STAT 250 Dr Kari Lock Morgan Hypothesis Testing

STAT 250 Dr. Kari Lock Morgan Hypothesis Testing: Conclusions SECTION 4. 3 • Significance level (4. 3) • Statistical conclusions (4. 3) • Statistical significance (4. 3) Statistics: Unlocking the Power of Data Lock 5

Resveratrol �https: //www. youtube. com/watch? v=a. Rpcdbh. Af 64 �A powerful antioxidant found in grapes and red wine with many potential benefits Statistics: Unlocking the Power of Data Lock 5

Question #1 of the Day Does red wine (resveratrol) promote weight loss? If so, why? Statistics: Unlocking the Power of Data Lock 5

Red Wine and Weight Loss • Resveratrol has been shown to promote weight loss in rodents. Today we’ll look at a study on Grey Mouse Lemurs (a primate). • A sample of lemurs had various measurements taken before and after receiving resveratrol supplementation for 4 weeks: • body mass • resting metabolic rate • locomotor activity • food intake Bio. Med Central (2010, June 22). “Lemurs lose weight with ‘life-extending’ supplement resveratrol. Science Daily. Statistics: Unlocking the Power of Data Lock 5

Study Design Can we use this study to make conclusions about causality? a) Yes b) No Statistics: Unlocking the Power of Data Lock 5

Resveratrol and Weight Loss Which of the following tests gives the strongest evidence against the null hypothesis of no difference? a) Body mass (p-value = 0. 007) b) Resting metabolic rate (p-value = 0. 013) c) Locomotor activity (p-value = 0. 49) d) Food intake (p-value = 0. 035) Statistics: Unlocking the Power of Data Lock 5

Formal Decisions A formal hypothesis test has only two possible conclusions: 1. The p-value is small: reject the null hypothesis in favor of the alternative 2. The p-value is not small: do not reject the null hypothesis Statistics: Unlocking the Power of Data Lock 5

Reject the Null? H 0: ⍴ = 0 H a: ⍴ > 0 r = 0. 6 Based on the randomization distribution, do you think we should reject the null? a) Yes b) No Statistics: Unlocking the Power of Data Lock 5

Reject the Null? H 0: ⍴ = 0 H a: ⍴ > 0 r = 0. 1 Based on the randomization distribution, do you think we should reject the null? a) Yes b) No Statistics: Unlocking the Power of Data Lock 5

Reject the Null? H 0: ⍴ = 0 H a: ⍴ > 0 r = 0. 336 Based on the randomization distribution, do you think we should reject the null? a) Yes b) No Statistics: Unlocking the Power of Data Lock 5

Formal Decisions A formal hypothesis test has only two possible conclusions: 1. The p-value is small: reject the null hypothesis in favor of the alternative 2. The p-value is not small: do not reject the null hypothesis How small? Statistics: Unlocking the Power of Data Lock 5

Significance Level �The significance level, α, is the threshold below which the p-value is deemed small enough to reject the null hypothesis p-value < α p-value > α => Reject H 0 => Do not Reject H 0 �Often α = 0. 05, unless otherwise specified (Why 0. 05? ) Statistics: Unlocking the Power of Data Lock 5

p-value < α p-value ≥ α Results would be rare, if the null were true Results would not be rare, if the null were true Reject H 0 Do not reject H 0 We have evidence that the alternative is true! Our test is inconclusive Statistics: Unlocking the Power of Data Lock 5

Resveratrol and Weight Loss It is hypothesized that resveratrol decreases body mass. For the hypothesis test on body mass, what are the relevant hypotheses? B = before resveratrol supplementation A = after resveratrol supplementation a) H 0: p. B = p. A; Ha: p. B < p. A b) H 0: p. B = p. A; Ha: p. B > p. A H 0 : μ B = μ A ; H a: μ B < μ A d) H 0: μB = μA; Ha: μB > μA c) Statistics: Unlocking the Power of Data Lock 5

Resveratrol and Weight Loss In the test to see if the mean body mass is lower after treatment, the p-value is 0. 007. Using α = 0. 05, we should… a) Reject H 0 b) Not reject H 0 Reject Ha d) Not reject Ha c) Statistics: Unlocking the Power of Data Lock 5

