Research Methods and Statistics

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Research Methods and Statistics

• rhys.davies_at_newport.ac.uk

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The Scientific Cycle
Form hypothesis crystallise your idea from
theory, observation or model
Design a study to test your hypothesis and derive
predictions
Modify theoretical concepts publicise results
publish?
Analyse and investigate results, confirm or
revise hypothesis
Conduct study and test predictions
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A statistic is

• A structured piece of data, carrying meaningful
  information
• Research begins when we start to analyse these
  statistics systematically
• Broadly, there are two sorts of statistical
  analysis
• Descriptive statistics
• Inferential statistics
• Very much concerned with the distributions, of
  data sets, hypothetical distributions of
  populations and sampling distributions

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There are two sorts of analysis

• Descriptive statistics
• Describe a set of data graphs, mean etc
• analyse the characteristics of a sample and
  assess the parameters of a population
• Inferential statistics
• involves hypothesis testing using a sample to
  test differences in a population.

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Displaying the data

• How can data be displayed?
• Percentage
• Ratio
• Bar Chart
• Box and Whisker
• Pie chart
• And so on
• Each describes the characteristics of the sample,
  hence descriptive statistics!

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Hypothesis testing

• You have an idea you want to test -
• Gender influences examination results
• This is the experimental hypothesis, H1
• There is also a null hypothesis, H0, which would
  state that gender does not influence examination
  results
• You would collect data and test your hypothesis,
  one of the above must be true

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Variables

• Independent variables
• set up independently before the experiment begins
  (reading scheme - no reading scheme baby crawled
  not crawled)
• Dependent variables
• Dependent on experimenters manipulation of the
  independent variable (reading test score
  Movement ABC score)
• Confounding variables
• Change outcome of experiment in some unforeseen
  way (reading lessons at home age for MABC test)

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Reliability and Validity

• Validity
• How confident we are that our interpretation of
  the data is valid. That our findings actually
  show what we think they show.
• External validity - a random sample is necessary
  to ensure results generalise would a sample
  from here on education knowledge accurately
  describe knowledge in the British population as a
  whole?
• Internal validity random assignment of
  participants to groups helps ensure that our
  results mean what we think they mean for
  instance DO NOT put timid in one group and self
  confident in another.

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Reliability

• Reliability
• how confident we are that a given finding can be
  reproduced - that it can be replicated that it
  is not a chance result, a freak occurrence.
• E.g. inter rater reliability, test-retest
  reliability

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Examples of Research Methods

• Controlled experiments
• Interviews
• Observation
• Questionnaires
• Case studies
• These are methods of collecting data
• Data may or may not support theoretical
  predictions

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Data Collection and Disposal

• We have information, we need to convert it into
  data using a coding framework
• This framework consists of variables (attributes)
  relating to the domain of concern
• People are sampled representatively so clues as
  to the nature of the population can be calculated

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Issues coding choosing categories

• Exhaustivity
• All cases are covered by the options
• Exclusivity
• Each case has only one possible option
• Relevance
• Item must pertain to the domain of concern
• Adequate domain coverage
• Specificity
• Definition of each category must be precise
  consistent coding (inter-rater reliability)

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Levels of Data

• Data appears in four forms,
• we have to be aware of the level of data
• Nominal (categorical) allocates into categories
• e.g. child won sack race OR child did not win
• Ordinal value is ranked relative to others
• e.g. Ben finished in 3rd place, Tom in 2nd, Jerry
  1st
• Interval continuous numerical scale with equal
  intervals
• e.g. Tom came second, 2.3 seconds after Jerry
• Ratio as interval but with an absolute zero
• e.g. Jerry came 1st (35 seconds), Tom 2nd
  (37.3sec)

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Measures of Central Tendency

• Three measures that give an average of the data
  set
• Mean the arithmetic average, most appropriate
  for interval and ratio data
• Median the middle value of the data set, most
  appropriate for ordinal level data
• Mode most commonly occurring value, most
  appropriate for nominal data

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These averages can vary

• Take the data set 0, 0, 0, 2, 4, 5, 10
• What is the mean?
• Ans 3 (00024510)/7
• What is the mode?
• Ans 0 most common appears 3 times
• What is the median?
• Ans 2 middle value of the seven

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Measures of Dispersion

• Dispersion the extent to which the scores vary,
  all clumped together or spread out (box plot)
• Range the distance from the lowest to the
  highest score, in our previous example the Range
  was 10 0, 0, 0, 2, 4, 5, 10
• Standard Deviation (s or s) the average
  deviation from the mean, in previous example it
  is 3.4 MSexcel or SPSS can easily work this out.
• Variance (s2) result in squared units which
  does not have a direct intuitive interpretation

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Normal Distribution

• A bell curve, a reflection of naturally occurring
  values where the mean, the median and the mode
  are the same.
• This distribution of scores allows specific
  assumptions to be made about the population
  parameters. Specific methods of analysis can
  then be used.

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Parametric Non-Parametric Tests

• A normal distribution is something of an ideal
  and an assumption of normality is made to employ
  a parametric test, other assumptions are also
  required a statistics book will explain these
  clearly.
• If not normal, then non-parametric (distribution
  free) methods of analysis should be used.