Population vs. Sample

Population: a set which includes all measurements of interest to the researcher(The collection of all responses, measurements, or counts that are of interest)

Sample:A subset of the population

Why sampling?Get information about large populations Less costs Less field time More accuracy i.e. Can Do A Better

Job of Data Collection When it’s impossible to study the

whole population

Sampling Techniques

Samples• Having clearly identified a thesis

statement or question, as well as the population, variables and type of data involved, a researcher can begin to conduct his or her study;

• To conduct research, data from a sample must be collected, which could involve medical testing, laboratory analyses, surveys, etc.

Samples• The sample must be:

1. representative of the population;2. appropriately sized (the larger the better);3. unbiased;4. random (selections occur by chance);

• The above criteria are interrelated.

Samples • To ensure that the four criteria are

met, careful planning is needed (any errors in the sample will result in unreliable conclusions);

• One of several methods can be chosen to achieve randomness when selecting a sample.

Types of samplingNon-probability samples

Probability samples

PROBABILITY SAMPLING

• A probability sampling scheme is one in which every unit in the population has a chance (greater than zero) of being selected in the sample, and this probability can be accurately determined.

• . When every element in the population does have the same probability of selection, this is known as an 'equal probability of selection' (EPS) design. Such designs are also referred to as 'self-weighting' because all sampled units are given the same weight.

Probability samples• Random sampling

– Each subject has a known probability of being selected

• Allows application of statistical sampling theory to results to: – Generalise – Test hypotheses

Conclusions• Probability samples are the best

• Ensure – Representativeness– Precision

Methods used in probability samples

Simple random samplingSystematic samplingStratified samplingMulti-stage sampling Cluster sampling

Non probability samplesAny sampling method where some elements of population have no chance of selection (these

are sometimes referred to as 'out of coverage'/'undercovered'), or where the

probability of selection can't be accurately determined. It involves the selection of elements based on assumptions regarding the population of interest, which forms the criteria for selection.

Hence, because the selection of elements is nonrandom, nonprobability sampling not allows

the estimation of sampling errors.

Example:

We visit every household in a given street, and interview the first person to answer the door. In any household with more than one occupant, this is a nonprobability sample, because some people are more likely to answer the door (e.g. an unemployed person who spends most of their time at home is more likely to answer than an employed housemate who might be at work when the interviewer calls) and it's not practical to calculate these probabilities.

Non probability samples

Convenience samples (ease of access)sample is selected from elements of a

population that are easily accessibleSnowball sampling (friend of

friend….etc.)Purposive sampling (judgemental)

• You chose who you think should be in the study

Quota sample

Non probability samples

• Probability of being chosen is unknown• Cheaper- but unable to generalise• potential for bias

Random Sampling Methods

Six methods are commonly employed.1. Simple Random Sampling

→ all individuals in the population have an equal likelihood of being chosen;→ for example, number all students and select the numbers from a hat (minimize the level of control that the researcher has).

Simple random sampling

Random Sampling Methods - Continued

2. Systematic Random Sampling→ used when you are sampling a fixed percentage of the population;→ randomly select a starting point, then select every nth individual;→ n is referred to as the sampling interval (n = pop size/sample size);→ for example, number all students in a list, randomly select a starting point in the list, and select every nth individual.

Systematic sampling

Random Sampling Methods - Continued

3. Stratified Random Sampling→ population is divided into strata, or groups;→ randomly select members of each stratum (the number selected is proportional to the stratum’s size);→ for example, divide our population into 9’s, 10’s, 11’s and 12’s, and randomly select members in each grade.

Random Sampling Methods - Continued

4. Cluster Random Sampling→ population is organized into groups;→ groups are randomly selected, and all members of the group are sampled;→ for example, divide our school into homerooms, randomly select homerooms, and sample all students in selected homerooms.

Cluster sampling

Section 4

Section 5

Section 3

Section 2Section 1

Random Sampling Methods - Continued

5. Multi-Stage Random Sampling→ population is organized into groups;→ randomly select groups, and then randomly select members in these groups (an equal number selected per group);→ for example, repeat the steps for Cluster Random Sampling, but then randomly select students in each selected homeroom.

Random Sampling Methods - Continued

6. Destructive Sampling→ applicable to products only;→ products chosen randomly, tested for quality control.

Random Sampling Methods - Continued

• The sampling method chosen depends on the population of interest;

• Sometimes, methods can be combined;

• Careful planning is the key to generating reliable results – always have contingency plans!

1. Determine the type of sampling method used in each scenario.a) The Ontario government randomly

selects five high schools in Ontario and surveys each teacher in those schools.

Cluster random sampling

b) You wish to survey 100 employees at Trillium Shopping Plaza (contains 216 stores). You randomly select 10 stores, then randomly select 10 employees from each store.

Multi-staged Random Sample

c) Every fiftieth family in the Unionville telephone book is surveyed by phone.

Systematic Random Sample

d) Jonathon randomly selects three cards from a standard deck of cards.

Simple Random Sample

2. In a town of 120 000 people, smoking has been banned in all restaurants. A committee of students wants to find out what the whole town thinks of this new law. The committee wants to survey 1460 people. Which sampling technique is most appropriate?