Chapter 1:
Data Collection

161250 Data Analysis

Census, Survey & Experiments

• In a census, every element of the population is contacted, counted, and other information collected or evaluated.

• In a survey, a sample from the population is selected (using sampling schemes) and information collected.

• Experiments are active than surveys due to application of a treatment. Experiments aim is to study the effects of induced conditions.

Types of data

• Categorical (or Qualitative)

  • Nominal data a label is assigned to nominal data

    Mathematical manipulation of nominal data makes no sense

  • Ordinal data e.g. rating scales

• Quantitative Data

  • Discrete data
  • Continuous data

• Ratio & Interval scales

  • interval scale - division & subtraction may not be meaningful
  • ratio scale - all arithmetic manipulation can be done

Measurement issues

• Measuring Devices or Instruments

  • a physical device - measuring rule to gauge the heights of plants
  • a counting device - a Geiger- counter for measuring radioactive material
  • a questionnaire - requires a more subjective response.

• Measurement Error

  • arises if the instrument tends to be faulty

• Indirect measures

  • e.g. measure of fitness - using BMI?
  • temperature - gauged by expansion of mercury!

Non-response

• a non-sampling error

• Selection stage: an element may be selected but not found

  • e.g. sheep in a flock may be tagged with individual identification number but one may not be found at the time of the survey.

• Collection stage: it may not be possible to take a measurement

  • some respondents may forget, or refuse, to answer the questionnaire

• Documentation stage

  • Incorrect record of measurement

• Call-backs reduce non-response

Census related concepts

TARGET POPULATION the population under study

FRAME operationalises data collection from a target population. e.g. listing of elements in population.

ACTUAL POPULATION is the resulting set of elements on which usable data have been collected.

Sampling related concepts

• Sample is a subset of the population

  • Sampling conserves resources - money, human-power, time etc
  • A well collected sample is more useful than a shoddily taken Census
  • Testing may be destructive

Principle of randomisation

• to avoid bias
• select a sample having similar properties of the population
• to estimate how closely a sample reflects the population
• epsem (equal probability of selection) sampling methods follow the randomisation principle

Bias vs variance

• sampling variation (ie. sample to sample variation) is different from bias

Simple Random Sampling (SRS)

• Random - refers to process not outcome

  • Each (sampling) unit has same chance of being selected
  • Units can be selected with & without replacement

To apply the SRS method, the population needs to be homogeneous

• SRS is easy to handle; suits even for a poor sampling frame

• SRS can be costlier; may lead to a politically incorrect sample!

• SRS estimates are more variable

Stratified Random Sampling (STRS)

• Suitable for heterogeneous populations

• Population is divided into homogeneous groups called strata and samples are selected from each stratum

• Sampling Approaches

  • Sample the larger strata more heavily (suits when all the strata are equally variable)
  • Sample the more varied strata are sampled

• Advantages of STRS

  • leads to efficient estimation That is, the variance (of an estimate) is usually less than that of SRS
  • sample is spread throughout population

Cluster sampling

• A convenient method of sampling

• population is composed of clusters (groups)

• Select certain clusters (randomly) and collect measurements from a random selection of the elements within the chosen clusters

• Larger variance than SRS!

Systematic Random sampling (SyRS)

• Select every \(k^{th}\) element!

• Random start within the first block of elements.

  • Convenient and also the sample will be representative of population

  • Variance of estimates - generally greater than those of SRS

  • Inefficient/inappropriate, if cycle or trend is present

PPS (probability proportional to size) sampling

• each element has its own probability of selection

• requires an associated variable to be known (e.g. previous census) and each element in the population has a value (size) of it

• e.g. “Dollar-Unit Sampling”

  • audit sampling depending on the size.
  • That is, the chance of selecting an account is proportional to its value.

Other Sampling methods

• Multistage
  • e.g. 1st stage - cluster; 2nd stage - SRS
• Volunteers
  • e.g. Blood donors…
  • randomisation?
• Snowball / opportunity / Purposive
  • e.g. Study of HIV/AIDS patients…
  • randomisation?
• Capture-Recapture Methods
  • e.g. estimating wild life populations

Example

Effective Sample size (thumb rule)

Sample Design	Design Effect (\(d\))	Effective Sample Size (\(\frac{n}{d}\))
SRS	1.00	\(n\)
STRS	0.80 to 0.90	\(\frac{n}{0.9}\) to \(\frac{n}{0.8}\)
Cluster	1.02 to 1.26	\(\frac{n}{1.26}\) to \(\frac{n}{1.02}\)
SyRS	1.05	\(\frac{n}{1.05}\)
Quota	2	\(\frac{n}{2}\)

Summary

• Issues to address

  • WHAT are collected?
  • WHO does the data collection?
  • HOW are the data collected?

• Bias occurs due to

  • SELECTION
  • COLLECTION
  • NON-RESPONSE (the single largest cause of bias!)

• A sample may have the same biases as a census along with sampling errors