Letter
THE CLAIM
OF
to the
OF
Editor
INTAKE ON
SERUM LIPID LEVELS”
“LACK
OF
EFFECT
HIGH
FAT
Dear
Sir:
The
paper
by
C.
V.
Mann
under
the
above the
cholesterol
data
are
in
conformity
with two the data
the
title
JOURNAL’
in
statistical dence.
impress
and that no 1955 of thishypothesis found could, in fact, provides an interesting casetudy s in In regard fallacy applied to inadequate evi-experiments. subject “G” show The resulting conclusions will notfor but this is not anyone who examines the data, but sistency the issue of May-June often scan.
the and to use
greater
emerge to S
consistency
from 12-20,
than
such
the true
same for
hypothesis
perfect subject B
‘ ‘ , ‘ ‘
conso
all
busy
papers to its some
reiders they
title underscore
forego It
failure the
critical be
of this example
analysis useful,
paper to to point
may
therefore,
Sf of the for young are young out increase results from useful
12-20
the
general
about
men
men in with
is not
with
supported,
the hypothesis
though diet
in Sf the 35-100
justify
consistent
the results that somein
Downloaded from www.ajcn.org by guest on June 5, 2011
this
the Sf
high
Sf 21-35
fat
12-20 and
results
serum. admit
in
of
an
The no
elementary and
evidence “control” men, diet. from
requirements analysis.
in blood this paper samples
in
is from
experimental
obtained each of
design
The two young
conclusion.
two
The cannot
consideration of question
use change
problem.
of
“t” these
The of
tests
key,
or
of
other but
course, particularly
elaborations will
lies the Where
followed 15
The noting
by on
can that possibilities
five a
be
samples special
and predicted any
during kind
limitations in
the of
advance.
conclusions
clarify
in the
succeeding
fat valid Aside conclusions
days
high the
variability,
of intra-individual
variability.
conclusions
must there
are with
and measures
large
the errors are and
numbers
familiar
of
procedure
subjects
would
and
be
be
restricted men changing
“pemmican” are great.
to this situation from the control
diet for 15 days,
of healthy diet used
the limitations
young observations to the followed,
tions the
computation
after normally experimental getting
of
standard
assurance
deviathat within This
distributed periods.
Obviously the hypothesis under question : Does the high fat diet elevation of one or more of the items
‘ ‘
test
result simplest of the of
is
in
the both control ais not possible,
observations andattempt
of
and it
course,
is
with
highly
only
hazardous
2 control
to
of measure-
ment
in be
the the values controls. be
blood situation are expected measured such data this
serum?”
The where all any
most
would mental ceding rarely characteristics ous lipid But cholesterol
impressive
confirmation
higher Such in as show, perfect the than high experiments have case
conceivable
the the spontanethese that
tions.
experi- young pre-have canthe found effect, serum before In for with United thepeated been
with But
men
so few suppose
are like so
as
5 experimental we assume
American may attribute
observathat these
men to ? Let who them us, in
other we
studied
consistency when with much
same
in
kind
more examine
of
the
intra-individual
studies quantitative the experiments. on healthy
variability
possibilities men hundreds in of the re-
extensive
variation fractions. the
undertaking “control” States studies we
surprisingly, consistency
have
made
blood
they of 100 even yield
samplings
intra-individual
on mg
the
the
same
individuals
devia-
hypothesis
same for recorded inconsistent. is subject true
obtains
for “G” values the but for
for
not Sf
both
for subject and
subjects.
of S Sf 12-20 “B.” 35-100
Theand
tions
standard
measurements 21-35
±
18
Theindividual are per 12-20. ml
to ± 20 cholesterol
about have
per means
individual had daythe
100 ml about the and 7 to ± 9 mg ±
means same intra-individual for S the experience
Others within
With
no
more
ado,
then,
we
conclude
that and
74
a single
January-February
LETTER
TO
THE
EDITOR
0
variability
ported2 average
is
large.