Conclusions p-value < α Generic conclusion: Reject H 0 p-value ≥ α H 0 Generic conclusion: Do not reject H 0 Ha Conclusion in context: We have convincing evidence that [fill in alternative hypothesis] Statistics: Unlocking the Power of Data Conclusion in context: We do not have convincing evidence that [fill in alternative hypothesis] Lock 5

Red Wine and Weight Loss In the test to see if the mean body mass is lower after treatment, the p-value is 0. 007. Using α = 0. 05, what can we conclude? a) We have convincing evidence that mean body mass is lower after resveratrol supplementation in lemurs b) We do not have convincing evidence that mean body mass is lower after resveratrol supplementation in lemurs c) We have convincing evidence that mean body mass is the same before and after resveratrol supplementation in lemurs Statistics: Unlocking the Power of Data Lock 5

Resveratrol and Weight Loss It is hypothesized that resveratrol may decrease body mass by increasing locomotor activity. For the hypothesis test on resting metabolic rate, what are the relevant hypotheses? B = before resveratrol supplementation A = after resveratrol supplementation a) H 0: p. B = p. A; Ha: p. B < p. A b) H 0: p. B = p. A; Ha: p. B > p. A H 0 : μ B = μ A ; H a: μ B < μ A d) H 0: μB = μA; Ha: μB > μA c) Statistics: Unlocking the Power of Data Lock 5

Resveratrol and Weight Loss In the test to see if the mean locomotor activity is higher after treatment, the p-value is 0. 49. Using α = 0. 05, we should… a) Reject H 0 b) Not reject H 0 Reject Ha d) Not reject Ha c) Statistics: Unlocking the Power of Data Lock 5

Red Wine and Weight Loss In the test to see if locomotor activity is lower after treatment, the p-value is 0. 49. Using α = 0. 05, what can we conclude? a) We have convincing evidence that mean locomotor activity is higher after resveratrol supplementation in lemurs b) We do not have convincing evidence that mean locomotor activity is higher after resveratrol supplementation in lemurs c) We have convincing evidence that mean locomotor activity is the same before and after resveratrol supplementation in lemurs Statistics: Unlocking the Power of Data Lock 5

Elephant Example H 0 : X is an elephant Ha : X is not an elephant Would you conclude, if you get the following data? • X walks on two legs • X has four legs Statistics: Unlocking the Power of Data Lock 5

Never Accept H 0 • “Do not reject H 0” is not the same as “accept H 0”! • Lack of evidence against H 0 is NOT the same as evidence for H 0! “For the logical fallacy of believing that a hypothesis has been proved to be true, merely because it is not contradicted by the available facts, has no more right to insinuate itself in statistical than in other kinds of scientific reasoning…” -Sir R. A. Fisher Statistics: Unlocking the Power of Data Lock 5

Statistical Significance When the p-value is less than α, the results are statistically significant. �If our sample is statistically significant, we have convincing evidence against H 0, in favor of Ha Statistics: Unlocking the Power of Data Lock 5

p-value < α p-value ≥ α Results would be rare, if the null were true Results would not be rare, if the null were true Reject H 0 Do not reject H 0 We have evidence that the alternative is true! Our test is inconclusive Results are statistically significant Statistics: Unlocking the Power of Data Results are not statistically significant Lock 5

Resveratrol and Weight Loss It is hypothesized that resveratrol may decrease body mass by increasing resting metabolic rate. For the hypothesis test on resting metabolic rate, what are the relevant hypotheses? B = before resveratrol supplementation A = after resveratrol supplementation a) H 0: p. B = p. A; Ha: p. B < p. A b) H 0: p. B = p. A; Ha: p. B > p. A H 0 : μ B = μ A ; H a: μ B < μ A d) H 0: μB = μA; Ha: μB > μA c) Statistics: Unlocking the Power of Data Lock 5

Red Wine and Weight Loss In the test to see if the mean resting metabolic rate is higher after treatment, the p-value is 0. 013. Using α = 0. 05, is this statistically significant? a) Yes b) No Statistics: Unlocking the Power of Data Lock 5

