Topic 8 - Sample Surveys

Question 1

L.O.

Answer 1

LO6 Use the box model to describe chance and chance variability, including sample surveys and the Central Limit Theorem

Question 2

Limitations of a census

Answer 2

Census:
- collect data from the whole population

Limitations:
- Time consuming
- Resources
- Cost
- DIfficult to ensure participation

Question 3

Parameters and estimates

Answer 3

Parameter:
- numerical fact about population, usually what we want to know

Estimate:
- A calculation of sample values best predicts the parameter

Question 4

Types of bias

Answer 4

Selection bias:
- exclude/ include one type of person

Non-Response bias:
- People who dont want to participate

Interview bias:
- Interviewer has to make a choice of participants in the survey

Measurement bias:
- When the form of questions in survey affects answers

Recall bias:
- People forget things

Social desireability bias:
- People lie

Lack of clarity:
- misinterpret question

Question 5

Bias and sample size relationship

Answer 5

Larger sample sizes may amplify the bias, not reduce

Question 6

Types of samples

Answer 6

Simple random sampling:
- Random individuals from population taken without replacement
- Equally random chance

Multi-stage Cluster sampling:
- Probability sampling technique, taking samples in stages and simple random sampling in each stage

Convenience Sampling:
- Not good
- non-probability sampling technique
- Subjects selected due to convenience
- NOT representative

Quota sampling:
- Not good
- non-probability sampling technique
- Assessbled sample has the same proportions as individuals as the entire population with respect to known characteristics

eg. 1500 males, 1000 females
20% from each = 300 males, 200 females

Question 7

Modelling a sample survey

Answer 7

Can use a survey as a box model

Box = population/ true parameter
Every sample = New survey

Question 8

Chance errors in Sample Surveys

Answer 8

Always contain chance error from population
Box model can be used to quantify size of chance error

Question 9

What affects accuracy?

Answer 9

Standard Error (SE) will be smaller in larger samples of the population
SE = SD/ root(n)

Surveys drawn without replacement

Question 10

Correction factor

Answer 10

• Adjusts the SE from the box model to get exact SE
• Involves both sample size and population sample

As the population gets very BIG compared to the sample size, the correction factor is almost 1

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Question 11

Confidence interval

Answer 11

How precisely does the survey measure the population

• Use sample to find an estimate

68%, 95%, 99.7%

Question 12

Simulating confidence intervals

Answer 12

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Question 13

Boot strapping

Answer 13

• The computational process that allows us to estimate the properties of the population, by using the properties of a particular sample
• Useful when there is no information about the population or where the assumptions about the population are questionable

Sample from population, then resample from original sample, then using means etc. create a histogram
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Question 14

Potential problem: Normal assumption

Answer 14

• If sample is large enough, the central limit theorum may apply
• Box model may grow past sensible results (110%)
• Instead of using a box model, bootstrapping can be sued

Question 15

Example of Boot strapping procedure

Answer 15

1. Assume original sample best represents population
2. Take a large amount of resamples of size n from the original sample with replacement
3. For each resample, calculate the proportions of 1’s, so there are n simulated proportions
4. Plot n proportions to investigate the true distribution of proportions

Question 16

Box Model Vs Boot strapping

Answer 16

Boot strap doesn’t exceed 1 as proportion cannot be over 1
Box Model = For population
Bootstrap = For sample

Spreads are similar