Mann
himself
standard
has
devi-
re- But tions.
observed
we We
have
two subjects
in other In
and the
sets
of
observathe and
intra-individual
should, probabilities.
words,
combine simplest
ations for repeated 24 hours to be,
100 in Sf size be from assuming
‘
blood samples for cholesterol, ± and
The
15.8
taken mg per
values
within per 100 ml
for
most yield
this
favorable results
would mean
case, having
that,
where identical
since
both
(0.23)
experiments probabilities,
(0.23) =
ml in 12-20 Te of can, an
8 patients
‘
± 10.5 ± 4.0
mg mg
fat
9 “controls.’ were effect
‘
corresponding
± 5.8 and
on and the
per
roughly diet
100
the that
ml.2
0.05,
we
could
accept
two
minimal 0.23 level of freedom,
in the
values of
most
for
therefore,
estimate high
corresponding least “t” or, with would bility
1 .36. Hence we
with the five degrees
might fat with hope,
proba=“t”
favor-
‘proved’
at
the 5 per the high
cent
level
of probability
observations,
2 control
5 experimental
able
case,
of
to
high
establish and of
the
two fat
hypothesis
experiments,
of observa-
an
each
values
the If deviation rug 100 per ml we
that on the
take of 100 for S
variability fat diet is no
true intra-individual
of the greater
standard to
serum effect than on having tions, 20.54
be ±18 in standeach
2 control
experimental
effect as
control
diet. the the ml for 12-20, individual cholesterol we can means and 7 ± compute
with atrue mean mg per 100 ml
of two subjects.
small
as
increase
in
cholesterol
mg
the
per between
ard the
error control S. E.
V,
VP-
of
the and
=
difference experimental
V’(N1 pooled
1)
(S.
E. duff.) means: V/(N1N2)
computed
1)
With proper experimental this should have been clear ments were made, in which larger and be devised. attempt more In to
of using
planning, all of before the expericase, no doubt, a plan would indefensible to by
on of levels mean Mann of control “t’of ‘ tests” each
Downloaded from www.ajcn.org by guest on June 5, 2011
diff.
is the
+
suitable any
“t”
experiment case, it is the
tests separately
N2)
disprove small series
the says, “the
hypothesis observations.
the
of
where
variance,
as
device
(N1
V1
+
(N2
V2
these
Let analysis
very
us who compared
of
procedure
follow
the in
the five (two
(N1-1)+(N2-l)
V2, of course, are the variances,
mean the
Vi
and
observations or control
=
during
with
the
Pemmican
treatment
standard and
In 5, error V1 15.1 the
=
deviations experimental
present
squared, means,
problem,
for
the 2, N2
proves
were
respectively. where N1 = the
means of the
observations) (pp. 230-231). readily
to They be are given
by
the application The cholesterol from
here TABLE in Table
I per Paper 10() ml, by
data Figs.
I.
are 2.
18
the mg Vi
=
=
V2, for
difference per
cholesterol, And E. reach of
by the for 5
standard S 12-20,
reconstructed
his
1 and
of
±
100
of
100 ml.
for
where
7
=
V2, to
we
S.
must
ml.
probability,
Ii& order i.e., the
divided be
=
diff. = the
insist
5.8 mg per 5 per cent level
that the error of of “t” that
Cholesterol Figs.
Values, 1 and
in 2 in
mg the
Read Mann2
Postexperiment
Off
from
value,
the Let means difference,
ratio
2.57
the
difference
degrees
between
Subject Control Experiment
standard
freedom.
“G”
“B”
248,
243
301,
271,
264, 301,
273, 316, 321
280 305
266
the
difference
between 38.8 mg the
the
means. per 100 cholesterol
298,
267
327, 304,
Then
ml,
/15.1 = 2.57 the difference
required S mg 12-20 per and we 100 5 to
and X= between
show have ml. In
=
The with 2.97 for
‘
‘t” “G,”
values of and
for freedom “t” =
cholesterol in 2.68 for each “B.”
prove case, ‘ ‘ t’
‘
to
=
be,
means For 14.9 control
statistical
significance.
5 degrees
2.57
other observations
and
words,
=
Standof
from no un-
experimental
ard statistical 2 freedom the
reached at at given “t”
effect less
many
could the by true about observations
be
demonstrated effect were :39 mg per to of the raise 100
at
=
P 0.05 fat
tables show that 5 per cent level “t” = 2.57 and the
=
5 degrees for
of probability 0.01 per cent
analysis on says cholesterol
is
mean
high the ml.
diet
in level
that,
4.03. two
The observations
“t”
cholesterol
the
level
to
start
with,
the
subsequent
five
observations
76
THE
AMERICAN
JOURNAL
OF
CLINICAL
NUTRITION
[Vol.
