Sampling (Part I)

Population

The entire collection of objects or outcomes about which information is sought.

Sample

A subset of population that contains the objects or outcomes actually observed.

Simple Random Sample (SRS)

A sample chosen so that each possible collection of n items from the population is equally likely to be selected.

Similar to drawing lottery tickets.

Like a fair _______, each population member has an equal chance of being selected,

And each possible sample has an equal chance of being chosen.

systemic bias

Random sampling ensures that there is no ______________ in selection, differences between sample and population only arise from random variation.

Sample of Convenience

A sample chosen in an easy or convenient way, rather than through a well-defined random method.

These may systematically differ from the population and can lead to misleading conclusions.

When there is reason to believe that no important systematic differences exist between the sample and the population.

When is a Convenience Sample may be acceptable?

Sampling Variation

Natural differences that occur between random samples drawn from the same population.

Matters a lot because it explains why repeated experiments produce slightly different results, even under identical conditions.

Independence in a Sample

Items are considered independent if knowing some values does not help predict others.

Independence in a Finite Population

Items in an SRS are not strictly independent since the population changes with each draw,

But if the population is large, dependence is negligible.

5% Rule for Independence

When the sample size is 5% or less of the population, items may be treated as independent.

Sampling with Replacement

Each item is returned to the population before the next draw, making the items truly independent.

Conceptual Population

A theoretical population consisting of all values that could possibly be observed under identical experimental conditions.

Tangible Population

A finite collection of actual physical objects (like bolts, students or blocks) from which samples are drawn.

When all values are measured under identical, unchanging conditions, such as repeated measurements on the same object with a stable instrument.

When can the data be a Simple Random Sample?

understanding, generated, conditions, identical

Determining whether a data form an SRS depends on _____________ how the data were ________ and whether _________ remained _________.

Trend Detection Plot

A plot of data v/s the order collected.

A simple random sample shall show no pattern or trend.

Example of a Dependent Data

When one measurement influences the next, such as consecutive chemical process yields or sequential sampling from a small group.

Example of a Large Population

In a population with a million items, two draws are practically independent, because removing one barely changes the probabilities.