sampling technique is generally applied in order to obtain a representative sample.

In this sampling, the population is divided into several sub-populations, i.e. more homogeneous than total population called **strata**. Then sample items are selected from each stratum. If the items selected from each stratum is based on simple random sampling. The entire procedure first stratification and then simple random sampling, is known asstratified random sampling.

### Criteria of stratification of forest area

- Topographic features
- Forest types
- Density classes
- Volume classes
- Height classes
- Age classes
- Site Classes, etc

### Merits

- More representatives than systematic and simple random
- Greater accuracy than simple random
- Administrative convenience

### Demerits

- More time and cost due to wide geographical area
- Sampling units for each stratum is necessary
- Require more prior information about population

### When to use

- When populations are heterogeneous
- If the sampling problems differ in various sections of the population

Assuming that a total of 150 sample units will be measured on the ground, there are two common procedures for distributing the field plots among the five volume classes. These methods are known as **proportional allocation** and **optimum allocation**.

Volume Class |
Stratum area, acres |
Std.dev., cords/acre |
Area×std. dev. |
---|---|---|---|

I | 15 | 20 | 300 |

II | 45 | 70 | 3150 |

III | 110 | 35 | 3850 |

IV | 60 | 45 | 2700 |

V | 70 | 25 | 1750 |

Total |
300 |
- |
11,750 |

### a. Proportional allocation of field plots

The sizes of the samples from the different strata are kept proportional to the sizes of the strata, which are mostly used. The more the size of strata, the more the sample plots. Suppose, if strata are of 4500 m^{2} and 3000 m^{2 }with a plot size of 30 m^{2} of a population of 8000. Then the former has more plots than the later.

This approach calls for distribution of the 150 field plots in proportion to the area of each type. The general formula is

*nh *=* *(*Nh/N*) * n

To compute no. of plots, for example; Class I: 15/300 ×150 = 7 plots

One disadvantage of proportional allocation is that large areas receive more sample plots than small ones, irrespective of variation in volume per acre. Of course, the same limitation applies to simple random and systematic sampling. Nevertheless, when the various strata can be reliably recognized and their areas determined, proportional allocation will generally be superior to a non-stratified sample of the same intensity.

### b. Optimum allocation of field plots

When the cost of selecting an item is equal for each stratum, there is no difference in within-stratum variances, and the purpose of sampling happens to be to estimate the population value of some characteristics. In case, the purpose happens to be to compare the differences among strata, then equal sample selection from each stratum would be more efficient even if strata differ in sizes. In cases, where strata differ not only in size but also invariability and it is considered reasonable to take larger samples from the more variable strata and smaller samples from the less variable strata. With this procedure, the 150 sample plots are allocated to the various strata by a plan that results in the smallest standard error possible with a fixed number of observatios. Determining the number of plots to be assigned to each stratum requires first a product of the area and standard deviation for each type, as derived earlier.

In general terms, for a sample of size *n*, the number of observations *n _{h}* to be made in stratum

*h*is:

The number of plots to be allocated to each stratum is computed by expressing each product of “area time’s standard deviation” as a proportion of the product sum, eg. 11,750. Thus, the 150 field plots would be distributed in the following manner:

Class I: 300/11,750 ×150 = 4 plots