2011. Vol.2, No.6, 631-632
Copyright © 2011 SciRes. DOI:10.4236/psych.2011.26096
The Effect-Size: A Simple Methodology for Determining and
Evaluating the “Effect-Size”
Marcel Lourel1, Nicolas Gueguen2, Alexandra Pascual3, Farida Mouda4
1Lecturer in PsychologyOccupational Health, University of Artois, IUFM Nord-Pas de Calais, France;
2Lecturer in Social and Cognitive Psychology, University of Bretagne-Sud, IUT de Vannes, France;
3Reader in Social Psychology, University of Bordeaux 2, Bordeaux, France;
4Psychologist, CREPS Rouen, France.
Received May 1st, 2011; revised July 8th, 2011; accepted August 16th, 2011.
Effect-size measurement is a practice that is gradually encouraged indeed required by psychological and social
behavior reviews in addition to the classical test of statistical significance. This paper is written as a methodo-
logical note that presents the conceptual interest of the effect-size, the main measurement indicators and their
Keywords: Effect-Size, Test of Significance, Statistical Evaluation
The Effect-Size Principle
When a statistical test is carried out such as a test comparing
2 means or an
2 independence test, we base our analysis and
our interpretation on the probability of the value produced by
the test (e.g. the value for the Student t for the purpose of a test
comparing 2 means or the
2 for an independence test). In fact,
if the probability seems below or equal to a reference probabi-
lity well known to any social sciences researcher – the famous
p = .05- we conclude that there is a “statistically significant”
effect. Whether or not the result is significant will subsequently
determine our way of interpreting our data which will cones-
quently directly affect the way in which we theoretically ex-
plain this effect. Furthermore, this significance or lack of sig-
nificance will also, as a consequence, affect our subsequent
research work. Most of the articles published are based on
works that demonstrate statistically significant effects. In fact,
the famous “.05” probability determines what is offered to the
scientific community since we rarely come across publications
that do not provide the main results with this level of signify-
scance. Accordingly, the impact made by this test interpretation
value is far from being insignificant.
Why Do We Need to Measure the Effect-Size?
If we query why it is necessary to quantify the effect-size,
this requires 2 major parameters to be taken into account for the
research: the size of the samples used to quantify the phenom-
ena that we study and the extent of the differences between the
variables subject of our analysis. However, in the case of infer-
ential statistics, sample size dependence is the same as for small
samples; major differences between variables are required if a
statistical difference is to be expressed to within .05 whereas in
the case of excessive numbers, minute deviations will be enough
to produce differences. Then, effect-size indicators become
completely relevant by reinstating their full meaning to the
amplitude of the deviations. In effect, we will intuitively under-
stand the force of conviction of a methodology that allows us to
increase the baccalaureat pass rate for a small lycée made up of
a few classes of students rather than report a significant 0.7%
difference between two schools. The effect-size once again
gives meaning to the deviations. Furthermore, quantifying the
importance of an effect frequently constitutes the first stage in
the collation of data that will be used for a meta-analysis.
However, once again, we have to accept that meta-analysis is a
way of synthetically analysing literature that has unseated the
classic review of questions especially given its predictive capa-
bility and its capacity for testing the validity of a hypothesis
using a wide corpus of data produced by various research works
(Lipsey & Wilson, 2010).
For the purpose of illustrating our argument, we shall take an
actual example involving a submission technique well-known
in the literature: The foot in the door. This technique consists in
putting a preliminary request before proceeding with the final
request: by so doing, the final request is more easily accepted
than if it had been submitted first. Talking of which, the ex-
periment carried out in 1999 (Guéguen & Fischer-Lokou, 1999).
involving a sample of 3280 people stopped in the street (two
groups of 1640 people) revealed a 28.3% acceptance rate under
control conditions and a 42.5% acceptance rate using the foot in
the door approach. This produced the following spread:
2 calculated here is:
2(1, 3280) = 72.38, p < .0001.
The same conclusion is reached in the precept study (Harris,
1972): the difference is significant in the probabilistic sense of
the word; however, in the Harris experiment (op.cit., 1972), the
value of
2 was found to be lower than that produced by the
experiment carried out by the authors (Guéguen & Fischer-
Table 1.
