Data Analysis
You have collected your data and represented it on maps, in graphs and tables and on annotated images. The next step is to analyse your data using a range of appropriate statistical techniques.
- Basic analysis techniques – means, medians, modes.
- Measures of dispersion – Standard Deviation
- Higher Order Statistical Techniques – Spearman’s Rank.
- Alternative Higher Order Stats (Optional)
Complete the sections of the following document to explain and evaluate your progress.
You can alter the document to reflect the work that you have done, but all sections must have something in them!
Add as much detail as you can – make note of things that go badly, as well as things that are successful.
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Sample Exam Question:
Evaluate the techniques used to analyse data in an investigation of…(insert topic here).
[10 marks]
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Basic numerical analysis
You need to calculate the average of a set of data in order to ascertain whether your data is reliable and shows a marked change or difference from what is “normal”,
Mean: The “average” of a set of data (add the data and divide by the number of pieces of data)
Median: The “central value” of a set of data (put the data in rank order and select the middle value)
Mode: The most “common” value in a set of data (the value that occurs most frequently)
Do your working (on Excel – use of ICT!) and add your values in the table below:
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Aim 1 |
Aim 2 |
Aim 3 |
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Mean |
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Median |
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Mode |
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Comment on these values (how useful are they? What do they tell you about the data?) Write a paragraph or some bullet points below:-
Standard Deviation
This is a measure of the dispersion of your data around a mean value (central tendency). It will give you a measure of how reliable your mean value is. The lower the Standard Deviation, the more reliable your mean (lower values = more centralized data)
Formula for Standard Deviation:
Where:
= the Standard Deviation
= the variable
= the mean of the variable
= the total number in the sample
Do your working (use Excel) and complete the table below:-
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Aim 1 |
Aim 2 |
Aim 3 |
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Standard Deviation |
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Comment on these values (how useful are they? What do they tell you about the data?) Write a paragraph or some bullet points below:-
Spearman’s Rank Correlation Co-efficient
For at least one of your aims you need to test for a relationship between two pieces of data. Your starting point is a scatter graph, before you attempt the statistical test.
Scatter Graph:-
(Insert Graph here…)
Description of the relationship shown by the graph:-
(Positive or negative correlation; anomalous data?)
Background reading
Spearman’s Rank is covered well in Waugh (3rd ed.), and in Lenon and Cleves (Fieldwork Techniques). There are also help sheets on Moodle. Read up about what the result of the test will tell you about the data, and how you go about doing the test.
Once you have done the reading, answer the next 2 questions.
- Why do I need to do a Spearman’s Rank Test?
- What will the result tell you about your data?
Spearman’s Rank Data Table.
Complete the following, or insert your table from Excel.
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Variable X |
Rank |
Variable Y |
Rank |
d |
d2 |
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Working for Spearman’s Rank: |
Rs =
=
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Alternative Statistical Tests
Your data might not be appropriate for a Spearman’s Rank, and so you will need to do a different higher order statistical test. These include:-
· Mann-Whitney U-test – to test for a difference in the same piece of data at two sites or times
· Chi-Squared Test – to test for a correlation or difference with a group of samples.
These are less common and there are help sheets available on Moodle in the G3(b) section. Ask your teacher for additional support.