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Graduate Student Journal of Psychology
2022, Vol. 19

Copyright 2022 by the Department of Counseling and Clinical Psychology
Teachers College, Columbia University

Evaluating the Sampling Precision of Social Identity 
Related Published Research

�ȅǈǓ�vǩǹșȅǿॹ���ƺΚǩǏ�eȖƺЙǾȅΛॹ��ƺǿǏ��eȅǿΡ�vƺǿǠॹ
New Mexico State University 

Cong Wang,
University of Nebraska Omaha

Social identity theory states that a person’s sense of who they are is based largely on their group membership(s). We 
categorize ourselves, identify with groups, and compare our groups with others, in the hopes that our self-esteem is 
ǾƺǩǿȠƺǩǿǓǏ�ȅȖ�ǈȅȅșȠǓǏ�ǟȖȅǾ�ȠǦǩș�ǉȅǾȒƺȖǩșȅǿঀ���ȒȖǓȖǓȕȣǩșǩȠǓ�ȅǟ�șǉǩǓǿȠǩЙǉ�ȖǓșǓƺȖǉǦॹ�ǓΚǓǿ�ȖǓǠƺȖǏǩǿǠ�șȅǉǩƺǹ�ǩǏǓǿȠǩȠΡॹ�ǩș�
ȠǦƺȠ�ȖǓșǓƺȖǉǦǓȖș�ǿǓǓǏ�Ƞȅ�ǈǓ�ǉȅǿЙǏǓǿȠ�ȠǦƺȠ�ȠǦǓ�ǓǾȒǩȖǩǉƺǹ�ǟƺǉȠș�ȖǓƺǹǹΡ�ƺȖǓ�ǟƺǉȠȣƺǹআ�ȠǦƺȠ�ǩșॹ�ȠǦƺȠ�ȠǦǓ�șƺǾȒǹǓ�șȠƺȠǩșȠǩǉș�ȖǓȒȅȖȠǓǏ�
accurately estimate corresponding population parameters; this is known as sampling precision, or how precisely our 
sample corresponds to our population. By employing the recently invented a priori procedure, the present research 
assesses the sampling precision with which published experimental and correlational social identity research statistics, 
across three time periods, estimate corresponding population parameters. We hypothesized 1: The precision of re-
search in the social identity area should be hopefully below the 0.10 level or at least the 0.20 level for true experimental 
designs and 2: Precision in the social identity area should be improving, with recent social identity research enjoying 
ƺ�ȒȖǓǉǩșǩȅǿ�ƺǏΚƺǿȠƺǠǓ�ȅΚǓȖ� ǹǓșș� ȖǓǉǓǿȠ� șȅǉǩƺǹ� ǩǏǓǿȠǩȠΡ� ȖǓșǓƺȖǉǦঀ���șƺǾȒǹǓ�ȅǟࢶࢸ��ƺǉƺǏǓǾǩǉ�ȒƺȒǓȖșॹ� ƺǉȖȅșșࢷࢵ��ǏǩАǓȖǓǿȠ�
journals was collected for analysis. For experimental studies, the mean precision level was 0.51 and the median pre-
cision level was 0.50 (n = 39). For correlational studies, the mean precision level was 0.24 and the median precision 
ǹǓΚǓǹ�Λƺșࢱ�ঀࢱࢳ�শǿ�઀ࢶࢶ�ষঀ�eǦǓ�Ǿƺǩǿ�ЙǿǏǩǿǠș�ƺȖǓ�ȒǓșșǩǾǩșȠǩǉॹ�ǈȣȠ�ΛǩȠǦ�ȠǦǓ�ǠǹǩǾǾǓȖ�ȅǟ�ǹǩǠǦȠ�ȠǦƺȠ�ȒȖǓǉǩșǩȅǿ�ǩș�ǩǾȒȖȅΚǩǿǠঀ�
?ǲͧ͡ȤȵǮȸ࣒�ȱȵǲǨȈȸȈȤȞ࣓�ǨȤȞϫǮǲȞǨǲ࣓�ȸȤǨȈǙȘ�ȈǮǲȞȿȈȿͧ�ȿȅǲȤȵ࣓ͧ�Ǚ�ȱȵȈȤȵȈ�ȱȵȤǨǲǮɂȵǲ࣓�ǲȸȿȈȝǙȿȈȤȞ

