Sampling and Basic Descriptive Statistics. Basic concepts and Techniques. Lecture 6 Leah Wild

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Sampling and Basic Descriptive Statistics. Basic
concepts and Techniques.Lecture 6Leah Wild
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Overview

• Sampling In Quantitative Research
• Basic Descriptive Statistics And Graphical
  Representation Of Data
• Quantification, Variables And Levels Of
  Measurement

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Sampling In Quantitative Research

• Total Population
• Representative sample
• Probability Sampling
• Non-Probability Sampling
• Sample Size

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Total Population

• The total collection of units, elements or
  individuals that you want to analyse.
• These can be countries, lab-rats, light bulbs,
  university students, banks, residents of a
  particular area, regional health authorities etc.
• The population for a study of infant health might
  be all children born in the U.K. in the 1980's.

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Sample

• A sample is a group of units selected from a
  larger group (the population). By studying the
  sample it is hoped to draw valid conclusions
  about the larger group.
• Using example for study of infant health the
  sample might be all babies born on 7th May in any
  of the years.
• samples selected because the population is too
  large to study in its entirety.
• Important that the researcher carefully and
  completely defines the population, including a
  description of the members to be included

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Representative sample

• A sample whose characteristics correspond to, or
  reflect, those of the original population or
  reference population
• To ensure representativeness, the sample may be
  either completely random or stratified depending
  upon the conceptualized population and the
  sampling objective (i.e., upon the decision to be
  made).
• A thorny issue in the social sciences- is it
  possible to achieve?

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Probability SamplingA probability provides a
quantitative description of the likely occurrence
of a particular event.

• A probability sampling method is any method of
  sampling that uses some form of random selection.
  In order to have a random selection method, you
  must set up some process or procedure that
  assures that the different units in your
  population have equal probabilities of being
  chosen (Clark 2002 37).

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Most Common Types of Probability Sampling

• Simple Random Sampling
• Stratified Random Sampling
• Systematic Random Sampling
• Cluster Or Multistage Sampling

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Simple Random Sampling

• where we select a group of subjects (a sample)
  for study from a larger group (a population).
  Each individual is chosen randomly and each
  member of the population has an equal chance of
  being included in the sample.
• Every possible sample of a given size has the
  same chance of selection that is, each member of
  the population is equally likely to be chosen at
  any stage in the sampling process. (Easton Mc
  Coll 2004).
• A lottery draw is a good example of simple random
  sampling. A sample of 6 numbers is randomly
  generated from a population of 45, with each
  number having an equal chance of being selected.

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Stratified Random Sampling

• Often factors which divide up the population into
  sub-populations (groups / strata)
• measurement of interest may vary among the
  different sub-populations.
• This has to be accounted for when we select a
  sample from the population to ensure our sample
  is representative of the population.
• This is achieved by stratified sampling.
• A stratified sample is obtained by taking samples
  from each stratum or sub-group of a population.
• Suppose a farmer wishes to work out the average
  milk yield of each cow type in his herd which
  consists of Ayrshire, Friesian, Galloway and
  Jersey cows. He could divide up his herd into the
  four sub-groups and take samples from these
  (Easton and Mc Coll 2004).

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Systematic Random Sampling

• Systematic sampling, sometimes called interval
  sampling, means that there is a gap, or interval,
  between each selection.
• Often used in industry, where an item is selected
  for testing from a production line (say, every
  fifteen minutes) to ensure that machines and
  equipment are working to specification.
• Alternatively, the manufacturer might decide to
  select every 20th item on a production line to
  test for defects and quality. This technique
  requires the first item to be selected at random
  as a starting point for testing and, thereafter,
  every 20th item is chosen.used when questioning
  people in surveys eg market researcher selecting
  every 10th person who enters a particular store,
  after selecting a person at random as a starting
  point
• interviewing occupants of every 5th house in a
  street, after selecting a house at random as a
  starting point.If researcher wants to select a
  fixed size sample. In this case, it is first
  necessary to know the whole population size from
  which the sample is being selected. The
  appropriate sampling interval, I, is then
  calculated by dividing population size, N, by
  required sample size, n, as follows
• If a systematic sample of 500 students were to be
  carried out in a university with an enrolled
  population of 10,000, the sampling interval would
  be
• I N/n 10,000/500 20

