SPS
SS: k With
hin-Groups
s ANOVA & Post Hoc
c Tests
e means of tw
wo or more qu
uantitative va riables obtai ned from dep
pendent samples
Application: To compare the
(repe
eated measu
ures or match
hed groups). The two or more
m
scores m
might be the same variablle measured at different
times or under different conditions, comp
parable variab
bles measure
ed at the sam
me time, or so
ome combina
ation.
Rese
earch Hypoth
hesis: The data come from
m the Pet sho
op database. The researccher hypothessized that stores would
tend
d to display more fish than other types of
o animals, few
wer reptiles, and an interm
mediate numb
ber of mamma
als.
H0: ffor this analy
ysis: Pet sto
ores display the same me
ean number o
of reptiles, fissh and mamm
mals.
Analyze Gen
neral Linear Model
M
R
Repeated Mea
asures
Repeated Me
easures Defin
nition Windo
ow
 R
o enter your name fo
or the IV in the
e “Within-sub
bject Factor N ame” box (pe
ettype)
o enter the number of
o conditions of
o the IV in the “Number off levels” window (2)
o click the
t “Add” buttton
o click the
t “Define” button
b
 R
Repeated Me
easures window -- highligh
ht the variable
es that are the
e DV score fo
or each condittion and click the arrow
 O
Options -- che
eck the “Desc
criptives” box
S Syntax
SPSS
GLM reptnum fish
hnum mamlnu
um
/WS
SFACTOR=Pettype 3
/ME
ETHOD=SSTY
YPE(3)
/PR
RINT=DESCR
RIPTIVE
/WS
SDESIGN=Pe
ettype.
 DV fo
or each IV con
ndition
 name
e of WG IV & # conditions
 get descriptive
d
sta
ats
 tells that
t
Pettype is a WG IV
1
.
Reme
ember, even if the printout shows it,
neverr report p = .000, because that would
sugge
est there is no
o possibility of a Type 1
error. Instead, repo
ort “p < .001”
The p-value of means th
hat there is
less than a .1% chance that this
result is a T
Type I error
Use the “S
Sphericity Assumed” df,
Mean Squa
are Error & p
2
LSD Pairwise Co
omparions Us
sing SPSS
SPSS
S will perform
m the analysis
s, but not via the
t GUI! If yo
ou click on the
e “Post Hoc” button it bring
gs up the scre
een, but you
can’tt select anythiing. But, we can
c get the LSD (uncorrec
cted) results b
by using synta
ax.
GLM reptnum fish
hnum mamlnu
um
/WS
SFACTOR=Pettype 3
/ME
ETHOD=SSTY
YPE(3)
/EM
MMEANS=TABLES(Pettype
e) compare(P
Pettype)
/PR
RINT=DESCR
RIPTIVE
/WS
SDESIGN=Pe
ettype
 asks for p
pairwise comp
parisons amo
ong WG condiitions
N
Notice that ea
ach pairwise ccomparison is
s
p
presented twicce!
Reptile vs F
Fish = Fish vvs Reptile
B
Be sure you g
get the directio
on of each
ssignificant me
ean difference
e right!!
Reptiles < Fish
Reptiles < Mammals
Fish
= Mammals
T
These LSD p--values can a
also be used
fo
for Bonferroni tests. Had w
we been
in
nterested in o
only the comp
parison of
R
Reptile vs Fish and Reptile
e vs
M
Mammals, we
e would want to test each
u
using p = .05 / 2 = .025.
S does not sh
how the comp
pute t-values for
f the pairwis
se compariso
ons. They can
n obtained as t = Mean Diffference /
SPSS
Std.E
Error. For Re
eptiles vs Fish
h, this would be
b t = -14.667
7 / 1.990 = 7. 370
3
LSD & HSD using
g the Post Hoc “Computators”
SPSS doe
es not provide
e post hoc an
nalyses for all ANOVA mod
dels (e.g., WG
G designs). Also, there may be
occasions when you
y want to co
ompare mean
ns from a stud
dy that didn’t p
post analysess, or did them
m differently th
han you would
d
have
e preferred. One additional advantage of using these is that you ca
an provide yo
our readers w
with the LSD o
or HSD values
s
that w
were the basis of your pos
st hoc tests.
http:://psych.unl.e
edu/psycrs/s
statpage/esc
comp.exe
http://psych.u
h
unl.edu/psyc
crs/statpage//computator_
_131a.xls
The ttwo Computa
ators will produce slightly different resultts, and those results mightt be slightly diifferent from tthe SPSS
results, because they
t
all use slightly differen
nt t-table values and Stude
ent’s t-table va
alues. The sp
pecific table ((with the
ze rounding) can be seen for the xls version if you exxtend the righ
ht side of the spread sheett.
applied sample siz
Applyying these LS
SD/HSD value
es to the pairw
wise comparis
sons… Rept iles = 9.25
Pair

