Class notes

Introduction to Null Hypothesis Significance Testing

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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...

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Uploaded on June 26, 2023
Number of pages 6
Written in 2022/2023
Type Class notes
Professor(s) Mellanie stollstroff
Contains Null hypothesis significance testing (nhst)

one sample t tests
independent samples t tes
paired samples t test
null hypothesis significance testing nhst

Institution
University of Toronto (U of T )
Education
Statistics
Course
STA130

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Comprehensive Notes for All of PSY201

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1. Class notes - Introduction to null hypothesis significance testing
2. Class notes - Introduction to statistics in psychology, central tendency, and variability
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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
-

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