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Cluster Or Multistage Sampling

• Cluster sampling is a sampling technique where
  the entire population is divided into groups, or
  clusters, and a random sample of these clusters
  are selected. All observations in the selected
  clusters are included in the sample.
• every element should have a specified (equal)
  chance of being selected into the final sample.
• typically used when the researcher cannot get a
  complete list of the members of a population they
  wish to study but can get a complete list of
  groups or 'clusters' of the population
• Cheap, easy economical method of data collection.

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Non-Probability Sampling

• Main Types
• Convenience/ opportunity/accidental sampling.
• Purposive/ judgemental sampling
• Quota sampling
• Snowball sampling

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Convenience/ opportunity/accidental sampling.

• volunteer samples
• Sometimes access through contacts or gatekeepers
• easy to reach population.

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Purposive/ judgemental sampling

• Involves selecting a group of people because they
  have particular traits that the researcher wants
  to study
• e.g. consumers of a particular product or service
  in some types of market research
• My own questionnaire research on New-Age
  Travellers.

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Quota sampling

• widely used in opinion polls and market research.
  
• Interviewers given a quota of subjects of
  specified type to attempt to recruit.
• eg. an interviewer might be told to go out and
  select 20 male smokers and 20 female smokers so
  that they could interview them about their health
  and smoking behaviours .

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Snowball sampling

• Involves two main steps.
• Identify a few key individuals
• Ask these individuals to volunteer to distribute
  the questionnaire to people who know and fit the
  traits of the desired sample (e.g. my research on
  Travellers)

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Sample Size

• In general, the larger the sample size (selected
  with the use of probability techniques) the
  better. The more heterogeneous a population is on
  a variety of characteristics (e.g. race, age,
  sexual orientation, religion) then a larger
  sample is needed to reflect that diversity.
  (Papadopoulos 2003)
• Response rates vary on the type of surveys (e.g.
  mail surveys, telephone surveys). Response rates
  under 60 or 70 per cent may compromise the
  integrity of the random sample. (ibid)

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Basic Descriptive Statistics And Graphical
Representation Of Data

• Can be divided into two types
• Descriptive.
• Inferential
• Some authors suggest a third type Associative
  (Downey 1975)

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Descriptive Statistics

• Statistics which describe attributes of a sample
  or population.
• includes measures of central tendency statistics
  (e.g., mean, median, mode), frequencies,
  percentages. minimum, maximum, and range for a
  data set, variance etc.
• organise and summarise a set of data

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Inferential Statistics

• Used to make inferences or judgments about a
  larger population based on the data collected
  from a small sample drawn from the population.
• Eg Exit polling used during US elections to
  determine how the population of voters voted
• A key component of inferential statistics is the
  calculation of statistical significance of a
  research finding.
• used to determine whether changes in a dependent
  variable are caused by an independent variable
  (Clark 2004)
• (HOMEWORK- WHAT ARE SOME OF THE PROBLEMS
  ASSOCIATED WITH THESE KIND OF STATISTICS?

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Quantification, Variables And Levels Of
Measurement

• Rowntree (2000) distinguishes between category
  variables and quantity variables.
• Category variables can be nominal or ordinal.
• Quantity variables can be discrete or continuous.

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Examples Nominal Data

• Type of Bicycle
• Mountain bike, road bike, chopper, folding,BMX.
• Ethnicity
• White British, Afro-Caribbean, Asian, Chinese,
  other, etc. (note problems with these
  categories).
• Smoking status
• smoker, non-smoker

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Ordinal Data

• A type of categorical data in which order is
  important.
• Class of degree-1st class, 21, 22, 3rd class,
  fail
• Degree of illness- none, mild, moderate, acute,
  chronic.
• Opinion of students about stats classes-
• Very unhappy, unhappy, neutral, happy, ecstatic!

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Discrete Data

• Only certain values are possible (there are gaps
  between the possible values). Implies counting.