Mean
n Difference 
Re
eptiles v Fish
Reptiles v M
Mammals
14.667 <
12.25
50 <
Fish = 23.92
2
Fish v Ma
ammals
> 2.417
LSD Result

<
<
=
HSD Result

<
<
=
RH:
RH: ssupport?
Mammalss = 21.50
The re
esearcher hyp
pothesized th
hat stores wou
uld tend to dissplay more fissh than otherr types of
animals, fewer repttiles, and an intermediate number of ma
ammals.


<
Supported
<
Supporte
ed
<
Not supporrted
 Pa
artial Support
4
Postt Hoc Follow--ups using t--tests
SPSS
S does not co
ompute post hoc
h tests for within-groups
w
comparisonss. However itt is simple enough to obtain pairwise
comp
parisons of the means usin
ng paired t-tes
sts. The results closely corrrespond with
h an LSD ana
alysis -- both p
produce
unco
orrected p-valu
ues.
SPSS Sy
yntax
pare Means  Paired-Sa
amples T testt
Analyze  Comp
Highlight the conditions/var
c
riables of eac
ch pair
 H
 U
Use the arrow
w to move then into the “Pa
aired Variable
es”
w
window
WITH
T-TEST PAIRS= repttnum reptnu
um fishnum
fish
hnum mamln
num mamlnu
um (PAIRED)
/MISSIN
NG=ANALYS
SIS.
The 3 co
ondition pairs
RH: The research
her hypothesized that storres would tend to display m
more fish than
n other types of animals, fe
ewer
reptiiles, and an in
ntermediate number
n
of ma
ammals.
These resu
ults tell us tha
at
As hypothe
esized - more
e fish than rep
ptiles in
these store
es.
As hypothe
esized – more
e mammals th
hen
reptiles in tthese stores.
Contrary to
o the hypothe
esis – equivale
ent
numbers o
of fish and ma
ammals.
These p
p-values can also be used
for Bonfferroni tests. Had we been
n
interested in only the
e comparison
n v Private & Private v
of Chain
Coop, w
we would wan
nt to test each
h
using p = .05 / 2 = ..025.
5
Reporting the Results
Results based on the LSD tests
Table 1 summarizes the data for the numbers of animals displayed at the stores. There was a significant difference
among the distributions of the three types of animals (F(2,22) = 22.22, p < .001, Mse = 33.391). Pairwise comparisons
using LSD revealed that, consistent with the research hypothesis, more fish than reptiles were displayed on average and
also more mammals than reptiles were displayed on average (p < .01 for each) . However, contrary to the research
hypothesis, there was not a significant difference between the average number of fish and mammals displayed (p = .291).
These results provide partial support for the research hypothesis.
Results based on the pairwise t-tests
Table 1 summarizes the data for the numbers of animals displayed at the stores. There was a significant
difference among the distributions of the three types of animals (F(2,22) = 22.22, p < .001, Mse = 33.391). Pairwise
comparisons using LSD revealed that, consistent with the research hypothesis, more fish than reptiles were displayed on
average, t(11) = 7.371, p < .001, and also more mammals than reptiles were displayed on average, t(11) = 4.335, p =
.001. However, contrary to the research hypothesis, there was not a significant difference between the average number of
fish and mammals displayed. These results provide partial support for the research hypothesis.
6