1. Department of Information Studies Research Methods Day Working with numbers Oliver Duke-Williams o.duke-williams@ucl.ac.uk

2. Working with numbers Scientific method Sampling Statistical measures Where to go next?

3. Theories, hypotheses and laws A hypothesis is an (educated) guess about phenomena, based on observation and prior knowledge A theory summarises a hypothesis or set of hypotheses which have good experimental support and seeks to explain observations A law is an inviolable description of observations

4. Falsifiability Approach popularised by Karl Popper –Popper, K (1963) Conjectures and Refutations: The growth of scientific knowledge, Routledge A statement is falsifiable if a reproducible experiment can show it to be wrong –“Water boils at 100°C” Scientific theories are never ‘proven to be correct’, they have simply not yet been proven to be wrong

5. Constructing hypotheses In using mathematical methods to conduct research it is therefore necessary to construct falsifiable hypotheses that can be tested We generally start with a null hypothesis, that there is no difference between things we are interested in

6. A null hypothesis “The launch of a website will not make a difference to the number of visitors to a museum” –Identify a set of museums with pre- and post-website visitor data –Compare the two sets of visitor data: is there a statistically significant difference? –Yes We can reject the null hypothesis –No We have failed to reject the null hypothesis

7. An alternative hypothesis Having rejected a null hypothesis, we can then test an alternative hypothesis –“The launch of a website will increase the number of visitors to a museum”

8. Sampling How many museums would you need to observe? –This is quite tricky, as we do not consider all museums to be essentially the same Sampling is easier to understand with human subjects –“Men are taller than women” –How many men and women should we measure?

9. Sampling approaches Census Random sampling Systematic sampling Stratified sampling

10. Statistical measures Summary statistics –Means, medians, modes –Variance and standard deviation Correlation –Is there dependence between two variables? Student’s t-test –Is the mean of two sets of observations different?

11. Statistical software SPSS, SAS, STATA Many tests can be done using Excel –But there are known weaknesses

12. Correlation If there is a (strong) relationship between two variables, they are correlated Consider the relationship between physical visits to a museum, and website visits

13. Correlation Institution Total Physical Visits 2010-2011 Total Unique Web Visits 2010- 2011 British Museum5,869,39621,496,815 Geffrye Museum104,691527,082 Horniman Museum584,974252,867 Imperial War Museum2,317,6398,587,082 Museum of Science and Industry in Manchester638,347330,000 National Gallery5,084,9294,500,000 National Maritime Museum2,450,15510,052,347 National Museums Liverpool2,635,9933,176,266 National Museum of Science and Industry4,093,46315,020,206 National Portrait Gallery1,758,48813,724,626 Natural History Museum4,812,1977,397,821 Royal Armouries462,753403,379 Sir John Soane's Museum109,604365,099 Tate Gallery7,450,00019,427,000 Tyne and Wear Museums Service2,018,2331,006,250 Victoria and Albert Museum3,049,00024,976,400 Wallace Collection357,538305,609 Total Visits43,797,400131,548,849 See: http://melissaterras.blogspot.co.uk/2012/03/physical-versus-website-visitors-to.html

14. 0.699646681

15. Is this significant?

16. The correlation coefficient varies between -1 and +1 At 0 there is no correlation at all At -1 there is a perfect (negative) correlation At +1 there is a perfect positive correlation

17. Is this significant? We normally test for significance at the 5% level –There is a probability of 0.05 that the relationship we have observed might have occurred due to chance Tests can be one-tailed or two-tailed; a two-tailed test means that difference might be either positive or negative We need to compare our calculated coefficient to a table of critical values e.g www.sussex.ac.uk/Users/grahamh/RM1web/Pearsonstable.pdf

18. Testing significance Coefficient=0.699 Degrees of freedom = pairs-of- observations – 2 = 17 -2 = 15.482

19. Student’s t-test The student’s t-test tells us whether the means of two sets of data are (significantly) different As with correlations, a value (‘t’) is calculated, and then compared to critical values Excel’s TTEST function returns the P-value (the probability) directly

20. Is the geography of library-going the same as the geography of museum-going? Data from: –http://data.london.gov.uk/datafiles/art-culture/library- museum-art-participation-borough.xlshttp://data.london.gov.uk/datafiles/art-culture/library- museum-art-participation-borough.xls –Includes % (in sample) used a library in past 12 months % (in sample) visited a museum or gallery in past 12 months

21. 0.000129372

22. Where to go next? UCL Graduate School –“Basic statistics for research” –http://courses.grad.ucl.ac.uk/course- details.pht?course_ID=1813