Lecture 4

Question 1

Interpretation of results depends on

Answer 1

The study design

Question 2

The study design should be tailored to..

Answer 2

..the research question

Question 3

Methods of statically analysis and information produced will depend on

Answer 3

The study design

Question 4

Two main types of study design

Answer 4

• descriptive studies
• analytic studies

Question 5

Descriptive studies

Answer 5

• studies which describe things
  E.g surveys
• descriptive studies are often simply referred to as surveys
• generally use a sample from the population of interest

Question 6

Analytic studies

Answer 6

• studies which test hypotheses

Experimental studies e.g. randomised controlled trials
Observational studied e.g. cohort studies; case-control studies

Question 7

What is a population

Answer 7

• a complete set of entities or elements or units people that we wish to describe or make inference about

Well-defined population:
- the collection of poems by W.B Yeats
Not well-defined population:
- the population of NZ

Question 8

What is a sample

Answer 8

• a subset of a population

Question 9

How to provide a ‘ representative’ sample of the population

Answer 9

• random sampling (random selection) of study units os important

Question 10

What is random sampling is impossible ?

Answer 10

• need to consider carefully how likely it is that our sampling procedure will produce a repressentiative sample
• sometimes we can compare the characteristics of the sample to known facts about the population

Question 11

Sampling frame

Answer 11

• list of items in a population from which a sample is drawen
• rearely coincides with the entire population of interest
• often doesn’t exist

Even without a list we can ensure an ‘unbiased’ sample if every individual has the known chance of being drawn

Question 12

Random sampling to obtain a subgroup

Answer 12

• choose the sample in such a way that every individual in the population has a known change of being selected
• in a simple random sample, everyone has an equal chance of being chosen
• this method is the best way of obtaining a sample which is represtiticve of the population

Question 13

Sample mean equation

Answer 13

Sample mean = population (true) mean + error

Error could be systematic or random

Question 14

Random error occurs due to…

Answer 14

… natural variability

Question 15

In regards to random error… increasing the sample size will….

Answer 15

Reduce the random fluctuations in the sample mean

Statistical methods allow us to quantify the influence of random error on our estimate

Question 16

Two types of error

Answer 16

• Random
• systematic

Question 17

Systematic error in a destructive study (bias) occurs due to..

Answer 17

Aspects of the design or conduct of the study which systematically distort the results

Question 18

Systematic error in a descriptive study can/cant be reduced by increasing sample size

Answer 18

Can’t be reduced by increasing the sample size

Question 19

Two types of bias that cause systematic error in a descriptive study

Answer 19

Selection bias - if a sample is not representative of the population
Information bias - if the information collected from the sample members is incorrect

Question 20

We want out sampling frame to..

Answer 20

Match the population of interest

Question 21

Probability sampling is important because..

Answer 21

It helps justify the statistical models which roll be introduced in this course

Question 22

The key characteristic of probability sampling is..

Answer 22

That we know the probability of being selected for everyone in the sample frame

Question 23

Simple random sample

Answer 23

• the simplest form of probability sampling
• for a finite population of size N draw a sample of size n such that each possible sample has the same probability of being selected

Question 24

Simple random sample

Answer 24

Question 25

Stratified sampling - variation

Answer 25

- much of statistical design theory is about controlling variation - more variation in the data means less precise inference

Question 26

When is stratified sampling useful?

Answer 26

When the population comprises of several groups of similar individuals - take a simple random sample from within each stratum - sampled with probability proportional to size - everyone has the same chance of being selected OR - sampled with equal numbers from each strata - those in smaller strata are more likely to be selected

Question 27

What is a stratum?

Answer 27

- a population sub-division of similar units

Question 28

Stratified random sample diagram - probability proportion to size

Answer 28

Question 29

Stratified random sample - equal numbers form each strata - those in smaller strata are more likely to be selected

Answer 29

Question 30

Stratified sampling vs simple random sample

Answer 30

- stratified sampling gives a more precise estimate then for the same sample size from a simple random sample - can take different sized samples from different strata (this reduces overall variability) - useful is you are interested int eh results for each stratum and some of the strata are small

Question 31

Cluster samples

Answer 31

Cluster samples take a simple random sample of groups - for a single stage cluster sample include all units in the selected groups

Question 32

Cluster sampling is used when

Answer 32

The population may be composed of similar and naturally occurring groups

Question 33

Cluster random sample diagram

Answer 33

Everyone in each sampled cluster is included in the study

Question 34

Two stage cluster random sample

Answer 34

- simple random sample of one person from each cluster - probability of someone being in the study depends on the number in their cluster

Question 35

How to do two stage rCluster sampling

Answer 35

- take a simple random sample of units within a group E.g: a simple random sample of schools - a single-stage cluster sample would include all students at the selected schools - a two-stage cluster sample would take a simple random sample of schools, then a simple random sample of students at each school

Question 36

Cluster samples are useful..

Answer 36

- when the clusters are easy to sample

Question 37

Cluster sampling pro and con compared to simple random sample or a stratified sample of the same size

Answer 37

- usually cheaper - usually less precise Can compensate by raking a larger sample

Question 38

Can combine methods

Answer 38

- stratified sampling of clusters etc

Question 39

How we analyse the data depends on…

Answer 39

.. how we chose the data The formulae for computing estimates from simple ransom sampling, stratified sampling, cluster sampling etc are all different - common mistake is to use top simple methods when the data are from a complicated design - this analysis will give misleading results