1. Difference Two Groups 1

2. Content Experimental Research Methods: Prospective Randomization, Manipulation Control Research designs Validity Construct Internal External Statistical Process for Analysis of Difference Scale of Measurement Z and t 2

3. Research Steps Overview http://www.experiment-resources.com/ 3

4. Experimental Research Prospective Analysis of Difference Random selection and assignment of participants to treatment and conditions Manipulation and control used to establish causality between variables Investigator manipulates and controls participants and conditions 4

5. Methods: Theoretical framework “a priori” Participant selection and assignment random Precision of Measurement Numerical Data Manipulation Present Control Maximized 5

6. Two Group Experimental Designs RX integrated treatment O RX standard of care O Or Change Score ROX integrated treatment OO-O = Δ ROX standard of care OO-O = Δ Key: R = Random Assignment X = Treatment O = Measurement Observation 6

7. Validity Internal Validity “truth in the experiment” – How sure are you that the manipulation of the independent variable caused the outcome in the dependent variable? Construct Validity “theoretical validity” – How well does your theory, measures, independent and dependent variables fit together? 7

8. Validity Statistical Conclusion – Is there truth in measurement and inference? External Validity – Do these results generalize to the real world? 8

9. Validity Considerations Construct Validity External Validity Statistical Conclusion Validity Internal Validity 9

10. ? Process for Analysis of Difference Check assumptions to select appropriate test statistic Design, select, control, assign appropriate to study purpose 10

11. Measurement Scale 11

12. Z Normal Distribution 12

13. Testing for Normal Distribution Normal Distribution Assumption for Parametric Tests The Shapiro Wilk test evaluates your sample for normal distribution To use the mean as a central tendency measure for your sample, you want your sample distribution to not differ statistically from the normal distribution For this assumption you want the null hypothesis of no statistical difference of your sample distribution from the true normal distribution You want your p value to be greater than 0.05 for the Shapiro Wilk test to be in the “accept null region” ; This would mean your sample data can be considered normal Results:: n = 10 Mean = 86.8 SD = 1.4757295747452441 W = 0.9367971792829276 Threshold (p=0.01) = 0.781000018119812 --> HO accepted Threshold (p=0.05) = 0.8420000076293945 --> HO accepted; p=0.842 which is greater than 0.05 threshold Threshold (p=0.10) = 0.8690000176429749 --> HO accepted --> Your data seems normal http://dittami.gmxhome.de/shapiro/http://dittami.gmxhome.de/shapiro/ results from Shoulder Range data 84 85 89 86 87 88 87 13

14. t distribution basic introduction understandable http://www.youtube.com/watch?v=QoV_TL0IDGA Z and t probability table two tailed http://statpages.org/pdfs.html t distribution probability graphic http://www.stat.tamu.edu/~west/applets/tdemo.html t distribution probability graphic one and two tail http://onlinestatbook.com/calculators/t_calc.html 14

15. Check assumptions for 2 Independent Groups Independent t test – 2 independent groups – Normal distribution each group – Equal variance between groups (note alternate form of test that does not require equal variance) – Interval or ratio scale Mann-Whitney – 2 independent groups – Ordinal, interval, or ratio scale Chi-square Fisher Exact – 2 independent groups – Nominal scale (discussed later in the semester in detail) 15

16. Mean and 95% CI; Medians and IQ Range

17. Null and Alternative Hypothesis Based on Statistical Inference The criteria for acceptance and rejection of the null hypotheses can be demonstrated using the normal probability distribution. The null hypothesis written as Ho: p ≥ 0.05 indicates no statistical difference between measures. With a probability greater than 0.05, you are within the non-rejection region of the null hypothesis. The null hypothesis of no statistical difference is retained (accepted). The alternative hypothesis written as Ha: p ≤ 0.05 indicates statistical difference between measures. With a probability less than 0.05, you are within the rejection region of the null hypothesis. The null hypothesis of no statistical difference is rejected and the alternative hypothesis of difference is retained. non-rejection region 95%

18. Confidence interval of Difference Graphic of Statistical Difference To answer the question statistically the 95% confidence interval of difference will need to be calculated. For this question the alpha was set at 0.05, 5% which means we would need to compute our confidence interval of difference at 95%. All three two group comparisons overlap the zero point as an indication of no difference. All three pairwise treatment conditions retained the null hypothesis of no difference. For example, the 95% confidence interval of difference between the control and experimental group 1 indicates that there is 95% confidence that the degree of difference between these two treatment populations was between a negative -5.8⁰ to a positive 9.2⁰. Since the confidence interval crosses zero, we fail to have statistical difference between these two treatment approaches

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20. Distinguish Between Statistical Difference and Clinical Relevance Statistical difference is math based on probability. It does not establish if there is a clinical difference in client outcome. Clinical relevance should result in a discernible change for client outcome. http://www.rehabmeasures.org/rehabweb/allmeasures.aspx?PageView=Shared http://www.rehabmeasures.org/rehabweb/allmeasures.aspx?PageView=Shared Beyond statistical difference, a study should also address if there is a clinical difference in client outcome

21. References and Links Experiment-Resources.com (2008). Research Methodology. Retrieved 17 Aug. 2012 from Experiment Resources: http://www.experiment-resources.com/research-methodology.html http://www.experiment-resources.com/research-methodology.html Research Steps, Design, Construct, Internal, External, Construct, Statistical Conclusion Validity http://www.experiment-resources.com/ http://www.experiment-resources.com/ Z and t probability table two tailed http://statpages.org/pdfs.html http://statpages.org/pdfs.html t distribution good basic content introduction http://www.youtube.com/watch?v=QoV_TL0IDGA http://www.youtube.com/watch?v=QoV_TL0IDGA t distribution a little more detail in content discussion (optional) http://www.youtube.com/watch?v=XU_3fLy2SKs&feature=c-shelf-119 http://www.youtube.com/watch?v=XU_3fLy2SKs&feature=c-shelf-119 How to calculate a t test Please watch (for understanding only, you do not have to do this hand calculation) http://www.youtube.com/watch?v=OeH3Uzrjavg&feature=plcp Vassar Stats Online Textbook: Chapter 11 Independent t test (optional http://vassarstats.net/textbook/ http://vassarstats.net/textbook/ 21