Red Wine and Weight Loss In the test to see if the mean resting metabolic rate is higher after treatment, the p-value is 0. 013. Using α = 0. 05, what can we conclude? a) We have convincing evidence that mean resting metabolic rate is higher after resveratrol supplementation in lemurs b) We do not have convincing evidence that mean resting metabolic rate is higher after resveratrol supplementation in lemurs c) We have convincing evidence that mean resting metabolic rate is the same before and after resveratrol supplementation in lemurs Statistics: Unlocking the Power of Data Lock 5

Resveratrol and Weight Loss It is hypothesized that resveratrol may decrease body mass by decreasing food intake. For the hypothesis test on food intake, what are the relevant hypotheses? B = before resveratrol supplementation A = after resveratrol supplementation a) H 0: p. B = p. A; Ha: p. B < p. A b) H 0: p. B = p. A; Ha: p. B > p. A H 0 : μ B = μ A ; H a: μ B < μ A d) H 0: μB = μA; Ha: μB > μA c) Statistics: Unlocking the Power of Data Lock 5

Red Wine and Weight Loss In the test to see if mean food intake is lower after treatment, the p-value is 0. 035. Using α = 0. 10, is this statistically significant? a) Yes b) No Statistics: Unlocking the Power of Data Lock 5

Red Wine and Weight Loss In the test to see if mean food intake is lower after treatment, the p-value is 0. 035. Using α = 0. 01, is this difference statistically significant? a) Yes b) No Statistics: Unlocking the Power of Data Lock 5

Statistical Conclusions Formal decision of hypothesis test, based on = 0. 05 : Statistically significant Not statistically significant Informal strength of evidence against H 0: Statistics: Unlocking the Power of Data Lock 5

Resveratrol and Weight Loss � Body mass (p-value = 0. 007) evidence that resveratrol decreases body mass � Resting metabolic rate (p-value = 0. 013) evidence that resveratrol decreases metabolic rate �Food intake (p-value = 0. 035) evidence that resveratrol decreases food intake �Locomotor activity (p-value = 0. 49) evidence that resveratrol increases activity Statistics: Unlocking the Power of Data Lock 5

Conclusions p-value < α Generic conclusion: Reject H 0 p-value ≥ α H 0 Generic conclusion: Do not reject H 0 Ha Conclusion in context: We have (strong? ) evidence that [fill in alternative hypothesis] Statistics: Unlocking the Power of Data Conclusion in context: We do not have convincing evidence that [fill in alternative hypothesis] Lock 5

Question #2 of the Day What aspect of sunlight might help protect against multiple sclerosis? Statistics: Unlocking the Power of Data Lock 5

Multiple Sclerosis and Sunlight • It is believed that sunlight offers some protection against multiple sclerosis, but the reason is unknown • Researchers randomly assigned mice to one of: • Control (nothing) • Vitamin D Supplements • UV Light • All mice were injected with proteins known to induce a mouse form of MS, and they observed which mice got MS Seppa, Nathan. “Sunlight may cut MS risk by itself”, Science News, April 24, 2010 pg 9, reporting on a study appearing March 22, 2010 in the Proceedings of the National Academy of Science. Statistics: Unlocking the Power of Data Lock 5

Study Design Can this study be used to make conclusions about causality, at least in mice? a) Yes b) No Statistics: Unlocking the Power of Data Lock 5

Multiple Sclerosis and Sunlight �For each situation below, write down Null and alternative hypotheses Informal description of the strength of evidence against H 0 Formal decision about H 0, using α = 0. 05 Conclusion in the context of the question �In testing whether Vitamin D provides protection against MS (Vitamin D vs control group), the pvalue is 0. 47. �In testing whether UV light provides protection against MS (UV light vs control group), the p-value is 0. 002. Statistics: Unlocking the Power of Data Lock 5

Multiple Sclerosis and Sunlight �In testing whether Vitamin D provides protection against MS (Vitamin D vs control group), the p-value is 0. 47. Statistics: Unlocking the Power of Data Lock 5

Multiple Sclerosis and Sunlight �In testing whether UV light provides protection against MS (UV light vs control group), the pvalue is 0. 002. https: //www. youtube. com/watch? v=Kb. Jqyh. Tk. YSY Statistics: Unlocking the Power of Data Lock 5

To Do �Do HW 4. 1, 4. 2 (due Friday, 3/3) �Do HW 4. 3 (due Wednesday, 3/15) �Enjoy spring break!!! Statistics: Unlocking the Power of Data Lock 5