1

Critical Review of Sampling ModesCritical Review of Sampling Modes

Sampling is a selecting process, but there are two categories of selecting processes.

The Probabilistic Selecting Process

For sampling to be accurate, all constituents of the lot are submitted to the selection process with a given, constant probability of being selected:

Sampling must be equiprobabilistic.

Non-Probabilistic Selecting Processes

• Deterministic

• Purposive

• Authoritative

2

Review of Non-Probabilistic Selecting Processes

Review of Non-Probabilistic Selecting Processes

There is no theoretical approach to non-probabilistic selecting processes.

Sampling errors are usually large enough to deprive the samples of any practical value.

Such methods are dangerous and it is astounding to note that they are in use where they can be most detrimental:

• Commercial Sampling

• Mining evaluations

• Process control

• Ore grade control

• Pilot plants

• Environmental assessments

Some standard organizations still mention and recommend these misleading, unacceptable methods.

3

Deterministic Sampling: Grab Sampling

The idea is: “Catch whatever you can, as long as it does not cost money.”

There is no over management misconception that will generate as severe, invisible costs.

In this case, the operator is collecting some material from the part of the lot that is easily accessible with:

• scoops,

• shovels,

• hands,

• coffee cans,…

Aware of segregation problems, perhaps, the operator tries to collect as many increments as practically possible. Nevertheless, a large fraction of the lot is systematically kept away from the sampling tool:

• bottom of a truck, or railroad car, or drum,

• center of a conveyor belt,

• center of a stockpile,…

Conclusion: Grab sampling cannot be accurate becausesome units making up the lot have a zero probability of beingselected, and because the selecting probability between unitscannot be maintained constant.

4

Purposive Sampling

If parts of the lot are not easily reachable, the operator may select units the best way he can, among those that are easily accessible. When doing so he may use his judgment to select some parts rather than others.

The accuracy of the sampling operation depends on the operator’s choice.

This kind of sampling is valid only if the objective is to collect specimens.

Purposive Sampling cannot be accurate, nor equitable.

5

Authoritative Sampling

Probability Sampling is contrasted with Authoritative Sampling, in which an individual who is well acquainted with the lot to be sampled selects a sample without regard to randomization.

The validity of data gathered in this manner is totally dependent on the knowledge of the operator. It is not a recommended practice.

However, Authoritative Sampling is often necessary for environmental assessments, in order to separate hot sectorsfrom others in a contaminated area. Then, each sector must be submitted to probabilistic sampling, of course.

6

Common Properties of Non-Probabilistic Selecting Processes

• An important fraction of the lot is submitted to the sampling process with a zero probability of being selected. Therefore, it cannot equitable.

• There is no possible Theoretical approach. Therefore, it is impossible to logically connect the various sampling errors to the Mode of Selection.

• Sampling is always biased to an unknown extent.

Conclusion: No specimen generated by a non-probabilistic selecting process should be used to reach important financial decisions.

Sampling is not gambling.

“I have little patience with scientists who take a board of wood, look for its thinnest part, and drill a great number of holes where drilling is easy.”

Albert Einstein

7

Probabilistic Sampling of Movable Lots

A batch of material is said to be “movable” when it is small or valuable enough to be economically handled in totality for the sole purpose of its sampling.

Example: All zero-dimensional samples that must be subsampled at the laboratory.

Two probabilistic processes can be used:

1. The increment process:

The batch of material is transformed into a one-dimensional stream, then a cross-stream sampler collects a certain number of increments to make up the sample.

2. The splitting process:

The batch of material is partitioned into several fractions, one of which is selected at random as a sample.

8

Probabilistic Samplingof Unmovable Lots

The only probabilistic sampling process applicable to unmovable lots is the “Increment Sampling Process”.

Then, the lot is represented by a set of increments extracted from the lot according to a certain “Selection Mode” and by means of a certain extracting device.

In practice:

• The probabilistic sampling of three-dimensional lots is impossible: Such a protocol cannot be defensible. The only solution is to transform the three-dimensional lot into a logical sum of two-dimensional lots. This is exactly what we do when we drill a mineral deposit.

• The probabilistic sampling of two-dimensional lots is difficult. It can be done if each sample is a drilled core representing the entire thickness of the lot.

• The probabilistic sampling of one-dimensional lots is relatively easy, and always possible.

9

Review of the VariousSampling Selection Modes

From a theoretical standpoint, we can classify the various Sampling Selection Modes as follows:

Systematic Sampling:

• Simple Systematic

• Random Systematic

Stratified Random Sampling:

• Simple Stratified Random

• Authoritative Stratified Random

Strict Random Sampling

From a practical standpoint, some of these Sampling Selection Modes should be rejected because they never provide a better alternative to the others. Therefore, we shall concentrate our attention on the 3 following Sampling Selection Modes:

• Random Systematic

• Simple Stratified Random

• Authoritative Stratified Random

10

Sampling Selection ModesFor Two-Dimensional Lots

Definitions:

Area: It is the entire starting lot. Its surface and contour are dictated by local conditions. For example:

• A contaminated area

• A copper cathode

Sector: It is a fraction of the area. Its size can be the object of recommendations by statisticians, or rules by local regulatory commissions.

1 2 3

4 5 6

7 8 9

Copper cathode

Area

Sector

1 2 3

4 5 6

7 8 9

Hot sector: Authoritative

Contaminated area

11

Sampling a Contaminated Area

1 2 3

45 6

7 8 9

Stratum Substratum

12

Sampling a Copper cathode

Stratum

Punch: Sample increment

13

Sampling a Copper Cathode:Random Systematic

14

Sampling a Copper Cathode:Stratified Random

15

Sampling Selection ModesFor One-dimensional Lots

Random Systematic Mode

The Random Systematic Mode is by far the most popular selection mode. It is also the most reproducible.

If we suspect the presence of cycles, this sampling mode must be avoided.

Systematic selection may be regarded as probabilistic, and as defensible, only if the starting point is positioned at random within the first stratum.

16

Stratified Random Mode

The Stratified Random Mode is not well known, but by far the most accurate in the presence of cycles.

StratumSubstratum

Cross-stream increment