Continuous Data
Theoretically, with a fine enough measuring
device. Implies counting.
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Relationships between Variables.

(Source. Rowntree 2000 33)
Variables
Quantity
Category
Continuous (measuring)
Discrete (counting)
Ordinal
Nominal
Ordered categories
Ranks.
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Quantification, Variables And Levels Of
Measurement

• Fielding and Gilbert (2000 15) distinguish
  between four levels of measurement.
• Nominal
• Ordinal.
• Interval
• Ratio.

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Interval and ratio variables

• According to Fielding Gilbert (2000) these are
  often used interchangeably, and incorrectly by
  social scientists.(pg15)
• Interval, ordered categories, no inherent concept
  of zero (Clark 2004), we can calculate meaningful
  distance between categories, few real examples of
  interval variables in social sciences. (Fielding
  Gilbert 200015)
• Ratio. A meaningful zero amount (eg income),
  possible to calculate ratios so also has the
  interval property (eg someone earning 20,000
  earns twice as much as someone who earns
  10,000).(ibid)
• Difference between interval and ratio usually not
  important for statistical analysis (ibid).

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Interval variables- Examples

• Fahrenheit temperature scale- Zero is arbitrary-
  40 Degrees is not twice as hot as 20 degrees.
• IQ tests. No such thing as Zero IQ. 120 IQ not
  twice as intelligent as 60.
• Question- Can we assume that attitudinal data
  represents real, quantifiable measured
  categories? (ie. That very happy is twice as
  happy as plain happy or that Very unhappy
  means no happiness at all). Statisticians not in
  agreement on this.

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Ratio variables-Examples

• Can be discrete or continuous data.
• The distance between any two adjacent units of
  measurement (intervals) is the same and there is
  a meaningful zero point (Papadopoulos 2001)
• Income- someone earning 20,000 earns twice as
  much as someone who earns 10,000.
• Height
• Unemployment rate- measured as the number of
  jobseekers as a percentage of the labour force
  (ibid).

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IMPORTANT! SEE TYPES OF DATA REVISION SLIDES
ON MY WEBSITE FOR EXTRA INFORMATION ON TYPES OF
DATA
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Frequencies and Distributions

• Frequency-A frequency is the number of times a
  value is observed in a distribution or the number
  of times a particular event occurs.
• Distribution-When the observed values are
  arranged in order they are called a rank order
  distribution or an array. Distributions
  demonstrate how the frequencies of observations
  are distributed across a range of values.

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Example

• Look at the distribution below
• This distribution shows the recorded ages of
  patients receiving treatment for heart disease in
  the Stroud district. There are 50 observed
  values. We can easily see how often each value
  occurs. What is the frequency of the following
  values, 79 81 94? What is the range of this
  distribution?(r h l ). What is the mode?
  What is the median? From this distribution we can
  also tell that most of the values tend to cluster
  around the middle of the range.

62 64 65 66 68 70 71 71 72 72
73 74 74 74 75 75 76 77 77 78
78 78 79 79 79 80 80 80 81 81
81 81 81 82 82 82 83 83 85 85
86 87 87 88 89 90 90 92 94 96
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Two elements to a distribution

• Scale with a number of values -(Usually arrange
  the scores from the highest to lowest).
• Corresponding observations- Tally up the scores,
  convert them into frequencies.

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Types of Distribution

• Frequency distribution
• Class Intervals
• Relative (Proportional or percentage
  distributions)
• Cumulative distributions.

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Frequency Distributions

• Shows number of cases having each of the
  attributes of a particular variable. Divided into
  two types
• Ungrouped distribution-scores not collapsed into
  categories, each score represented as a separate
  values
• Grouped distribution. Scores collapsed into
  categories so that several scores are presented
  together as a group. Groups usually referred to
  as a class interval.

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Relative (proportional or percentage)
distributions

• The proportion of cases in the whole distribution
  observed at each score or value.

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Cumulative distribution.

• The number of cases up to and including the scale
  value. Can appear in grouped or ungrouped format.
• Cumulative relative distribution for any
  particular value is the the total up to, and
  including, that value