a primer for hypothesis testing i.e., the last “third” of this course (and just what do these...
TRANSCRIPT
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A Primer for Hypothesis Testing
i.e., the last “third” of this course
(and just what do these jokers know about it?)
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“It's so easy to defend the Status Quo,
- NOFX, 180 degrees
But when you see the end don't justify the means...
with everyone so cool and cynical.
it's just that 180 degrees.”
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Proof by Contradiction: the heart of Hypothesis Testing
Caffeine and Heart Rate Article
Sit on back whilst we do a little geometry and remember what a proof by contradiction is...
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ResultsCaffeine at 1.5 and 3.0 mg/kg body weight significantly lowered, by a range of 4 to 7 bpm, HR during all three submaximal exercise intensities compared to placebo(P < 0.05) but not at rest (P > 0.05) or maximal exercise (P > 0.05).
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“Research” Hypothesis – a belief to be tested using statistical methods...in this case, that caffeine will significantly lower HR during and after certain levels of exercise.
“Null” Hypothesis – the “status quo”… different than (often, the opposite of) the research hypothesis...in this case, that caffeine does not lower HR.
Hypothesis Test – the statistical method(s) used to support either the research or null hypothesis.
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“Caffeine significantly lowered HR during all three sub maximal exercise intensities compared to placebo (P < 0.05) but not at rest (P > 0.05) or maximal exercise (P > 0.05).”
Experimental Group vs. Control Group
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“Caffeine significantly lowered HR during all three sub maximal exercise intensities compared to placebo (P < 0.05) but not at rest (P > 0.05) or maximal exercise (P > 0.05).”
In any experiment, you start by assuming the opposite of what you’re trying to show (“assume the null”)
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“Caffeine significantly lowered HR during all three sub maximal exercise intensities compared to placebo (P < 0.05) but not at rest (P > 0.05) or maximal exercise (P > 0.05).”
P is called the “P – value” (“probability value”)
• P(get the data we did | null hypothesis is true)
• In this case, P(HR was lowered | caffeine had no lowering effect)
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“Caffeine significantly lowered HR during all three sub maximal exercise intensities compared to placebo (P < 0.05).”
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“Caffeine significantly lowered HR during all three sub maximal exercise intensities compared to placebo (P < 0.05).”
P(we got lowered HR data| caffeine had no lowering affect on HR during sub maximal
exercise) < 0.05
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“Caffeine significantly lowered HR during all three sub maximal exercise intensities compared to placebo (P < 0.05) but not at rest (P > 0.05) or maximal exercise (P > 0.05).”
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“Caffeine significantly lowered HR during all three sub maximal exercise intensities compared to placebo (P < 0.05) but not at rest (P > 0.05).”
P(we got our nonlowered HR data| caffeine had no lowering affect on HR at rest) > 0.05
“Caffeine significantly lowered HR during all three sub maximal exercise intensities compared to placebo (P < 0.05) but not at rest (P > 0.05) or maximal exercise (P > 0.05).”
P(we got our nonlowered HR data| caffeine had no lowering affect on HR during
maximal exercise) > 0.05
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The “big” idea:
• Large P – values imply that nothing unusual has happened…in other words, whatever
effect you’re studying…well, had no effect.
• “Large” P – values imply that the two pieces of your conditional probability ________…i.e.:
P(we got our nonlowered HR data| caffeine had no lowering affect on HR during
maximal exercise) > 0.05
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The “big” idea:
• Large P – values imply that nothing unusual has happened…in other words, whatever
effect you’re studying…well, had no effect.
• “Large” P – values imply that your data falls within ____________________
• “Large” P – values are generally those greater than ________________
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The “big” idea (continued):Small P – values (less than 5%) imply the
opposite…whatever you’re studying had a measurable effect.
• “Small” P – values imply that the two pieces of your conditional probability ________...i.e.:
P(we got our lowered HR data| caffeine had no lowering affect on HR during sub
maximal exercise) < 0.05
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The “big” idea (continued):Small P – values (less than 5%) imply the
opposite…whatever you’re studying had a measurable effect.
