Introduction to Null Hypothesis Significance Testing

Frequently used by

#thesis ↑ social, behavioral,

significance testing. and biological sciences



↳ 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

faction
↑ 3. Draw conclusion



ONE-Generate He/Hi
#
->Ho:MiFM2-Factions 6. Find defect size


(I
7. Calculate


↳ 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
-