Beginners statistics

1. Beginners statistics Assoc Prof Terry Haines

2. 5 simple steps • Understand the type of measurement you are dealing with • Understand the type of question you are asking • Select a test • Focus today on tests of difference • Check assumptions where relevant • Run the test

3. Measurement • Assigning numerals to variables • Nominal • Ordinal • Interval • Ratio • Count

4. Nominal • Categories without order • Gender • Male / Female • Diagnosis • Orthopaedic / neurological / cardiorespiratory

5. Nominal • Entering categorical data on a spreadsheet • Binary / dichotomous data • Eg. gender • One column (female=0, male=1) • Polytomous data • Eg. Diagnosis • Can have one column (ortho=0, neuro=1, cardio=1) • Risk that the numeric values will be misused • Can have three “dummy” variables / columns • Ortho (no=0, yes=1) • Neuro (no=0, yes=1) • Cardio (no=0, yes=1)

6. Ordinal • Categories with order, but we don’t know how much better one place is than another • Finishing order in a race • 1st, 2nd, 3rd • Likert scaled surveys • Strongly agree, agree, undecided, disagree, strongly disagree • Entering data • One column – make sure you record what numbers mean

7. Interval • Equal intervals between numbers, but not a true zero • Eg. Degrees centigrade, IQ test scores, calendar years AD • Entering data • Input the number

8. Ratio • Equal intervals between numbers, a true zero • Eg. Distance, age, time, weight • Entering data • Input the number

9. Count • Whole, non-negative numbers indicating the frequency of an event • Eg. Number of falls, number of steps, number of therapy sessions

10. Manipulating data • Can turn a higher level of measurement into a lower level, but not vice versa • Eg. IQ scores • 0-50 below average • 51-100 average • 100-150 above average • This leads to a “loss” of data and can conceal the true relationship between two variables This converts interval data to ordinal

11. Nominal, ordinal, interval, ratio, count Can manipulate data down this scale but not up Be careful in doing this Loss of data Would need a really good reason to do so Questions on measurement scales? Measurement

12. What sort of question is being asked? • Is A≠B? • Is A>B? • Is A<B? • Is A=B? • Is A~B? Difference Agreement / reliability / prediction Correlation

13. Difference A B A B A B

14. Difference • The confusing thing is that we test a null hypothesis. • What is the probability that there is no difference in the broader population • For the one null hypothesis, there are three alternate hypotheses possible • Is A≠B? • Is A>B? • Is A<B? • The magnitude of difference can also be measured

15. Agreement / reliability / prediction • To what extent do two variables tell us exactly the same thing, or can one variable predict a later variable? A B A B

16. Agreement / reliability / prediction • The statistical procedures of agreement / reliability / prediction test a null hypothesis • What is the probability that the amount of agreement / reliability / prediction observed occurred by chance? • The magnitude of agreement can also be described

17. Correlation • To what extent do two variables co-relate to each other • They do not have to agree in order to co-relate • The statistical procedures of correlation test a null hypothesis • What is the probability that the amount of association observed occurred by chance? • The magnitude of correlation can also be described

18. Understand the question • Any questions on • Difference • Agreement / reliability / prediction • Correlation

19. Statistical testing • Why do it? • Eg. The average height of men in this room is 179 cms, the average height of women is 163 cms. • I know the men in this room are taller by 16 cms – Why do a test?

20. Statistical testing • We normally want to extrapolate the results from our sample to a broader population • It is the nature of the relationship between A and B in the broader population that is of greatest interest than what is going on just inside this room

21. Select a test • Tests will vary depending on • Measurement scale of variable A and variable B • The type of question being asked • Whether there are repeated measures or correlated samples involved

22. Tests of difference

23. Mock data

24. T-test versus regression

25. What the data says

26. Is there a difference? T-test

27. Is there a difference? Regression

29. Selecting a test: Correlation • First check visually, then • Pearson’s R • Can also use linear regression for further description of the correlation

30. Correlation • Height vs weight • Pearson’s r

31. Regression

32. Regression line is line of best fit

33. Y = bX + c What do these numbers mean? For each one unit increase in weight, there is a 0.87 increase in height. Height = 0.87*weight + 104.04

34. Does this work when one variable is dichotomous? Height = 13.3*gender(0,1) + 166.7

35. Some tricky questions • Can we have: • A is different to B, but A correlates with B? • A agrees with B, and A correlates with B? • A is not different to B, and A does not correlate with B?

36. Some more mock data

37. A and B are different, but highly correlated Confidence intervals so narrow and p-value so low they can’t be calculated

38. A and C have a negative correlation, and are different

39. B and D are not different, and not correlated

40. But is there really no relationship here? Linear regression only looks for linear (straight line) relationships. Data transformations or other forms of regression are needed here.

41. Checking assumptions • Many assumptions surround most statistical tests • Need to check to make sure you are doing the right thing by your data • There are specific tests to check assumptions • When in doubt, use visual examination of your data

42. Run the tests • Can use Excel for some tests • Gives you a single number output • We have been using Stata today • Lot’s more output to help you interpret your data

43. Any questions? • Next month – 31st March • Starting small and research question development • Dr Elizabeth Skinner