P-value
ONE TAIL: If your null hypothesis is that a vaccine does not increase autism, what do you do if the vaccine decreases autism?
Always attribute the opposite to chance.
If you were so wrong about the system that you predicted the opposite results, what is the next step?
Study it better before you make any more predictions
What is the null hypothesis usually?
That the two statistics are identical
how do you tell the P value looking at a histogram?
the p value is a proportion of the total area
The P value definition:
the probability, under the assumptions of the null hypothesis, of obtaining a result equal to or more extreme than what was actually observed.
Why do statisticians like C.I.'s?
they are more straight forward and informative
P value is NOT the probablity that the null hypothesis is ___
true
Disadvantage of One tail
unusual results on the unexpected side of the null distribution will always be attributed to chance
Why do scientists like P values?
prefer to test hypothesis (choose between alternatives)
P value is actually the
probablity of getting your results if you assume that the null hypothesis is true
The probability that you would observe smaller differences is
1-P value
At the end of the day, you have to interpret the P value. What are two ways to interpret it?
1. You say, my P value is low, and my hypothesis makes sense, so I will reject the null hypothesis. 2. You say, this may have been due to chance so I choose not to reject the null hypothesis.
For populations with SYMMETRICAL distributions, the one tailed P value =
1/2 of the two tailed P value
What does a P value begin with?
A tentative assumption (null hypothesis)
when do you predict which way data falls in 1 tail P value?
Before Data is collected
Statisticians tend to prefer ___
C.I.
What does P value tell you?
probability of obtaining a result equal to or "more extreme" than what was actually observed, assuming that the NULL hypothesis under consideration is true
What else?
If the p-value is equal to or smaller than the significance level (α), it suggests that the observed data are inconsistent with the assumption that the null hypothesis is true and thus that hypothesis must be rejected (but this does not automatically mean the alternative hypothesis can be accepted as true).
What is the correct interpretation of P=.03
If the two populations are identical (null hypoth is true), then there is a 3% chance that you could observe the differences you observed or larger/smaller.
Advantage of one tail?
Lower sample size (20%)
Can you switch back to a two tailed test when results are unexpected?
NO
Is the P value the probability that the result occurred due to sampling error?
NO
Is the null hypothesis usually true?
NO, usually false!
Can you use your old data for your new experiment?
No
Is the null hypothesis the same for 1 and 2 tail?
No
When is it appropriate?
Only when you have predicted which way the data will sway
Scientists tend to use ___ values
P
Simple definition of P value:
P value is the probability of getting the observed result or more extreme under the null model.
The null hypothesis is an ASSUMPTION about the _____
POPULATION not the sample
One tailed P values are an _ ___ decision
a priori
How do you get the P value?
add the probabilities of all your extremes
One tailed P value
asks about 1 extreme
two tailed P value
asks about 2 extremes
1-P value is not the probability that the null hypothesis is _____
false
advantage of one tail
gives more focused hypothesis so it reduces your necessary sample size (decrease cost and risk)