Chapter Thirteen Evaluating the Evidence In this chapter, you will:
Analysing your evidence. What sort of evidence/data will you have? You need to plan how you will...
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Transcript of Analysing your evidence. What sort of evidence/data will you have? You need to plan how you will...
Analysing your evidence
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
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
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. Different formats can make the data look more or less
significant Can help you to tell the story
Inferential statistics Inferential statistics are concerned with making
inferences about populations and hypotheses Inferential statistics are values which are
calculated from 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)
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.
Variables
Quantitative variables - variables which differ only in amount Height (1.62 metres, 3 inches) Time (2.58 seconds, 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)
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 events on the basis on an underlying scale of measurement
Scale of measurement that already exists or one that you design/apply
Levels of measurement Nominal level Ordinal level Interval level Ratio level
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
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
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
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.
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
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
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
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
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
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 median
usually describes the most “typical” value much better than does the mean (which is greatly affected by extreme scores)
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 is very skewed or truncated. Strictly speaking it requires data measured at the
interval or ratio level
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 median
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
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.
Validity“The extent to which a test, questionnaire
or other method or operation is really measuring what the researcher intends to measure”.
Internal validitywhether procedures are standardised or controlled
External validitygeneralisability, whether the findings can be applied to the wider population
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
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.
Qualitative data How are we going to analyse more
qualitative, often “free text” information
This type of information is often rich, adding important social information
Need to plan to identify and draw out themes, strands
Which parts of the analysis goes in the dissertation, where? The appendix should be used for:
Examples of questionnaires (blank) Examples of completed questionnaires that
illustrate particular themes/strands (not all) The body of the dissertation should
have in it the stages and conclusions of the analysis e.g. scattergrams which first identified trends, followed by the graphic representations of the results
Any questions? Preparation for presentation
session