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Hypothesis Testing

Hypothesis Testing. Introduction to Study Skills & Research Methods (HL10040). Dr James Betts. It is easy (i.e. data in  P value out) It provides the ‘Illusion of Scientific Objectivity’ Everybody else does it. Why do we use Hypothesis Testing?.

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Hypothesis Testing

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  1. Hypothesis Testing Introduction to Study Skills & Research Methods (HL10040) Dr James Betts

  2. It is easy (i.e. data in  P value out) It provides the ‘Illusion of Scientific Objectivity’ Everybody else does it. Why do we use Hypothesis Testing?

  3. P<0.05 is an arbitrary probability (P<0.06?) The size of the effect is not expressed The variability of this effect is not expressed Overall, hypothesis testing ignores ‘judgement’. Problems with Hypothesis Testing?

  4. Lecture Outline: • What is Hypothesis Testing? • Hypothesis Formulation • Statistical Errors • Effect of Study Design • Test Procedures • Test Selection.

  5. Statistics Descriptive Inferential Correlational Organising, summarising & describing data Generalising Relationships Significance

  6. What is Hypothesis Testing? Null Hypothesis Alternative Hypothesis • A B • A B We also need to establish: 1) How …………………….. are these observations? 2) Are these observations reflective of the ………………………….?

  7. Is there any difference in the length of time that males and females can sustain an isometric muscular contraction? Example Hypotheses: Isometric Torque Alternative Hypothesis There is a significant difference in the DV between males and females. Null Hypothesis There is not a significant difference in the DV between males and females

  8. Example Hypotheses: Isometric Torque • Is there any difference in the length of time that males and females can sustain an isometric muscular contraction? N♀ N♂ n♀ n♂ 16 17 18 19 20 Sustained Isometric Torque (seconds)

  9. Type 1 Errors -Rejecting H0 when it is actually true -Concluding a difference when one does not actually exist Type 2 Errors -Accepting H0 when it is actually false (e.g. previous slide) -Concluding no difference when one does exist Statistical Errors

  10. Independent t-test: Calculation n♀ n♂ 16 17 18 19 20 Sustained Isometric Torque (seconds)

  11. Independent t-test: Calculation Step 1: Calculate the Standard Error for Each Mean SEM♀ = SD/√n = SEM♂ = SD/√n =

  12. Independent t-test: Calculation Step 2: Calculate the Standard Error for the difference in means SEMdiff = √ SEM♀2 + SEM♂2=

  13. Independent t-test: Calculation Step 3: Calculate the t statistic t = (Mean♀ - Mean♂) / SEMdiff =

  14. Independent t-test: Calculation Step 4: Calculate the degrees of freedom (df) df = (n♀ - 1) + (n♂ - 1) =

  15. Independent t-test: Calculation Step 5: Determine the critical value for t using a t-distribution table Degrees of Freedom Critical t-ratio 44 46 48 50 2.015 2.013 2.011 2.009

  16. Independent t-test: Calculation Step 6 finished: Compare t calculated with t critical Calculated t = Critical t =

  17. Independent t-test: Calculation Evaluation: The wealth of available literature supports that females can sustain isometric contractions longer than males. This may suggest that the findings of the present study represent a type error Possible solution:

  18. Independent t-test: SPSS Output Swim Data from SPSS session 8

  19. Advantages of using Paired Data • Data from independent samples is heavily influenced by variance between subjects

  20. Paired t-test: Calculation …a paired t-test can use the specific differences between each pair rather than just subtracting mean A from mean B (see earlier step 3)

