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