Introduction to Null Hypothesis Significance Testing
6 views 0 purchase
Course
STA130
Institution
University Of Toronto (U Of T
)
This is a brief introduction to the logical process and formulaic aspects of null hypothesis significance testing (NHST). It includes a basic run-down of the three possible t-tests involved in doing NHST. There are also practice work included. Conceptually, NHST can be difficult to understand and a...
↳ NHST
is statistical procedure thatproduces true.
probabilities when
accurate NH is
↳ Many
positive cases Do
alternative hypothesis
NotDove another
e ↳ Null Hypothesis IS Set
against (AH)
↳ All predicts difference -> Hi:Mr M,
↳ Predicts equality - Ho: Mo=M, :onretainHill when youreset the
#
Null: Supports Att
↳
Rejecting
Retained Null:Does not move it, simply allows ita s
↳ a
possibility
AlternativeHypothesampleDifference
(i
Wall: You cannotchoose between Ho and A,
↳
Retaining
: Ponebbainesaudelaaonshore
↳ Directional
Drawingconcedefrom Al
e table):
RejectHot Air
Basic Null Steps (NHST
↑ population
mean(4r) ↳ Observed - a critical + (from table):Retain Ho (B)
1. Describe Ho and Hi
SSES
o *
=
*
2. Gather Data
3. Choose Statistical test
n. T-values and compare
Conclusion
↳
5. Statement
S**
Standard Erran Estimated
Pop'nvariability - 5 =
NAST:One (1) -
Sample test
↳
Statistical testof the hypothesis thata sample has same mean as the population (0:unknown)
H0:X Mo
H.:F Mo
=
Ho:M, Mo =
Ho:M, F Mo
EX. Are the Toronto
↳ Is observed sample
Raptorstaller
mean
than the
the same
GE
as
Canadian?
an estimated population mean?
=
**
S*
(estimate
(sample)
mean population mean) ↳ Same steps apply
SDD X-Mo = From t-table:Whatyou need?
Drawing conclusions) Ex 2.4
=
↳ You need
↑ A
- 1. Alpha (a)
38 astribution
2.
3.
2 failed
Degrees
or 1-tailed
of Freedom (n-1)
test?
pop'n +- distribution
sample tribution sampling
Difference(SDD)
of
(df n
=
-
1 4)
=
(Mo x SDD)- =
-> continous values
EffectSize (d) -
Aquantification ofthe degree of separation between (2) distributions
↳ d 0.2
=
Small Effect KEY:Effect size is
largest
=oll; Il
When the difference
a a = ↳ d 0.5 = medium Effect
Effects
between mean is largest
4 d 0.8 =
Big
and estimated popin.v
unknown &
is smallest.
At
equality
Note: you use two-tailed
testing for All" because itincorporates
possibility m ore
of or less from mean
(meaning, 2 ends of normal distribution) null always KEY:Significance level denoted by
Two-tailed one-tailed
↑ contains
equality
(A) alpha specifies the size of
Ho: M 23
=
Ho:M123 Hr:M123 the rejection region in distribution
Hi:M=23 H,:M<23 H,: > 63
(lefttalled) (Right failed)
, dependent
# samples t-test that
evidence not strong conclude effect
↑
is to an
↳ The
meaning probability (P): p is the probability of exists; suggests the sample is too small and
the obtained statistical test value when Ho (NH) is too high. Alow p-value
variability shows that
true (I
rejection region) the effect is large, replicable, and
significant.
↳ p-how likely is the observed difference between to ↳
knowing p does reveal
not information
groups due chance
to
-
high P-value suggests about a (degree of Separation)
Independent
Samples t-test:
↳) used to compare two (2) sample means (X) from meted factions; usedto
compare if (21 population means are indeeddifferent. Pairedsampled tests are
usedwhen there Intrinsic, related
is a natural, non-experimentally connection
between (2) factions
↳ Independent -
Do men own more shoes than women?1.Ho and Hi
↳ Paired -
Do husbands own more shoes than wives? 2. Gather data
3. Choose test
Example-Does gender effect show collection size? 4. Calculate t's
↳ Ho: ll, le
Determ (x)
men andwomen same # of shoes
=
-
own
0.05-
↳
Hi:M, FM2
=
men andwomen own different# of shoes
-
two-tailed test (2.5%)
STEP
THREE (Step 2:data
given) -
statistical test
FOUR
STEP T- critical and observed t-value When N, Nz =
↑
-
faction () Faction (a)
↑ Mean
mean
t=
2;d Nz 2 =
actions
scx,
+Ex-
↳ Sample Sie
⑤- *
L Standard Error Differenc N,(N.-13
sampling distribution ofdiference)
(*Yo+it)
when it
Six,-xil=
STEP FIVE-
Drawing conclusions
-
The benefits of buying summaries with Stuvia:
Guaranteed quality through customer reviews
Stuvia customers have reviewed more than 700,000 summaries. This how you know that you are buying the best documents.
Quick and easy check-out
You can quickly pay through credit card or Stuvia-credit for the summaries. There is no membership needed.
Focus on what matters
Your fellow students write the study notes themselves, which is why the documents are always reliable and up-to-date. This ensures you quickly get to the core!
Frequently asked questions
What do I get when I buy this document?
You get a PDF, available immediately after your purchase. The purchased document is accessible anytime, anywhere and indefinitely through your profile.
Satisfaction guarantee: how does it work?
Our satisfaction guarantee ensures that you always find a study document that suits you well. You fill out a form, and our customer service team takes care of the rest.
Who am I buying these notes from?
Stuvia is a marketplace, so you are not buying this document from us, but from seller mashiyatahmed. Stuvia facilitates payment to the seller.
Will I be stuck with a subscription?
No, you only buy these notes for $9.09. You're not tied to anything after your purchase.