Distribution of subjects by condition (experimental vs control).
Condition addressed
Subject response Foot-in-the-Door Control
Request accepted 697 464
Request rejected 943 1176
Lokou, 1999). whereas there were greater deviations between
the two groups (See Table 1): 33.3% (44.4% - 11.1) for one
(Harris, 1972) compared with 14.2% (42.5 - 28.3) for the others
(op.cit., 1999). Measuring the effect-size merely consists in
translating the deviation and no longer the probability of ob-
taining said devia- tion on the basis of the size of the sample.
Determining Effect-Sizes
The ideal would consist in identifying an indicator that is in-
dependent of the sample size so that the surveys can be com-
pared with each other and, above all, so that we can assess the
effect-size observed. Indeed, sample size sensitivity is one of
the first reasons that led statisticians to work on the concept of
the effect-size.
The contingency coefficient Phi (written
) is one of the in-
dicators used to quantify this significance of deviations between
our two proportions. It is easily applied because we only need
to calculate
(n being the total number of individuals
Accordingly, if we take the data provided by the two contin-
gency tables above,
72.383280 or 0.15 in the case
of the Guéguen and Fischer-Lokou experiment (1999).
What is the next step once this coefficient
has been calcu-
lated and the effect-size assessed? Cohen (1988) put forward
coefficient values used to measure the effect-size. Three cate-
gories were identified: the low effect (0.1); the medium effect
(.03) and the high effect (0.5)
The effect is qualified as low/medium in the survey [2]. Thus,
therefore, we can be allowed to question the scope of the analy-
sis from the mere statistical significance viewpoint or as an
assessment of the value for ² (the opposite of the importance
The Various Effect-Size Indicators
In order to be able to calculate the various indicators used for
measuring effect-size on the basis of the types of variable or of
the analyses carried out, we have separated the headings so that
you can quickly identify the appropriate procedure. We have
used standard indicators for quantifying the effect-size (see
Cohen, 1988 for a more in-depth review). As far as we are
aware, there are many others (e.g. comparison of a mean with a
standard; comparison of 2 means from separate samples; com-
parison of 2 means for linked samples; comparison of frequent-
cies in a contingency table etc.) (see Rosenthal & Rosnow,
1999 for a more in-depth review). In the case of some indica-
tors, it is clear that the effect-size is easily calculated because
the indicator had been produced from earlier analyses (e.g. the
linear correlation coefficient). Furthermore, when the analysis
is performed, most statistics processing software offer options
allowing the user to access these indicators. We should also
note that there are online statistical resources available on the
Internet for calculated these various “effect-sizes” such as:
Measuring effect-size is an approach that the social psycho-
logy researcher must now include, whenever possible, into his
data analysis. This becomes all the more important when exten-
sive samples are used because they encourage the effect to be
revealed even when these are limited. Foreign psychology re-
views and especially the Anglo-Saxon reviews increasingly
tend to demand that these indicators be presented on the same
footing as the various strategic inferential tests used. Some
research used to the meta-analysis computation based an ad-
justed variance and/or upon a pooled variance of effect size.
Berk and Freedman (2003) are skeptical regarding the effect-
tiveness of the meta-analysis. The authors questioned the as-
sumed independence of studies and to randomization for forced
inclusion of studies. It’s a very important problem for scientific
research. Further, the authors are skeptical about the social
dependence (and financial) between the some pool of peer-
review journals and then taken to a subsequent meta-analysis
by the scientific community. For authors: “In the present state
of our science, invoking a formal relationship between random
samples and populations is more likely to obscure than to clar-
In this article, we have attempted to present the principle of
this quantification and the way in which customary indicators
are calculated. Obviously, there are presently a great many
indicators that refer to specific analysis cases and that take
various utilisation criteria into account. However, determining
these indicators can help the social psychology researcher to
break free from the classic inferential model used in statistical
analysis and to opt for a method for assessing his data based on
a more equitable assessment of the effects. Many researchers
expose the imperialism of the inferential method and the .05
value as objectionable and recommend that these indicators be
imposed (Thompson, in press). Therefore, if we use these indi-
cators, we would be led to view some of our theoretical analy-
ses and interpretations in a different light.
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