1. Hypothesis Testing: Conclusions
STAT 250
Dr. Kari Lock Morgan
Hypothesis Testing: Conclusions
SECTION 4.3
Significance level (4.3)
Statistical conclusions (4.3)
Statistical significance (4.3)

2. Resveratrol https://www.youtube.com/watch?v=aRpcdbhAf64
A powerful antioxidant found in grapes and red wine with many potential benefits

3. Does red wine (resveratrol) promote weight loss?
Question #1 of the Day
Does red wine (resveratrol) promote weight loss?
If so, why?

4. 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
BioMed Central (2010, June 22). “Lemurs lose weight with ‘life-extending’ supplement resveratrol. Science Daily.

5. Study Design
Can we use this study to make conclusions about causality?
Yes No

6. Resveratrol and Weight Loss
Which of the following tests gives the strongest evidence against the null hypothesis of no difference?
Body mass (p-value = 0.007)
Resting metabolic rate (p-value = 0.013)
Locomotor activity (p-value = 0.49)
Food intake (p-value = 0.035)

7. Formal Decisions
A formal hypothesis test has only two possible conclusions:
The p-value is small: reject the null hypothesis in favor of the alternative
The p-value is not small: do not reject the null hypothesis

8. Reject the Null? H0: ⍴ = 0 Ha: ⍴ > 0 r = 0.6
Based on the randomization distribution, do you think we should reject the null?
Yes No

9. Reject the Null? H0: ⍴ = 0 Ha: ⍴ > 0 r = 0.1
Based on the randomization distribution, do you think we should reject the null?
Yes No

10. Reject the Null? H0: ⍴ = 0 Ha: ⍴ > 0 r = 0.336
Based on the randomization distribution, do you think we should reject the null?
Yes No

11. Formal Decisions How small?
A formal hypothesis test has only two possible conclusions:
The p-value is small: reject the null hypothesis in favor of the alternative
The p-value is not small: do not reject the null hypothesis
How small?

12. Significance Level p-value > α => Do not Reject H0
The significance level, α, is the threshold below which the p-value is deemed small enough to reject the null hypothesis
p-value < α => Reject H0
p-value > α => Do not Reject H0
Often α = 0.05, unless otherwise specified
(Why 0.05?)

13. 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 H0
Do not reject H0
We have evidence that the alternative is true!
Our test is inconclusive

14. 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
H0: pB = pA; Ha: pB < pA
H0: pB = pA; Ha: pB > pA
H0: μB = μA; Ha: μB < μA
H0: μB = μA; Ha: μB > μA

15. Resveratrol and Weight Loss
In the test to see if the mean body mass is lower after treatment, the p-value is Using α = 0.05, we should…
Reject H0
Not reject H0
Reject Ha
Not reject Ha

16. Conclusions p-value < α p-value ≥ α H0 Ha Generic conclusion:
Reject H0
Generic conclusion:
Do not reject H0 Ha
Conclusion in context:
We have convincing evidence that [fill in alternative hypothesis]
Conclusion in context:
We do not have convincing evidence that [fill in alternative hypothesis]

17. Red Wine and Weight Loss
In the test to see if the mean body mass is lower after treatment, the p-value is Using α = 0.05, what can we conclude?
We have convincing evidence that mean body mass is lower after resveratrol supplementation in lemurs
We do not have convincing evidence that mean body mass is lower after resveratrol supplementation in lemurs
We have convincing evidence that mean body mass is the same before and after resveratrol supplementation in lemurs

18. 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
H0: pB = pA; Ha: pB < pA
H0: pB = pA; Ha: pB > pA
H0: μB = μA; Ha: μB < μA
H0: μB = μA; Ha: μB > μA

19. Resveratrol and Weight Loss
In the test to see if the mean locomotor activity is higher after treatment, the p-value is Using α = 0.05, we should…
Reject H0
Not reject H0
Reject Ha
Not reject Ha

20. Red Wine and Weight Loss
In the test to see if locomotor activity is lower after treatment, the p-value is Using α = 0.05, what can we conclude?
We have convincing evidence that mean locomotor activity is higher after resveratrol supplementation in lemurs
We do not have convincing evidence that mean locomotor activity is higher after resveratrol supplementation in lemurs
We have convincing evidence that mean locomotor activity is the same before and after resveratrol supplementation in lemurs

21. Elephant Example H0 : 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

22. Never Accept H0 “Do not reject H0” is not the same as “accept H0”!
Lack of evidence against H0 is NOT the same as evidence for H0!
“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

23. 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 H0, in favor of Ha

24. 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 H0
Do not reject H0
We have evidence that the alternative is true!
Our test is inconclusive
Results are statistically significant
Results are not statistically significant

25. 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
H0: pB = pA; Ha: pB < pA
H0: pB = pA; Ha: pB > pA
H0: μB = μA; Ha: μB < μA
H0: μB = μA; Ha: μB > μA

26. Red Wine and Weight Loss
In the test to see if the mean resting metabolic rate is higher after treatment, the p-value is Using α = 0.05, is this statistically significant?
Yes No

27. Red Wine and Weight Loss
In the test to see if the mean resting metabolic rate is higher after treatment, the p-value is Using α = 0.05, what can we conclude?
We have convincing evidence that mean resting metabolic rate is higher after resveratrol supplementation in lemurs
We do not have convincing evidence that mean resting metabolic rate is higher after resveratrol supplementation in lemurs
We have convincing evidence that mean resting metabolic rate is the same before and after resveratrol supplementation in lemurs

28. 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
H0: pB = pA; Ha: pB < pA
H0: pB = pA; Ha: pB > pA
H0: μB = μA; Ha: μB < μA
H0: μB = μA; Ha: μB > μA

29. Red Wine and Weight Loss
In the test to see if mean food intake is lower after treatment, the p-value is Using α = 0.10, is this statistically significant?
Yes No

30. Red Wine and Weight Loss
In the test to see if mean food intake is lower after treatment, the p-value is Using α = 0.01, is this difference statistically significant?
Yes No

31. Statistical Conclusions
Formal decision of hypothesis test, based on  = 0.05 :
Statistically significant
Not statistically significant
Informal strength of evidence against H0:

32. 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

33. Conclusions p-value < α p-value ≥ α H0 Ha Generic conclusion:
Reject H0
Generic conclusion:
Do not reject H0 Ha
Conclusion in context:
We have (strong?) evidence that [fill in alternative hypothesis]
Conclusion in context:
We do not have convincing evidence that [fill in alternative hypothesis]

34. What aspect of sunlight might help protect against multiple sclerosis?
Question #2 of the Day
What aspect of sunlight might help protect against multiple sclerosis?

35. 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.

36. Study Design
Can this study be used to make conclusions about causality, at least in mice?
Yes No

37. Multiple Sclerosis and Sunlight
For each situation below, write down
Null and alternative hypotheses
Informal description of the strength of evidence against H0
Formal decision about H0, 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 p- value is 0.47.
In testing whether UV light provides protection against MS (UV light vs control group), the p-value is

38. Multiple Sclerosis and Sunlight
In testing whether Vitamin D provides protection against MS (Vitamin D vs control group), the p-value is 0.47.

39. Multiple Sclerosis and Sunlight
In testing whether UV light provides protection against MS (UV light vs control group), the p- value is

40. To Do Do HW 4.1, 4.2 (due Friday, 3/3) Do HW 4.3 (due Wednesday, 3/15)
Enjoy spring break!!!