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

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

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StatisticsDescriptiveInferentialCorrelational Relationships GeneralisingOrganising, summarising & describing data Significance

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

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

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Example Hypotheses: Isometric Torque Is there any difference in the length of time that males and females can sustain an isometric muscular contraction? Sustained Isometric Torque (seconds) N N n n

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Statistical Errors Type 1 Errors - Rejecting H 0 when it is actually true -Concluding a difference when one does not actually exist Type 2 Errors - Accepting H 0 when it is actually false (e.g. previous slide) -Concluding no difference when one does exist

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Sustained Isometric Torque (seconds) n n Independent t-test: Calculation MeanSDn

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Independent t-test: Calculation MeanSDn Step 1: Calculate the Standard Error for Each Mean SEM = SD/n =

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Independent t-test: Calculation MeanSDn Step 2: Calculate the Standard Error for the difference in means SEMdiff = SEM 2 + SEM 2 =

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Independent t-test: Calculation MeanSDn Step 3: Calculate the t statistic t = (Mean - Mean) / SEMdiff =

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

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Independent t-test: Calculation MeanSDn Step 5: Determine the critical value for t using a t-distribution table Degrees of FreedomCritical t-ratio

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

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Independent t-test: Calculation MeanSDn 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:

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

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

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Paired t-test: Calculation MeanSDn Week Week …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)

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Paired t-test: Calculation SubjectWeek 1Week 2Diff (D)Diff 2 (D 2 ) D =D 2 = Steps 1 & 2: Complete this table

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

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Paired t-test: Calculation Steps 4 & 5: Calculate the df and use a t-distribution table to find t critical Degrees of Freedom Critical t-ratio (0.05 level) Critical t-ratio (0.01 level)

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

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

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

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

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…assumptions of parametric analyses 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.

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Non-Parametric Tests 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.

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Non-Parametric Tests Independent Measures –Mann-Whitney Test Repeated Measures –Wilcoxon Test

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Mann-Whitney U: Calculation Step 1: Rank all the data from both groups in one series, then total each Student School ASchool B Student Grade Rank 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. B- B- A+ D- B+ A- F D C+ C+ B- E C- A Median = ; RA =RA = RB =RB =

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Mann-Whitney U: Calculation Step 2: Calculate two versions of the U statistic using: U 1 = (n A x n B ) + 2 (n A + 1) x n A - R A AND… U 2 = (n A x n B ) + 2 (n B + 1) x n B - R B

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Mann-Whitney U: Calculation Step 3 finished: Select the smaller of the two U statistics (U 1 = ………; U 2 = ……..) …now consult a table of critical values for the Mann-Whitney test n Calculated U must be critical U to conclude a significant difference Conclusion Median A Median B

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Mann-Whitney U: SPSS Output

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Wilcoxon Signed Ranks: Calculation Step 1: Rank all the diffs from in one series (ignoring signs), then total each Athlete Pre-training OBLA (kph) Rank J. S. L. D. H. L. M. J. T. M. T. S. P. H Signed Ranks = Post-training OBLA (kph) Diff. Signed Ranks Medians =

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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 Calculated T must be critical T to conclude a significant difference Conclusion Median A Median B

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Wilcoxon Signed Ranks: SPSS Output

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

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