8.2 P-value And Conclusion Flashcards
P-value
Shows how unusual (the shaded area) p^ WOULD be if the null is true since we always assume its true
Probability of getting p^ in the shaded area being the same or more extreme (exceeding expectation) than test statistic
TRanslate: IF Ho is true about Ho percentage of CURRENT poopulation, then the probability of p^ percentage (Ha) being idenitical to Ho percent, or MORE/LESS (>/<) extreme in the random sample (not pop but the # of successes being close to predicted Ho percent even tho they have different n) is p-value #
So if the probability that is represented by p-value is big, then p^ wins over po !!
!!!“There is 0.148 chance that p^ percent will be successes in sample”
So if number of successes (p^) is closer to mean (po) successes (p^ = 7 and po = 8) that is
p-value > (plausible, dont reject Ho, not SS)
Think of this !!!- when po and p^ are close on graph, the p-value is going to be big (only going up from 0.05 at mean, otherwise if its going the other direction, !!!***!!! its automatically smaller than 0.05)
P-value < when p^ is FARTHER from mean (SS)
When p-value gives evidence, its a bad thing for Ho (not plausible)
Statistically signiifcant
(Small) P-value < .05 = YES statistically significant (null true)
Here they say “have statistically significant evidence to REJECT Ho”
(big) P-value >.05 = NOT statistically significant (null untrue)
!!!! So a positive statistical significance would be when Ha is correct so think of how its significant to us, the statisticians
Support Ho - our hypothesis was wrong
But they’re terms are “fail to reject Ho” also “result (null) is consistent cuz its not proven wrong”
!!! Reject= statistically significant
Remember language
Context : null hypothesis is betting that the people in the trial are guessing and there are 22 trials, HALF with soda X and other HALF with soda Y
When the conditions are evenly distributed in the trials like this, the null is 50% chance (guessing)
Foundational things
Successes in trials= proportions from a sample -> p^
So they are p^ tick marks on the graph
So if number of successes (p^) is closer to mean (po) successes (p^ = 7 and po = 8) that is p-value >
When “if null hypothesis is true”
There will be n and null
If it the percentage (po) was true, then how many actual variables would there be in every n -> 22% times 200 !!
Looking at p^ on graph (greater than less than UD)
Where the man made tick is
Shaded area goes left or right
Left is < (!!p^ is less than p)
Going right is > ( !!p^ is more than p)
Going both ways : p^ has two man made ticks (p^ /= p)
One sided test + what makes p-value graphs special
looks for an “increase” or “decrease” in the po (parameter) whereas a two-tailed test looks for a “change” (could be EITHER increase or decrease, so you use test both) in the parameter.
One sided as in the graph has one side shaded (> or <)
ONLY PVALUE GRAPHS have tail only shaded areas
What to do on graph
P , SE, locate p^, shade area, reject or support Ho (p^ is in 2 SEs or not)
Significance level
Alpha
Anything below decisive p-value is small (reject Ho)
P-value !!!***!!! SMALL threshold (rejecting null) + sample/ pop remmebr
!!Threshold breaks into SUPPORTING null zone
Threshold = level of significance (a)
There is no “big threshold” - LOS doesn’t affect it when p-value is = or >
THIS LOS IS 0.05 WHEN NOT SPECIFIED
!!! P-value < 0.05 (small) = big z-score (more than 2/ !! Doesn’t match up with p) so reject null
If its 0.01 FE, all you do is see if your p-value is smaller (rejects null) or bigger (supports null)
!!!Even if p value is near .05 by even a significant amount, it supports Ho still, its only when p-value is really small
- we actually determine if there is a huge percentage difference between p^ and p by the p-value, not by eyeballing (p-value < o.o5, this means there is a huge difference)
!! Remember .05 is 5% so if you make your p value a percent would it be bigger than 5%?
!! Big p-value means the percentages are closer together
Big p-value means the man made tick started near the center (po)
If its within 0.05 from p (closer) its supporting (THIS MEANS TECHNICALLY ITS BIGGER THAN P and on the RIGHT hand side of it)
And when Ho is true, z-stat is always closer to 0 since 0 means “at the mean/ p”
This determines something about population from which sample came from, not sample itself f
Statcrunch
Stats
Prop
1 sample w/ summary
Look at summary table to see if it matches (look for z-stat and p-value)
Interpreting z score
P^ is from a sample
So on the graph it is certain amount of SEs (deviations from mean) from the Ho
Its not exactly SE since this pertains to specifically po and ho
Equation: p^ - po / SE Find SE by: SQR p(1-p)/ n
! Round SE to FOURR places for z stat
Z stat is how many SEs in between the p^ and po
SE is how number between p^ and p
If p value is small and z score is large, it’s obviously not supporting null
Watch out / another p-value determinant key
Watch out for z stats like 1.89 (big) since those automatically wont support Ho
Big z stat and small p-value = reject Ho
Smallest p value always means biggest z stat (like around 3)
Farther away z stat is from 0 -> smaller it end tails are (smaller p value area )
Rate remember
N times given p percent puts rate in action
