1. Measurement Errors Introduction to Study Skills & Research Methods (HL10040) Dr James Betts

2. Lecture Outline: Measurement Errors Continued Types of Errors Assessment of Error Introduction to Inferential Statistics Chi-Squared tests Assessment Details.

3. Measurement Errors Virtually all measurements have errors –i.e. Measured Score = ‘True’ Score  Error Therefore inherently linked to SD Reliability and Measurement Error are not the same, rather Reliability infers an acceptable degree of Measurement Error.

4. This variability between methods is caused by both systematic and error factors Direct Record Retrospective Recall SD

5. Total Variance (SD 2 ) This total variance can then be ‘partitioned’ Systematic Variance Error Variance Caused by systematic error Caused by random error

6. Types of Errors Systematic Error –Any variable causing a consistent shift in the mean in a given direction e.g. Retrospective diet records tend to omit the snacks between meals Random Error –The fluctuation of scores due to chance e.g. Innaccurate descriptions of the food consumed

7. Systematic Error Skin-Fold Callipers Hydrostatic Weighing % Body-fat Subject 1Subject 2Subject 3Subject 4 1012811 17221412

8. Random Error Skin-Fold Callipers Hydrostatic Weighing % Body-fat Subject 1Subject 2Subject 3Subject 4 1418109 11152117

9. Assessment of Error Systematic Error Evidence of bias between means

10. Assessment of Error Random Error r 2 = 0.278 r = 0 infers lots of error r = 1 infers no error In general, good agreement requires r > 0.7

11. Assessment of Error Systematic & Random Error Callipers HydroStat. 10.0017.00 12.0022.00 8.0014.00 11.0012.00 14.0011.00 18.0015.00 10.0021.00 9.0017.00

12. Assessment of Error Systematic & Random Error Callipers HydroStat. Difference Mean 10.0017.007.0013.50 12.0022.0010.0017.00 8.0014.006.0011.00 11.0012.001.0011.50 14.0011.00-3.0012.50 18.0015.00-3.0016.50 10.0021.0011.0015.50 9.0017.008.0013.00

13. Assessment of Error Systematic & Random Error The “Bland-Altman” Plot 3 points of visual assessment: -Systematic Error: are points evenly distributed about the zero line? -Random Error: do points deviate greatly from the mean line? -Nature of error: is the error consistent left-right?

14. Examples of Bland-Altman Plots Mean difference Zero

15. Examples of Bland-Altman Plots Mean difference Zero

16. Examples of Bland-Altman Plots Mean difference Zero

17. Examples of Bland-Altman Plots Mean difference Zero

18. Examples of Bland-Altman Plots Zero

19. Why is Error Important Measurement Error is clearly of importance when evaluating the agreement between two measurement tools A consideration of error is also relevant when attempting to establish intervention effects/treatment differences i.e. where some of the variance between trials is due to the independent variable...

20. Total Variance between trial 1 & trial 2 Systematic Variance Error Variance Dependent Variable Extraneous/ Confounding (Error) Variables Independent Variable

21. Systematic Variance Total Variance between trial 1 & trial 2 Systematic Variance Error Variance Dependent Variable Extraneous/ Confounding (Error) Variables Independent Variable Primary Variance So researchers strive to increase the proportion of variance due to IV.

22. Total Variance between trial 1 & trial 2 Systematic Variance Error Variance Dependent Variable Extraneous/ Confounding (Error) Variables Independent Variable Primary Variance So researchers strive to increase the proportion of variance due to IV. Increase control Maximise effect (20 pints?)

23. Introduction to Inferential Statistics Before our next lecture you will be conducting some inferential statistics in your lab classes All you need to be aware of at this stage is that the ‘P-value’ represents the probability that total variance is not due to primary variance i.e. P = 0.01 infers a 99 % probability variance in the DV is not due to pure chance (i.e. 1 % likelihood of your result occurring if there is in fact no effect)

24. Introduction to Inferential Statistics Before our next lecture you will be conducting some inferential statistics in your lab classes All you need to be aware of at this stage is that the ‘P-value’ represents the probability that total variance is not due to primary variance i.e. P = 0.10 infers a 90 % probability variance in the DV is not due to pure chance (i.e. 1 % likelihood of your result occurring if there is in fact no effect)

25. Introduction to Inferential Statistics Before our next lecture you will be conducting some inferential statistics in your lab classes All you need to be aware of at this stage is that the ‘P-value’ represents the probability that total variance is not due to primary variance In exercise science, we must be at least 95 % sure that our effect is due more than pure chance before concluding a ‘significant’ difference. i.e. P  0.05 n.b. this DOES NOT mean that you will find this result in 95/100 test-retests or that your false positive rate is 5 %

27. Quantitative Analysis of Nominal Data Recall that nominal data infers that variables are dichotomous, i.e. belong to distinct categories e.g. Athlete/Non-Athlete, Male/Female, etc. We know that such qualitative data can be coded quantitatively to allow a more objective analysis Nominal data does not require any consideration of normality and is analysed used a Chi 2 test.