4,
No.
1
on
‘
‘(V
‘
during
in
‘
Pemmican less
‘
feeding 4 per cent
5 of per the
would of
cent two
arise
experiment the
observations controls. Let
are us
not combine
homogeneous the on control 4 and means But 2 control post-exof these the observa-
by chance those on
The ments
than
less probabilities
trials
of
‘B’
in
than
and with tions trials.
trol
on
and as
“G”
and
“B”
by
of the
expressing
mean then, 94.5, the
the
each
convalue
combined
experi-
post-experiment percentage
observations We have 105.5, 10.0,
feeding
fewer
indicate would
than 2 out
that arise
of
the by
1,000
higher chance
trials.
values on fat subject for that in something
The best
subject.
101.0, values, 100.0 and 99.0,
mate
to mg
. But
from
a high per
these
fat of 100 ml, says no his The G
> 0.05)
experiments
results in 32.1 for evidence
is that
mean rises
the
in
change
11.7
esti- values, periment
108.4, 108.2,
diet
serum being
respectively.
cholesterol Mann
±
that
10.8,
“G” and his that lipid only
and
“B,” use
31.3 ±
of by Sf the B this 12-20 been possible
respectively. “t” had high levels evidence increased from Mann
standard ± 2.63
testence
errors and
between
100.0)3.42
of
means
=
these
means
error of and
prove
the “t”
=
to
differ-
be
± 0. 1 6, standard
2.40. the
universe
is 3.42 ±
“revealed fluenced intake. subject
(0.10 >
subject and
serum cholesterol indicated that
‘ ‘
levels
(108.2 infreedom fat
to of one belong values.
this
that in the
means
the same
that
post-experiment
At 4 degrees of odds are about 14
values as do the not control
suggestive had is this his
P
they How in
Downloaded from www.ajcn.org by guest on June 5, 2011
by
these
the
treatment.
data ?
Perhaps “control,”
computation
-ANCEL
KEYS,
PH.D.
included
part cated But used of he if we his
the
post-experiment
though
observations
he explicitly
as
mdiare additional
1.
MANN,
Laboratory University
of of
Physiological Minnesota
Hygiene
used two the unwittingly
observations
introduce
and
an
not
three.
REFERENCES G. 1955. H. G. in \. serum L., LAWRY, : Spontaneous lipoproteins.
E.
post-experiment
observations
V. : lipid
Lack levels.
of
effect AM. J.
of
CLIN.
a high
fat
intake 3:
on
hypothesis tions
fat diet
: are not
and
“The influenced
are proper
post-experiment by
samples
observaprevious
of the
serum
NUTRITION
the this? that
high
control
2.
230,
CHANDLER, MANN,
V.,
POTEE,
K. induced
G., 8:
and varia723.
and
universe.” trary,
Can computation
we
prove indicates
On the conthese post-
tions 1953.
Circulation
COMMENT
BY
DR.
MANN
Dear
Sir:
I believe
iie These treatment levels. more It of bias
that
in the
Keys
do appears
is coirect
of serum to me indicate the
when
these that that
he
the it
accuses
data. dietary would
experience-
interpretation
extent
we have environment alterations. be findings
of
and my
observed both Since
these experiments facilities-with the
in with we necessary with of a positive very per rapidly low levels 100 in for Walker’ calorie fat of ml, which 2S diet two three adult and have to men
were variability
in their dietary
the
usual these
observations increased now between at compare the several the
cholesterol
without published use we the
appropriate
to
compare
control observations levels will show be and
the
rather as I
observed
treatment than fIrst
it
is
not
plentiful
differences
levels to
but
In short did
still
the period
undocumented
studies with cholesterol
estimates
of
found balance
Keys.
that accomthe a
measured
and
method of about It chance.
as
Keys
with 0.01
so
differences that interest
elegantly
these to might compare
elaborated.
a probability attributed this
Theplished
serum and to another limited gained 70
increased young
38 men
In men conwhile young
mg experiment2 weight
respectively. days
is
of