8.4 Comparing Proportions From 2 Populations Flashcards
P-value interpretations
Probability of getting a value (p^) as extreme or MORE/lESS than the one obtained (p), ASSUMING p is true (Ha is not true)
Supporting Ho means
WO4- X “exactly the same effect between Ho and Ha variables “
WO4- any definitive explanations to either Ho or Ha. There is ALWYAS the chance of missing or being incorrect!!
Two studies (samples) instructions
Find sample percentage of TOI for both
- p^ = successes/ sample size
- maybe -> % times n for successes
Is TOI variable’s p^ bigger than other TOI variables?
(Statistically significantly bigger -> 0.05 level
Since what i wrote out above is confusing, call one sample 1, and the other sample 2
Hypotheses for TWO samples : !!!! Ho =always= p1 = p2 = 0 !!!!
Ha : the TOI variable is more/less/ or different than the control group (placebo)
Ha: p1 > p2
- language- conducted on the efficacy of TOI 1 -> this language implies that it is effective in the 1st place and now are testing it!!!
!! This also means that TOI 1 is null
Test statistic (z)- use TOI as the stagnant # in hypothesis equation
SC
Stat.- prop - 2 sample - w summary
Hypothesis test for p1 - p2
P^1 - p^2 = 0
Often wont let you change level to 0.01
Test statistic z
Z from our sample = (p1 - p2) - 0 / SE
Z comparing to = p^1 - p^2
Means- contextualizes the p-value
PV is probability of getting the z (p1 - p2) as extreme or more than that from your samples if Ho is true
Language on hypothesis
When the studies are different time periods, the Ha will be about “declining or increasing results”
Its hard to know which sample is Ha, so from 2016 to 2018 it would be p1 > p2 if it declined
OH
What does the
PV is smaller if sample proportions are FAR APART _ large diff between the two (far away) gives larger absolute value of p1 - p2
Smaller sample size and imp on PV
N bigger -> SE small -> z bigger (REMEMBR when z is big, it doesn’t support Ho, and when p is small it doesn’t support Ho)
