6 - Sampling Samples + Central Limit Theorem

Population

1. Large group

2. Area to be studied

3. Entire group

4. Whole

Sample

1. Small group selected from population

2. Size depends on research needs

3. Representative (make generalisations)

4. Can’t study everyone

Sample vs Population

Sample:

• Subset of population

  1. Representative

  2. Minimise sampling error

Population:

• Everybody fitting population criteria

  1. Must be clearly defined

Selecting a Sample

1. Population characteristics must be clearly defined - strong sample data

Theory of Sampling

Features of Sampling

1. Economy

2. Reliability

3. Detailed study

4. Scientific base

5. Greater sustainability

Limitations of Sampling

1. Less accurate

2. Changeability of units

3. Misleading conclusions

4. Need for specialised knowledge

Characteristics o an Ideal Sample

1. Representativeness

2. Independence

3. Adequacy

4. Homogeneity

Methods of Sampling

1. Probability Sampling

2. Non-probability sampling

Probability Sampling

Random sampling

1. Simple random sampling

2. Stratified

3. Systematic

4. Multistage

Advantages of Probability Sampling

1. Detailed info about population

2. Measured precisely

3. Inherently unbiased

4. Evaluate relative effectiveness of sample designs

Disadvantages of Probability Sampling Methods

1. High degree of skill / expertise

2. Time consuming to plan

3. Higher costs

Probability Sample - Simple Random Sampling

Individual units constituting the sample are selected at random

1. Guarantee equal chance of being chosen

2. Allocate number

3. Random generator e.g. hat

Advantages of SRP

1. Simple - math procedures

2. Unbiased

3. Representative - equal chance

4. Errors easy to detect

Disadvantages of SRP

1. Selection strictly from random basis not possible

2. Lack control of research

Probability Sample - Stratified Sampling

1. Proportionate

2. Disproportionate

3. Stratified weight sampling

Advantages of Stratified Samples

1. Greater control of the investigator

2. Representative

3. Replacement of units possible

Disadvantages of Stratified Samples

1. Bias

2. Difficult to achieve proportion

3. Difficult making sample representative

4. Difficult placing cases under level

Probability Sampling - Systematic Sampling

Advantages of Systematic Sampling

1. Simple drawing sample

2. Smaller variances

3. Ordered population - reduces variability

Disadvantages of Systematic Sampling

1. Interval - increase variability

2. Stratification effect - estimates of error

Probability Sample - Multistage Sampling

Uses a form of random sampling in each of the sampling stages where there are more than 2 stages

Advantages of Multistage Sampling

1. Complete list of population not required

2. Lists only required for sampling units selected in sample

3. Geographically defined - cut down field costs

Disadvantages of Multistage Sampling

1. Errors larger than other sampling

2. Error increase as numbers of selected sampling units decrease

Non Probability Sampling Methods

Non-random sampling

1. Judgement/purposive

2. Convenience

3. Snowball

4. Quota

Non Probability Sample - Judgement Sampling

Sampling the choice of sample items depends primarily on judgement of the researcher

Advantages of Judgement Sampling

1. Inclusion of important units

2. Representative - look into unknown traits

3. Practical

Disadvantages of Judgement Sampling

1. Risk of conforming to researcher preconceived ideas

2. No objectivity evaluating reliability of sample results

Non Probability Sampling - Convenience Sampling

Unsystematic, accidental, opportunistic

May be used:

1. Population not well defined

2. Sample unit unclear

3. Complete source unavailable

Non Probability Sampling - Snowball Sampling

Researcher contacts small number of people in target group then uses these people to establish new contact

Disadvantges of Snowball Sampling

1. Inaccessible sampling frame

2. Unrepresentative - difficult to generalise

Non Probabilty Sampling - Quota Sampling

Non-random form of stratified sampling

1. Classify population into various types - assume to be relevant to characteristics being researched

2. Determine proportion of population - fall into each type based composition of population

3. Setting quotas for each interviewer - responsible of selecting respondents so total sample interviewed contains proportion of each level

Advantages of Quota Sampling

1. Reduce cost of preparing sample/field work

2. Stratifaction effect

Disadvantages of Quota Sampling

1. Investigator bias

2. No random sampling - errors of method cannot be estimated by statistical procedures

Reliability of Sampling

1. Size of sample - adequate for study

2. Representative of sample - possess characteristics of all units

3. Parallel sampling - another sample for testing

4. Homogeneity of samples - possess same features of population

5. Unbiased selection - free from bias + prejudice

Types of Sample Errors

1. Sampling Variability - different sample from same population not always produce same mean + SD

2. Sampling Error - mean of sample not same as mean of population

3. Non-sampling Error - errors not connected with sampling method e.g. leading Q’s

How Large Should a Sample Be?

1. Population with greater variability (Big SD) - larger sample

2. Fit with study budget

3. Greater precision requires larger sample

Areas Under Normal Distribution Curve

Sample Means

Means of different samples

1. Distribution of SM from pop - approximately normally distributed

2. Mean of SM approximately equal pop mean

Distribution of Sample Means

1. SM forms normal distribution

2. Each sample has mix of high scores which tend to be cancelled out by low ones

3. SD of SM is smaller than SD of individual scores in the population.

Sample Distribution Properties

1. SD of SM smaller than SD of individual pop values

2. Larger number of samples have less variability

3. Standard Error (New SD) accommodates this

Standard Error (SE) Formula

1. 1 Z score = 1 SE

Null Hypothesis

no effect, no difference, or no relationship between variables in a study. It represents the default assumption that any observed differences are due to chance

Rejecting Null Hypothesis

1. 5% + 1% are common thresholds

2. SM is in rarest (5% or 1%) - NH not true

3. Reject NH, accept Alternate Hypothesis (H1)

Conclusions of Central Limit Theorem

1. Samples of size n from pop will have:

   *Approx normally distributed means

   *Mean of SM = Pop mean

   *SD of SM = SE