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## Hypothesis Testing

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**Hypothesis Testing**A hypothesis is an assumption that appears to explain certain phenomena, which must be tested to see whether or not it is true Palmer College of Chiropractic West**Usually thought of as the total number of inhabitants of a**given area, but in research, a population refers to the units from which a sample is drawn. Population Random Selection A subset of a population that is selected for a given study. Sample Random Assignment Group A Group B Drugs Chiropractic Palmer College of Chiropractic West**Group A**Group B Low-back pain patients Palmer College of Chiropractic West**The Hypothesis (H1)**• Chiropractic patients will have better ROM than Drug patients • To see if this is true, compare the average ROM of the Drug group with the average ROM of the Chiropractic group • Drug≈50 degrees • Chiropractic≈70 degrees • Is this difference real or merely due to chance? Palmer College of Chiropractic West**Coin Toss Probability**• Hypothesis testing deals with probabilities • In a coin toss, what is the probability of getting heads or tails? • The probability of getting heads = the probability of getting tails (0.5 or 50%) Palmer College of Chiropractic West**Coin Toss Cont.**• How about getting 2 heads in 2 tosses? (½ X ½ = ¼) 0.25 • 50 tosses • Likely to get around 25 H and 25 T • Unlikely to get 10 H and 40 T • Highly unlikely (but not impossible) to get 49 H and 1T Palmer College of Chiropractic West**Research (Alternative) Hypothesis (H1)vs. Null Hypothesis**(H0) • The null hypothesis assumes that there is no difference between the groups being tested • The research hypothesis is to be adopted only if the null hypothesis proves unlikely • In biomedical research it typically must be at least 95% unlikely • Similar to the “innocent until proven guilty” concept in our legal system Palmer College of Chiropractic West**Mean (average)**A130 A250 A360 A440 Variability(Spread) A5 70 A650 A730 A860 A950 A1070 A1160 A1250 A1330 A1440 10 20 30 40 50 60 70 80 Palmer College of Chiropractic West**A130 (-20)**A250 A360 (+10) Deviations from the mean A440 (-10) A5 70 (+20) A650 A730 (-20) A860 (+10) A950 A1070 (+20) A1160 (+10) A1250 A1330 (-20) A1440 (-10) 10 20 30 40 50 60 70 80 Palmer College of Chiropractic West**-20+10-10+20-20+10+20+10-20-10**0 400100100400400100 400100400100 2500/13 = 192.3 Add squared deviations, then divide by n-1 to get the Variance The square root of the Variance is the Standard Deviation Palmer College of Chiropractic West**Drug**50 70 Chiro Hypothesis testing involves comparing means, which seems obvious at first 50 70 Chiropractic appears to clearly be superior 50 70 50 70 20 30 40 50 60 70 80 90 100 Palmer College of Chiropractic West**Consider a study dealing with chiropractic adjustments for**tension headaches • There was 38% improvement with chiropractic • 23% with placebo • 29% with a drug The question is . . . are these differences enough to say that chiropractic was better? How much difference is needed to be significant? Palmer College of Chiropractic West**Statistical Significance**• The term indicating that a study’s results are unlikely to be the result of chance at a specified probability level, leading to rejection of the H0 and acceptance of the H1 Palmer College of Chiropractic West**Statistical Significance**• Something is statistically significant if it is unlikely that the event would occur by chance less than a specific proportion of the time • If no specific proportion is given, the 5% level is assumed Palmer College of Chiropractic West**Statistical Significance**• In statistics “significant” means probably true (not due to chance) • A research finding may be true without being important (not clinically significant) • When researchers say a result is “highly significant” they mean it is very probably true • They do not (necessarily) mean it is highly important Palmer College of Chiropractic West**30 50**SD = 13.9 50 70 60 80 40 60 70 90 50 70 30 50 60 80 50 70 70 90 60 80 50 70 t-test Significance 0.001 30 50 40 60 20 30 40 50 60 70 80 90 100 Palmer College of Chiropractic West**Significance of 0.001**• Significance of 0.001 means that the likelihood that the conclusion was a mistake is only 0.1% • You can be 99.9% confident that the decision to accept the H1 was a correct decision . . . that chiropractic care appears to be better than drugs for low-back pain Palmer College of Chiropractic West**30 40**SD = 13.9 50 60 60 70 40 50 70 80 50 60 30 40 60 70 50 60 70 80 60 70 Significance 0.067 (not significant), so the means cannot be considered to be different 50 60 30 40 40 50 20 30 40 50 60 70 80 90 100 Palmer College of Chiropractic West**P-value**• P≤ 0.05 is the typical cutoff point in biomedical research (AKA α) • Which means you can be 95% confident that the decision* was correct • P-values above 0.05 are not significant and the study’s hypothesis would not be supported * Your decision to conclude that the means were different and Chiropractic was better than Drugs Palmer College of Chiropractic West**30 50**A – SD = 13.9 50 60 B – SD = 6.2 6060 40 60 7070 50 60 30 50 6060 50 60 7070 6060 50 60 t-test Significance 0.032 30 50 40 60 20 30 40 50 60 70 80 90 100 Palmer College of Chiropractic West**How the results of this study would appear in a journal**• Chiropractic was found to be superior to drug therapy in improving lumbar ROM in a group of low-back pain patients (P<0.05) • The Balon et al. asthma study – “. . . No significant differences between the groups in the degree of change from base line (morning peak expiratory flow, P=0.49 at two months and P=0.82 at four months). Palmer College of Chiropractic West**Histogramof Group A**• Adjoining bars represent • the frequency of each value Notice the values form a shape 5 4 3 2 1 50 3050 60 30 40 50 60 70 3040 50 60 70 30 40 50 60 70 80 90 100 Palmer College of Chiropractic West**Normal curve**Palmer College of Chiropractic West**Relationship between 95% CIs and P values**• Information about the P value is contained in the 95% CI • The P value can be inferred based on whether the finding of “no difference” falls within the CI Palmer College of Chiropractic West**Caution**• A 95% chance of something being true means there is a 5% chance of it being false • This means that of every 100 tests that show results significant at the 95% level, the odds are that five of them are false • If you took a totally random set of data and did 100 significance tests, about five tests would be falsely reported to be significant Palmer College of Chiropractic West**Summary**• Hypothesis testing determines whether or not a study’s results are significant. • The means of the different groups are commonly compared using a t-test. • P-value must be equal to or less than 0.05 (typically). • There is a 5% or less chance that the conclusion is wrong. Palmer College of Chiropractic West**70**90 50 90 40 80 60 10030 70 50 90 70 110 50 90 50 90 50 90 40 80 50 90 60 100 Decision to accept or reject depends upon: The amount of the difference between the means 50 Variability of the data (standard deviation) A large difference between means and a low standard deviation is best Palmer College of Chiropractic West