# Sampling & Survey #2 – Simple Probability Samples

So recall that we are interested on the statistical aspects of taking and analysing a sample, and a good sample will be representative in the sense that characteristics of interest in the population can be estimated form the sample with a known degree of accuracy.

Here, we will use Probability Sampling to conduct surveys. Probability sampling means each unit in the population has a known non-zero probability of being included in the sample. At the same time, we will make the following assumption:

1. Sampled population = target population
2. Sampling frame is complete, no non-response or missing data
3. No measurement error

Clearly, with these assumptions, we have removed non-sampling error and only observe sampling error.

Simple Random Sample

• Simplest form of probability sample
• Each unit has an equal probability to be in the sample
• Each sample of size has the same chance of being the samples

Systematic Sample

• Units are equally spaced in the list

Stratified sample

• Elements in the same stratum often tend to be more similar.
• Simple random sample selected from each stratum, and sample random samples in the strata are selected independently

Cluster Sample

• Elements are aggregated into larger sampling units (cluster)
• The cluster is sampled:
• One – stage (entire cluster is sampled)
• Two – stage (probability sampling within the cluster)

So here is an example to sample 20 integers from the population {1, 2, …, 100} using the above methods

1. Simple random sample: Use a computer to randomly generate 20 integers from 1 to 100.
2. Systematic sample: Use a computer to randomly generate an integer from 1 to 5, then take every element. Suppose it was 2, then the sample contains units 2, 7, 12, 17, …
3. Stratified sample: Divide the population into 10 strata, {1, 2, …, 10}, {11, 12, …, 20}, …, {91, 92, …, 100}, and a simple random sample of 2 numbers will be drawn from each of the 10 strata.
4. Cluster sample: Divide the population into 20 clusters {1, 2, 3, 4, 5}, {6, 7, 8, 9, 10}, …, {96, 97, 98, 99, 100}. A simple random sample of 4 of these clusters is selected.

Now we move on to developing some concepts and tools to analyse our sample.

For most samples, we are establish a characteristic of interest, y. Let be the characteristic of interest for unit i.

1. Population mean,
2. Population proportion, p
This is a special population mean.
Let be binary variable, taking value of 1 if unit i have characteristic and 0 if unit i does not have characteristic.
3. Population Total t

4. Population variance

S is the standard deviation of y.
5. Coefficient of variation CY(y)
The coefficient of variation is a measure of relative variability; it is the ratio of the standard deviation of y with .

Next, we will delve deep into each of the sampling methods above.

Sampling & Survey #1 – Introduction
Sampling & Survey #2 – Simple Probability Samples
Sampling & Survey #3 – Simple Random Sampling
Sampling & Survey #4 – Qualities of estimator in SRS
Sampling & Survey #5 – Sampling weight, Confidence Interval and sample size in SRS
Sampling & Survey #6 – Systematic Sampling
Sampling & Survey #7 – Stratified Sampling
Sampling & Survey # 8 – Ratio Estimation
Sampling & Survey # 9 – Regression Estimation
Sampling & Survey #10 – Cluster Sampling
Sampling & Survey #11 – Two – Stage Cluster Sampling
Sampling & Survey #12 – Sampling with unequal probabilities (Part 1)
Sampling & Survey #13 – Sampling with unequal probabilities (Part 2)
Sampling & Survey #14 – Nonresponse

Comments
pingbacks / trackbacks
• […] & Survey #1 – Introduction Sampling & Survey #2 – Simple Probability Samples Sampling & Survey #3 – Simple Random Sampling Sampling & Survey #4 – […]

Contact Us

CONTACT US We would love to hear from you. Contact us, or simply hit our personal page for more contact information

Not readable? Change text.

Start typing and press Enter to search