Analysing your evidence

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Analysing your evidence

• MSc IT
• Dissertation Preparation
• Linda Taylor
• Director of Learning Resources
• Liverpool Hope University College

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What sort of evidence/data will you have?

• You need to plan how you will analyse the data
  before you collect it
• If not you may
• Produce data that you cannot easily analyse
• Not make the most of the evidence you have at
  your disposal
• If you are going to use statistical methods, do
  it properly

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Statistical methods

• Are used to
• Describe a set of data in an efficient and
  meaningful manner
• Make decisions about a larger population of
  potential observations of which the data are a
  sample
• Test hypotheses

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Descriptive statistics

• Describe data and events refer to
• Frequency distributions
• Central tendencies or averages
• Variability of the data or dispersion by
  examining the range or standard deviation of
  scores
• Graphical representations
• Useful to convey information. It is often good to
  look at graphic representation prior to further
  analysis so you can see patterns of data.
• Bar charts, Histograms, Pie charts etc.

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Inferential statistics

• Inferential statistics are concerned with making
  inferences about populations and hypotheses
• Inferential statistics are values which are
  calculated form a sample and used to estimate the
  same values for a population
• Types
• Mean and Standard Deviation
• Chi-Square
• Correlation
• T-Tests
• Analysis of Variance (ANOVA)

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Variables

• Any property that may vary, i.e. that may take
  different values
• Qualitative variables - variables which differ
  only in kind
• Gender (male, female)
• Nationality (English, French)
• Occupation (Nurse, teacher) etc.

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Variables

• Quantitative variables - variables which differ
  only in amount
• Height (1.62 metres, 3 inches)
• Time (2.58 secs, 5 hours)
• IQ (98,124)
• Continuity versus discreteness
• Continuous scale e.g. length
• Only a finite number of values (discrete) (e.g.
  dress sizes, test scores, degree classifications)

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Types of numerical data

• Two main kinds
• Frequencies
• Count the number of events occurring in
  particular categories e.g. 12 right handed people
  in the room category right handed people in the
  room frequency 12
• Measurements (metric data)
• Results of giving scores to individual people,
  objects or vents on the basis on an underlying
  scale of measurement

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Levels of measurement

• Nominal level
• Ordinal level
• Interval level
• Ratio level

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Levels of measurement

• Nominal level
• Use of numbers or letters to classify events
  differing only in kind
• BBC radio stations
• Ordinal level
• Use of numbers or letters to indicate an ordered
  relationship between events
• Finishing positions in a race
• Grades awarded to essays, degree classifications

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Levels of measurement

• Interval level
• Indicates not only the relative position of
  events but also the size of the differences
  between events
• There is a constant unit of measurement which
  means that the arithmetic difference between 2
  scores accurately represents the size of the
  actual difference measured
• E.g. temperature

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Levels of measurement

• Ratio level
• Is simply interval measurement with an absolute
  zero (i.e. a score of 0 really indicates the
  total absence of the property being measured
• A score of 60 represents twice as much of a
  property as does a score of 30
• E.g. length, mass, time and volume

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Measurement data examining relationships

• When observing continuous variables e.g. age or
  tenure, a Correlation can be used to make
  inferences about relationship between the
  variables
• Correlations estimate the extent to which changes
  in one variable are related to or associated with
  changes in another variable.

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Measurement data examining relationships

• A correlation will examine the degree to which
  two or more variables are related. A correlation
  co-efficient will be calculated ranging from
• 1.00 indicates a positive relationship
• To
• -1.00 indicating a negative relationship
• Scattergrams or plots are used to pictorially
  identify whether there is likely to be any form
  of relationship, prior to statistical testing

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Examining group differences

• Descriptive or explanatory research may involve
  trying to determine whether two groups differ
  according to a specific quality. This may involve
  examining central tendency of results or scores
  on one group, and how this compares to another
• T-Test used to examine the values/scores of two
  groups
• ANOVA used to examine the values/scores of more
  than two groups
• These tests are used to determine whether groups
  have different mean values or scores
• These tests carry presumptions about the type of
  data e.g. based on normal distribution and equal
  variance in scores between the groups

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Symmetry

• Frequency distributions are not always
  symmetrical about the middle of the distribution
• Many of the group difference tests rely on data
  having a normal distribution
• Skew when you get bunching of scores at one end
  of the distribution

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Averages Mode

• Mode
• Most frequent value when data is grouped into
  class intervals
• Estimated by taking the midpoint of the interval
  that has the greatest frequency
• Easy to calculate
• It may be used for data at any level of
  measurement
• It is the only average that can be reported when
  data consists of frequencies in categories
• In such cases the mode is the category having the
  highest frequency

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Averages Median

• Median
• Midway point in a series of scores (i.e. 50th
  percentile point)
• To calculate
• Sort the scores in order of increasing value
• If there is an odd number of scores
• Median middle point
• If there is an even number of scores
• Median halfway point between the two middle
  values

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Averages Median

• Advantages of the Median
• It is the most appropriate average when data is
  measured at the ordinal level (because the median
  is based on rank order position)
• It is unaffected by extreme values, therefore
• With skewed distributions, the mean usually
  describes the most typical value much better
  than does the mean (which is greatly affected by
  extreme scores)

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Averages Mean

• Ordinary average that most people use
• Calculate by adding up all the scores and
  dividing by total number of scores
• Advantages
• More stable from sample to sample
• Uses more information than median or mode
• Disadvantages
• Affected by extreme scores and not the best
  average to report when the data very skewed or
  truncated.
• Strictly speaking it requires data measured at
  the interval or ratio level

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Averages summary of differences

• With a symmetrical, normal distribution, the
  mode, median and mean all coincide exactly
• With skewed distributions the mean is pulled
  towards the pointed end with respect to the mode
  and media
• In such cases, the different averages can give
  very different impressions of the data. The mean,
  in particular, can be very misleading if it is
  reported as reflecting a typical score.
• It is often informative to report more than one
  average

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Averages summary of differences

• The mode indicates the most common score
• The median indicates the score that is exactly in
  the middle of the distribution
• The mean indicates the centre of gravity of the
  distribution
• If in a particular set of date the median is very
  different from the mean, this will generally
  indicate that the distribution is skewed or
  truncated.

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Validity

• The extent to which a test, questionnaire or
  other method or operation is really measuring
  what the researcher intends to measure.
• Internal validity
• whether procedures are standardised or
  controlled
• External validity
• generalisability, whether the findings can be
  applied to the wider population

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Triangulation

• Helps with validity because
• Findings are judged valid when different and
  contrasting methods of data collection yield
  identical findings on the same participants and
  setting

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Reliability

• Refers to the consistency of the findings
• Concerned with whether the results can be
  replicated.
• In research we need to examine
• consistency over time involves administering a
  measure more than once
• Internal consistency is usually concerned with
  the internal coherence of a scale or measure i.e.
  whether different components link together
  perhaps to produce an overall score.