  21. Paired t-test: Calculation ∑D = ∑D2 = Steps 1 & 2: Complete this table

  22. Paired t-test: Calculation Step 3: Calculate the t statistic ∑D t = n x ∑D2 – (∑D)2 = √ (n - 1)

  23. Paired t-test: Calculation Steps 4 & 5: Calculate the df and use a t-distribution table to find t critical Critical t-ratio (0.05 level) Critical t-ratio (0.01 level) Degrees of Freedom 63.657 9.925 5.841 4.604 4.032 3.707 3.499 3.355 3.250 1 2 3 4 5 6 7 8 9 12.71 4.303 3.182 2.776 2.571 2.447 2.365 2.306 2.262

  24. Paired t-test: Calculation Step 6 finished: Compare t calculated with t critical Calculated t = Critical t =

  25. Paired t-test: SPSS Output Push-up Data from lecture 3

  26. Example Hypotheses: Isometric Torque • Is there any difference in the length of time that males and females can sustain an isometric muscular contraction? t-test Mean A Mean B 16 17 18 19 20 Sustained Isometric Torque (seconds)

  27. Example Hypotheses: Isometric Torque • Is there any difference in the length of time that males and females can sustain an isometric muscular contraction? Mean A Mean B 16 17 18 19 20 Sustained Isometric Torque (seconds)

  28. All data or paired differences are ND (this is the main consideration) N acquired through random sampling Data must be of at least the interval LOM Data must be Continuous. …assumptions of parametric analyses

  29. These tests use the median and do not assume anything about distribution, i.e. ‘distribution free’ Mathematically, value is ignored (i.e. the magnitude of differences are not compared) Instead, data is analysed simply according to rank. Non-Parametric Tests

  30. Independent Measures Mann-Whitney Test Repeated Measures Wilcoxon Test Non-Parametric Tests

  31. Mann-Whitney U: Calculation Step 1: Rank all the data from both groups in one series, then total each School A School B Student Student Grade Grade Rank Rank B- B- A+ D- B+ A- F 9 9 14 3 11 12.5 1 4 6.5 6.5 9 2 5 12.5 D C+ C+ B- E C- A- J. S. L. D. H. L. M. J. T. M. T. S. P. H. T. J. M. M. K. S. P. S. R. M. P. W. A. F. ∑RB= ∑RA= Median = ; Median = ;

  32. Mann-Whitney U: Calculation Step 2: Calculate two versions of the U statistic using: U1 = (nAxnB) + (nA + 1) xnA - ∑RA 2 AND… U2 = (nAxnB) + (nB + 1) xnB - ∑RB 2

  33. Mann-Whitney U: Calculation Step 3 finished: Select the smaller of the two U statistics (U1 = ………; U2 = ……..) …now consult a table of critical values for the Mann-Whitney test n 0.05 0.01 6 5 2 7 8 4 8 13 7 9 17 11 Conclusion Median A Median B Calculated U must be critical U to conclude a significant difference

  34. Mann-Whitney U: SPSS Output

  35. Wilcoxon Signed Ranks: Calculation Step 1: Rank all the diffs from in one series (ignoring signs), then total each Pre-training OBLA (kph) Post-training OBLA (kph) Athlete Diff. Rank Signed Ranks - + J. S. L. D. H. L. M. J. T. M. T. S. P. H. 15.6 17.2 17.7 16.5 15.9 16.7 17.0 16.1 17.5 16.7 16.8 16.0 16.5 17.1 0.5 0.3 -1 0.3 0.1 -0.2 0.1 6 4.5 -7 4.5 1.5 -3 1.5 6 4.5 4.5 1.5 1.5 -7 -3 Medians = ∑Signed Ranks =

  36. Wilcoxon Signed Ranks: Calculation Step 2: The smaller of the T values is our test statistic (T+ = ….....; T- = ……) …now consult a table of critical values for the Wilcoxon test n 0.05 6 0 7 2 8 3 9 5 Conclusion Median A Median B Calculated T must be critical T to conclude a significant difference

  37. Wilcoxon Signed Ranks: SPSS Output

  38. So which stats test should you use? Q1. What is the …………? Q2. Is the data …….? Q3. Is the data …………….. or ……………..?

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