28. The Chi-Squared Test Goodness of fit χ 2 test –A comparison of your observed frequency counts against what would be expected according to the null hypothesis i.e. null hypothesis infers equal dispersion (50:50) Contingency χ 2 test –A comparison of two observed frequency counts

29. Goodness of fit χ 2 test Is a leisure centre used more by males than by females? –n =150 Observed Frequency Expected Frequency Male6275 Female8875

30. Goodness of fit χ 2 test SPSS Output P-value AKA significance level i.e. significant difference in the proportion of users according to gender

31. Contingency χ 2 test Are elite athletes more likely to take nutritional supplements than non-athletes –n =60 Do take supplements Do not take supplements Athletes1812 Non-athletes1119

32. Contingency χ 2 test SPSS Output This is the test of interest i.e. no significant difference in the proportion of users according to group

33. Assumptions for Chi-Squared Although ND not required… Cells in the table should all be independent i.e. one person could have visited the leisure centre twice 80 % of the cells must have expected frequencies greater than 5 and all must be above 1 i.e. the more categories available, the more subjects needed Cannot use percentages i.e. a 15:45 split cannot be expressed as 25%:75%

34. Selected Reading I know error and variance can be confusing topics, try these: Atkinson, G. and A. M. Nevill. Statistical methods for assessing measurement error (Reliability) in variables relevant to sports medicine. Sports Medicine. 26:217-238, 1998. Hopkins, W. G. et al. Design and analysis of research on sport performance enhancement. Med. Sci. Sport and Exerc. 31:472-485, 1999. Hopkins, W. G. et al. Reliability of power in physical performance tests. Sports Medicine. 31:211-234, 2001. Atkinson, G., ''What is this thing called measurement error?'', in Kinanthropometry VIII: Proceedings of the 8th International Conference of the International Society for the Advancement of Kinanthropometry (ISAK), Reilly, T. and Marfell-Jones, M. (Eds.), Taylor and Francis, London, 2003.

35. Coursework (60% overall grade) Your coursework will require you to address 2 of the following research scenarios: –1) Effect of Plyometric Training on Vertical Jump –2) Effect of Ice Baths on Recovery of Strength –3) Effect of Diet on the Incidence of Muscle Injury –4) Effect of Footwear on Sprint Acceleration –5) Effect of PMR on Competitive Anxiety.

36. Coursework Outline For each of the 2 scenarios you will need to: –Perform a literature search in order to provide a comprehensive introduction to the research area –Identify the variables of interest and evaluate the research design which was adopted –Formulate and state appropriate hypotheses –Summarise descriptive statistics in an appropriate and well presented manner…

37. Coursework Outline Cont’d… –Select the most appropriate statistical test with justification for your decision –Transfer the output of your inferential statistics into your word document –Interpret your results and discuss the validity and reliability of the study –Draw a meaningful conclusion (state whether hypotheses are accepted or rejected).

38. Coursework Details (see unit outline) 2000 words maximum (i.e.  1000 for each) Any supporting SPSS data/outputs to be appended To be submitted on Thursday 11 th December Assessment Weighting Evaluation & Analysis (30 %) Reading & Research (20 %) Communication & Presentation (20 %) Knowledge (30 %)

39. Coursework Details All information relating to your coursework (including the relevant data files) are accessible via the unit web page: www.bath.ac.uk/~jb335/Y1%20Research%20Skills%20(FH10040). html Web address also referenced on shared area

40. Mid-Term Test (40% overall grade) NEXT WEEK This test will involve short answer questions covering all the information covered so far Mostly knowledge recall but will require understanding and possibly some calculations Duration = 50 min So…

41. Mid-Term Test (40% overall grade) Surnames: A-H –Arrive promptly at 11.10 am for start of test at 11.15 am –Exit in silence afterwards Surnames: I-Z –Arrive promptly at 12.10 am for start of test at 12.15 am –Exit however you like!

42. J.Betts@bath.ac.uk