• “Small” P – values imply that your data falls outside of ____________________
• “Small” P – values are generally those less than ________________
Green tea article...
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“The proportion of lost or non-responding patients among the cases was 1.2%, similar to the percentage among the controls. Potential control women were excluded if they had a previous diagnosis of either breast cancer or another malignant disease.”
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“The proportion of lost or non-responding patients among the cases was 1.2%, similar to the percentage among the controls. Potential control women were excluded if they had a previous diagnosis of either breast cancer or another malignant disease.”
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What is this study trying to show, with respect to green tea and breast cancer? That is, what is the Research
Hypothesis (AKA, H1)?
Therefore, what’s the Null Hypothesis (H0)?
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“Green tea consumption was associated with a reduced risk of breast cancer with a statistically significant test for trend (P < 0.001).”
95% CI (one – sided)
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“Green tea consumption was associated with a reduced risk of breast cancer with a statistically significant test for trend (P < 0.001).”
P(we got our lowered breast cancer rate data| green tea had no affect on lowering
cancer rates) < 0.001
Does it appear that green tea is associated with lower rates of breast cancer?
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If you observed *, which is more likely: that your results
came from the green tea drinkers or non – green tea drinkers?
Second Hand Smoke article...
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Measurements and Main ResultsAt 0 to 1 hour (time of initial SHS exposure) most lung function parameters were significantly reduced (P < 0.05), but at 3 hours they were at baseline levels (P > 0.05).
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“At 0 to 1 hour (time of initial SHS exposure) most lung function parameters were significantly reduced (P < 0.05), but at 3 hours they were at baseline levels (P > 0.05).”
H0 ?
H1 ?
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“At 0 to 1 hour (time of initial SHS exposure) most lung function parameters were significantly reduced (P < 0.05), but at 3 hours they were at baseline levels (P > 0.05).”
P(we got our lowered lung function data | SHS had no lowering effect on lung
function from 0 to 1 hour) < 5%
Does SHS appear to affect lung function from 0 to 1 hour?
Could we be wrong? How?
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“At 0 to 1 hour (time of initial SHS exposure) most lung function parameters were significantly reduced (P < 0.05), but at 3 hours they were at baseline levels (P > 0.05).”
H0 ?
H1 ?
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“At 0 to 1 hour (time of initial SHS exposure) most lung function parameters were significantly reduced (P < 0.05), but at 3 hours they were at baseline levels (P > 0.05).”
P(we got our nonlowered lung function data | SHS had no lowering effect on lung
function after 3 hours) > 5%
Does SHS appear to affect lung function after 3 hours?
Could we be wrong? How?
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Ways to be wrong with Hypothesis Tests!
If…
…you get a small P – value…
…the common response is “something changed!”
What’s the chance that you’re wrong?
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Ways that Hypothesis Tests can Unfold
If…
…you get a small P – value…
…the common response is “something changed!”
P(false positive) = P(Type I Error) = α…usually 5%
Ways to be wrong with Hypothesis Tests!
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Ways that Hypothesis Tests can Unfold
In the SHS article…
“At 0 to 1 hour (time of initial SHS exposure) most lung function parameters were significantly
reduced (P < 0.05).”
Define this Type I error…in context.
Ways to be wrong with Hypothesis Tests!
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Ways that Hypothesis Tests can Unfold
If…
…you get a large P – value…
…the common response is “nothing changed.”
What’s the chance that you’re wrong?
Ways to be wrong with Hypothesis Tests!
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Ways that Hypothesis Tests can Unfold
If…
…you get a large P – value…
P(false negative) = P(Type II Error) = β
Ways to be wrong with Hypothesis Tests!
…the common response is “nothing changed.”
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Ways that Hypothesis Tests can Unfold
In the SHS article…
At 3 hours, most lung function parameters were not reduced
(P > 0.05).
Ways to be wrong with Hypothesis Tests!
Define this Type II error…in context.
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The takeaway about error (more to come):
If you get a small P – value and react appropriately, you could make a Type I
error (with probability α). If you get a large P – value and react
appropriately, you could make a Type II error (with probability β).