Random Sampling

Select observations from a finite collection with or without replacement. Connect replacement to repeated selections, validate non-uniform probabilities, and choose a sample size that is possible under the stated rule.

Sampling selects some observations from a defined collection. The collection available for selection is the population, and the selected observations form the sample.

For example, a program may select four record identifiers from eight available identifiers:

Before interpreting the result, state the population, requested sample size, replacement rule, and selection probabilities. These choices define what samples are possible.

Sample with replacement

By default, rng.choice samples with replacement:

sample = rng.choice(record_ids, size=4, replace=True)

After each draw, the selected population item remains available for another draw. The same identifier can therefore appear more than once:

[104, 101, 104, 107]

This is not an error. The two occurrences of 104 represent two selections of the same population item.

With replacement, the requested sample may be larger than the population:

Only two outcomes are available, but either can be selected repeatedly.

Sample without replacement

Set replace=False when one population position may be selected at most once:

sample = rng.choice(record_ids, size=4, replace=False)

The selected identifiers are distinct because every value in record_ids is distinct. The requested sample size cannot exceed the population size:

rng.choice(record_ids, size=9, replace=False)

This call cannot select nine different positions from a population of eight, so NumPy raises an error.

Without replacement prevents repeated positions, not necessarily repeated values. Consider:

scores = np.array([8, 8, 9, 10])

Two different population positions contain the value 8. A sample without replacement can contain both values because the selected positions are different.

Use indexes when identity matters

Sampling values can hide which population positions were selected. When rows have an identity or several arrays must remain aligned, sample indexes:

One shared index array preserves each name–score pair. The next lesson applies the same principle when shuffling and splitting entire datasets.

Assign non-uniform probabilities

Without a p argument, each population position is equally likely at a draw. Pass one probability per population position when the selection rule is different:

The probability array must satisfy three basic conditions:

probability.shape == (population size,)
every probability >= 0
probability.sum() == 1, within floating-point tolerance

Each probability belongs to the population item at the same position:

If the labels are reordered without reordering the probabilities, the program implements a different sampling rule even though both arrays still have valid shapes.

Use np.isclose for a floating-point sum check:

Inspect one sample without overinterpreting it

Run the demonstration and change the seed or number of draws.

A probability of 0.70 does not guarantee exactly 21 occurrences in a sample of 30. It defines the probability at each draw. Finite sample counts vary. A larger number of draws often produces proportions closer to the specified probabilities, but any one sample still contains random variation.

Keep the output shape explicit

As with other generator methods, size determines the output shape:

batch_sample = rng.choice(record_ids, size=(2, 3), replace=True)

The result has shape (2, 3) and contains six selections. For sampling without replacement, those six selected population positions must be distinct across the complete output.

Before using a sample, useful checks include:

The unique-value count must be interpreted with the population. It proves that the sampled values are distinct only when population values are themselves distinct.

State what the sample can represent

Random selection removes one source of deliberate choice, but it does not automatically make a sample representative of a wider real-world population. The available population may already omit important groups, contain duplicates, or reflect a biased collection process.

Distinguish these questions:

1. Was the sampling code consistent with its stated rule?
2. Was the available population appropriate for the question?
3. Is the sample large and structured enough for the conclusion being drawn?

This lesson answers the first question. Later work in probability, statistics, and model evaluation develops the other two.

sample size: 3
indexes distinct: True
pairs valid: True

Retain the sampling contract

Describe every sample with:

population
+ sample size and shape
+ replacement rule
+ selection probabilities
+ recorded generator state or seed
= sampling contract

Then verify that the code follows the contract. Only after that check should you ask whether the available population and resulting sample support the larger conclusion.