Dr.KariLockMorgan HypothesisTesting:* Conclusions

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Statistics: Unlocking the Power of Data Lock5

Hypothesis Testing: Conclusions

STAT 250 Dr. Kari Lock Morgan

SECTION 4.3 •  Signi8icance level (4.3) •  Statistical conclusions (4.3) •  Statistical signi8icance (4.3) Statistics: Unlocking the Power of Data Lock5

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

Formal Decisions

How small?


SigniHicance Level � The signi-icance 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 speci8ied


p-‐value < α

Results would be rare, if the null were true

Reject H0

We have evidence that the alternative is true!

p-‐value ≥ α

Results would not be rare, if the null were true

Do not reject H0

Our test is inconclusive


Statistical Conclusions

In a hypothesis test of

H0: μ = 10 vs Ha: μ < 10

the p-‐value is 0.002. With α = 0.05, we conclude:

a)  Reject H0 b)  Do not reject H0 c)  Reject Ha d)  Do not reject Ha




H0: μ = 10 vs Ha: μ < 10


a)  There is evidence that μ = 10 b)  There is evidence that μ < 10 c)  We have insuf8icient evidence to conclude anything

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H0: μ = 10 vs Ha: μ < 10


a)  Reject H0 b)  Do not reject H0 c)  Reject Ha d)  Do not reject Ha




H0: μ = 10 vs Ha: μ < 10


a)  There is evidence that μ = 10 b)  There is evidence that μ < 10 c)  We have insuf8icient evidence to conclude anything


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

Elephant Example


“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 scienti:ic reasoning…” -‐Sir R. A. Fisher

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!


Statistical SigniHicance

When the p-‐value is less than α, the results are statistically signi-icant.

� If our sample is statistically signi8icant, we have convincing evidence against H0, in favor of Ha


p-‐value < α

Results would be rare, if the null were true

Reject H0

We have evidence that the alternative is true!

Results are statistically signi:icant

p-‐value ≥ α

Results would not be rare, if the null were true

Do not reject H0

Our test is inconclusive

Results are not statistically signi:icant

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Question #1 of the Day

Does red wine (resveratrol) promote weight loss?

If so, why?


•  Resveratrol, an ingredient in red wine and grapes, has been shown to promote weight loss in rodents. 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

Red Wine and Weight Loss

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


Study Design

This is a

a)  Experiment b)  Observational study


Study Design

Can we use this study to make conclusions about causality?

a)  Yes b)  No


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 difference statistically signi8icant? (should we reject H0: no difference?)

a)  Yes b)  No


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)  Mean resting metabolic rate is higher after resveratrol supplementation in lemurs b)  Mean resting metabolic rate is not higher after resveratrol supplementation in lemurs c)  Nothing

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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.


a)  Yes b)  No


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.


a)  Mean body mass is higher after resveratrol supplementation in lemurs b)  Mean body mass is not higher after resveratrol supplementation in lemurs c)  Nothing


Red Wine and Weight Loss In the test to see if locomotor activity changes after treatment, the p-‐value is 0.980.


a)  Yes b)  No


Red Wine and Weight Loss In the test to see if locomotor activity changes after treatment, the p-‐value is 0.980.


a)  Locomotor activity changes after resveratrol supplementation in lemurs b)  Locomotor activity does not change after resveratrol supplementation in lemurs c)  Nothing


Red Wine and Weight Loss In the test to see if mean food intake changes after treatment, the p-‐value is 0.035.


a)  Yes b)  No


Red Wine and Weight Loss In the test to see if mean food intake changes after treatment, the p-‐value is 0.035.


a)  Yes b)  No

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Informal strength of evidence against H0:

Formal decision of hypothesis test, based on = 0.05 :

statistically significant6 4 4 44 7 4 4 4 48

not statistically significant 6 4 4 4 4 44 7 4 4 4 4 4 48



Question #2 of the Day

What aspect of sunlight might help protect against

multiple sclerosis?


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 Lock5

Study Design

Can this study be used to make conclusions about causality, at least in mice?

a)  Yes b)  No


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 UV light provides protection against MS (UV light vs control group), the p-‐value is 0.002.

�  In testing whether Vitamin D provides protection against MS (Vitamin D vs control group), the p-‐value is 0.47.


Multiple Sclerosis and Sunlight � In testing whether UV light provides protection against MS (UV light vs control group), the p-‐value is 0.002.

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


Conclusions

p-‐value < α

Generic conclusion: Reject H0

Conclusion in context: We have (strong?) evidence that [:ill in alternative

hypothesis]

p-‐value ≥ α

Generic conclusion: Do not reject H0

Conclusion in context: We do not have enough evidence to conclude that

[:ill in alternative hypothesis]

H0

Ha


To Do � Read Section 4.3

� Do HW 4.2, 4.3 (due Friday, 10/23)

Dr.KariLockMorgan HypothesisTesting:* Conclusions

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