Welcome to the Quantitative Analysis (Statistics/EXCEL) Module

1. Welcome to the Quantitative Analysis (Statistics/EXCEL) Module John Gates Oxford Centre for Water Research School of Geography and the Environment

2. What is statistics? “…the collection and analysis of numerical data in large quantities.” – Oxford English Dictionary “The mathematics of the collection, organization, and interpretation of numerical data, especially the analysis of population characteristics by inference from sampling.” – American Heritage Dictionary “Statistics: the mathematical theory of ignorance.” – Morris Kline “It has long recognized by public men of all kinds ... that statistics come under the head of lying, and that no lie is so false or inconclusive as that which is based on statistics.” - H. Belloc “There are three kinds of lies - lies, damned lies and statistics.” –Benjamin Disraeli “Statistical thinking will one day be as necessary for efficient citizenship as the ability to read and write.” – H.G. Wells

3. Why statistics? • make quantified statements about a phenomenon we are interested in • frequently this phenomenon is too large to go out and measure exhaustively… • …so we collect samples as proxies of the greater population of individuals or items that make up the phenomenon we are interested in

4. Aims of the course • Introduction to basic statistics • Demonstrate geographical context • Learn to use analysis tools in EXCEL • Make you an intelligent user of data • Make you an intelligent user of statistics We will bypass much of the underlying maths, rather will emphasize the understanding of underlying principles

5. How the course works • Cover the statistical principles in lecture • course lecture notes • Go through lecture notes in own time beforepractical • use textbooks to supplement lecture notes • Attend practical • work through practical handouts • ask demonstrators for help • Take online assessments • theory – any time after lecture • practical – any time after finishing prac

6. Course Structure • Lectures on Mondays • in OUCE Lecture Theatre • Practicals on Tuesday afternoons (except next week) • in Medical Sciences Teaching Centre’s computing laboratory

7. Practicals

8. Course Information • ALL INFORMATION IS ON THE WEB • http://techniques.geog.ox.ac.uk • Lecture notes and glossary • Practical notes • Excel files • Internet resources • Recommended textbooks • Tests

9. Week 1 - Central Tendency • 1. Types of statistics • 2. Types of data • 3. Samples • 4. Frequency distribution • 5. Measures of central tendency • a) mode • b) median • c) arithmetic mean • 6. Precision and accuracy

10. 1a. Descriptive Statistics • Definition: Quantitative methods of organizing, summarizing, and presenting data numerical data in an informative way. • Describe the overall characteristics of a sample (and hence the population?) • Transform raw data into more easily understood forms • Central tendency – “average” character of the data.

11. 1b. Inferential (analytical) Statistics • Definition: The branch of statistics used to make inferences or judgments about a larger population based on the data collected from a smaller sample drawn from the population

12. 2. Types of Data • Interval • Ordinal • Nominal

13. 2. Types of Data • -- Can tell exactly how far any measurement is from any other • -- Examples: height, age, size • Interval • Ordinal • Nominal

14. 2. Types of Data • -- A set of observation ordered according to some criterion, i.e. ranking • -- Cannot tell how far one measurement is from the next • -- Examples: horses’ positions in race, the ten highest mountains in the world • -- Note that interval data can be converted into ordinal form • Interval • Ordinal • Nominal

15. 2. Types of Data • -- Also referred to as categorical data • -- Data are grouped into categories • -- Examples: land use type, ethnicity, rock type • -- Note that interval data can be converted into nominal form • Interval • Ordinal • Nominal

16. 3. Samples • Definition: A subset of the target population • Random: • the individuals in the samples are randomly selected • each member of the population has a known, but possibly non-equal, chance of being included in the sample • Independent: • a sample should have no effect and are not affected by other samples selected from the same population, or different populations

17. 4. Frequency Distribution • The spread of data along its range • either mathematical description • or (and) visual description… • …a frequency histogram • define categories or intervals or classes • count the number of measurements that fall into each class • plot classes along x-axis • plot counts (frequencies) on y-axis

18. 4. Frequency Distribution Grades for 1st Stats Practical (1991-2002) Grade (in percent)

19. Modal Class 5a. Mode • Definition: The most commonly occurring value • for nominal data we refer to the modal class • not appropriate for ordinal or (usually) interval data

20. 5b. Median • Definition:The central value in an ordered set of data

21. 5b. Median • even number of values

22. 5c. Arithmetic Mean

23. 5c. Arithmetic Mean data: 4, 2, 5, 1, 7, 10, 6

24. The “average” • average = central tendency • the mean, mode and median are all measures of “average” • average  mean

25. 6. Precision and accuracy • Precision: • The degree of refinement with which an operation is performed or a measurement stated • Accuracy: • Freedom from mistake or error

26. 6. Precision and accuracy

27. Week 1 - Central Tendency • 1. Types of statistics • 2. Types of data • 3. Samples • 4. Frequency distribution • 5. Measures of central tendency • a) mode • b) median • c) arithmetic mean • 6. Precision and accuracy

28. Excel skills in Practical 1 • Entering and sorting data • Calculating mean, median and mode • Creating frequency histograms • Introduction to formulas functions