MathMnemonics
Statistics Ditties
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PLAR = PeopleLove
A
Reason to Reject, but don't Reject Without a Reason--look
some more..
P Less
than Alpha, Reject
(If P Less than Alpha, then Reject Ho, but
if you can't reject, then still don't "accept")
"All Assumptions are False; else they wouldn't be assumptions"
and note assume can be decomposed to make an Ass/U/Me.
Seldom right, but never uncertain:
Since Ho is usually expressed as an equality, the probability it is exactly
on target is low. People who are never uncertain are seldom right. People
who assert things with no reservations are more often wrong than right.
Failing to reject a null hypothesis is not the same thing as "accepting"
it as the truth.
Just because you didn't have a big enough difference to show it false
doesn't mean you should accept it. Statistics means never having to say
you are certain.
ANOVA = Assume No Variables
Affect
the means unless they're shown to be significantly different by F>Fcrit;
P<alpha
Ho in Analysis of Variance (ANOVA) is that there are no differences.
Only if the evidence causes you to reject this do you conclude there are
significant effects.
APOR = Assume --> Predict --> Observe --> Reject (or not)
If the observations are consistent with predictions, and have a
high probability of happening just by chance, then you don't have enough
evidence to throw out the assumption.
on the other hand,
If Violets look red and Roses look blue: NO WAY this could happen!
Assumptions aren't true.
Reject Ho if observations don't fit the predictions. If the
probability of this happening is very low, then maybe you grabbed the wrong
bouquet. Adopt an alternative hypothesis.
8.02 E-08 = 0.0000000802 --- this is a very small
number.
If you see something like this for a Pvalue, it is smaller than
alpha, and so you should Reject the null hypothesis.
Is there a significant regression relationship? Beta big or Beta zero?
t tests tell the tail.
In regression, we are testing whether the coefficients are different from
zero.
Ho is that there is no effect, which would mean Beta is =0. t tests
are used because the coefficients can be either positive or negative
far enough different from zero that they can't reasonably be explained
by chance.
F>Fcrit; P<alpha are two ways of saying the same thing.
"way out" observations should make you question your assumptions.
Roses are Red
Violets are Blue
Adopt alternatives
Shown to be true.
Else:
Roses grow High
Violets grow Low
Live with the Null,
as the status quo.
The null hypothesis is usually the boring possibility assumed correct
unless strong evidence is provided to show it is unreasonable. Thus Ho
is often referred to as the "status quo" (The state in which things
will be unless changed). The alternative hypothesis is usually expressed
as a negation of Ho-- e.g. "No, they aren't the same, they are different."
(two tail) or, "No, they aren't the same, A is bigger than B." (one tail-specified
directionality). If there is enough evidence to reject the Ho, then
the alternative hypothesis is accepted as long as it is a negation, rather
than another "equals" statement (such as we used to estimate the probability
of a type II error).
Note "assume" connotes something different from "accept" --see assumptions
above. Then, of course, there is the issue of what is "enough evidence."
For Chi, Z, F or T--the meaning is the same for P
Pvalue is interpreted the same in all the tests:
(If Ho is true), the P-VALUE is the PROBABILITY of observing such a VALUE
(whether it be t, z, f, or X)
We reject Ho if Pvalue < alpha--if alpha is our reject region than
any value in that region is significant enough to reject our null hypothesis,
therefore, a Pvalue less than that is very significant that we should reject
Ho and that is also why Pvalue is also termed the "observed significance
level"
Chi, Z, F, T Big--> P small --they mean the same, reject them all
A test statistic larger than the critical value for a given alpha is the
same thing as saying the Probability of getting this result if Ho is true
is smaller than alpha. Thus, you reject the Null hypothesis.
Quadratic Plus means turning UP
Interaction and regression analysis:
concave upward--quadratic term is > 0
concave downward--quadratic term is < 0
Alpha
Larger than
P-value
Ha
Accepted
ARENA
Always Reject Every Null (hypothesis) After alpha
KISS
Keep It Simple Stupid
T>Tcrit and P<alpha is simply redundant.
F>Fcrit and P<alpha is simply redundant.
What test to use T or Z?
Use the word SNOW:
Standard Deviation
Not Known
Omit Z
We use T
Prepare. Attention. Review. Action.
Prepare: Read the chapter before the class, and height-light important
and questionable information in the book,
Attention: Pay attention to the professor while he or she is
lecturing, also need to take good notes for review. Ask questions,
and pay attention to other students¡¯ questions.
Review: Review the notes right after class, it¡¯s
good time to memorize the information while it still fresh and fully understand.
Action: After the materials are
prepared, educated, it¡¯s time to exam how much you have learned
and how efficient your study habit.
As long as students follow all these four easy step
and should get a decent grade.
Roses are red
Violets are Blue
Never assume
Ha to be true.
------------------------------------------------------------------
One boy ate
Nine pies with
Six spoons and puked
5% back up.
(referring to a +/- 1.96 rejection region at 5% alpha)
-------------------------------------------------------------------
Ripilts
Reject If Pvalue Is Less Than
Significance.
People
Like
A
Really
Nice
Home
P,L,A,R,N,H = if P is Less than Alpha, Reject
the Null Hypothesis
With a P value very low,
The closer we come to zero
It is not by mere chances
This event has come to pass us.
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