 The overarching idea of social identity theo-
ry is that the individual and the group are inter-
twined. People are born into social societies, they 
develop ties to social groups, they classify them-
selves as members of those social groups, and the 
ȣǿǩȕȣǓ� ǉȅǾǈǩǿƺȠǩȅǿș� ȅǟ� ȠǦȅșǓ� șȅǉǩƺǹ� ǉǹƺșșǩЙǉƺȠǩȅǿș�
create unique individuals. According to Stets and 
�ȣȖǷǓ� শࢱࢱࢱࢳষॹ� ǩǏǓǿȠǩȠΡ� ǩș� ȖǓМǓΠǩΚǓ� ǩǿ� ȠǦƺȠ� ǩȠ�ǾƺǷǓș� ǩȠ-
șǓǹǟ� ƺǿ� ȅǈǴǓǉȠ� ΛǦǩǉǦ� ǉƺǿ� ǈǓ� ǉƺȠǓǠȅȖǩΦǓǏॹ� ǉǹƺșșǩЙǓǏॹ�
ƺǿǏ� ǿƺǾǓǏ� ǩǿ� ȖǓǹƺȠǩȅǿ� Ƞȅ� ȅȠǦǓȖ� șȅǉǩƺǹ� ǉǹƺșșǩЙǉƺȠǩȅǿșঀ�
 Social identity is a person’s knowledge that they 
belong to a social group or category (Hogg & Abrams, 
1988). A social group consists of individuals who hold 
ƺ�șǓȠ�ȅǟ�ǉȅǾǾȅǿ�șȅǉǩƺǹ� ǩǏǓǿȠǩЙǉƺȠǩȅǿșঀ�eǦǓșǓ�ǠȖȅȣȒș�
are further categorized as the ingroup, which consists 
of individuals who are like the self, and the outgroup, 
which consists of individuals who are unlike the self. 
This process of accentuating the similarities with the 
ǩǿǠȖȅȣȒ�ƺǿǏ�ǏǩАǓȖǓǿǉǓș�ΛǩȠǦ�ȠǦǓ�ȅȣȠǠȖȅȣȒ�ǹǓƺǏș�Ƞȅ�ƺ�
second process called social comparison. The process 
of identifying and categorizing yourself is known as 
self-categorization. Social identity researchers com-
monly assume that by classifying social identities 
through self-categorization (and by extension accen-
tuating similarities with the ingroup, etc.), individ-
uals will enhance their own positive self-esteem by 
promoting the ingroup and denigrating the outgroup.

 No matter what the theoretical criticisms of so-
cial identity happen to be, the theoretical basis of 
identity and social identity research is not the current 
ȕȣǓșȠǩȅǿঀ�eȖƺЙǾȅΛ� ƺǿǏ�EΡȧΦ� শࢺࢲࢱࢳষ� ǏǓǾȅǿșȠȖƺȠǓǏ�
ǩǾȒȖǓǉǩșǩȅǿ� ΛǩȠǦ� ȖǓșȒǓǉȠ� Ƞȅ� ЙΚǓ� ƺȖǓƺș� ȅǟ� ȒșΡǉǦȅǹȅǠΡ�
(social, developmental, clinical, cognitive, and neuro) 
ƺǿǏ� eȖƺЙǾȅΛॹ� /ΡǾƺǿॹ� ƺǿǏ� ?ȅșȠΡǷ� শࢱࢳࢱࢳষ� ǏǓǾȅǿ-
strated imprecision with respect to marketing research 
șȒǓǉǩЙǉƺǹǹΡঀ� KȣȖ� Ǡȅƺǹ� ǿȅΛ� ǩș� Ƞȅ� ǓΠȒƺǿǏ� ȠǦƺȠ� ǹǩǿǓ� ȅǟ�
inquiry and address a potential criticism that, to our 
ǷǿȅΛǹǓǏǠǓॹ�Ǧƺș�ǿȅȠ�ǈǓǓǿ�ǾƺǏǓঀ�^ȒǓǉǩЙǉƺǹǹΡॹ�ȅȣȖ�Ǡȅƺǹ�
is to address the issue of the sampling precision of so-
cial identity research. Sampling precision is a measure 
of how close a sample’s descriptive statistics are to the 
corresponding population parameters. Usually, and in 
the present case, this is measured as a fraction of a stan-
dard deviation. If the sampling precision of that re-
search is impressive, it would imply that, whatever the 
ȅȠǦǓȖ� ǏǓЙǉǩǓǿǉǩǓș� ȅǟ� șȅǉǩƺǹ� ǩǏǓǿȠǩȠΡ� ȖǓșǓƺȖǉǦॹ� ƺȠ� ǹǓƺșȠ�
there would be good reason to trust that the sample 
statistics are a good estimate of the corresponding pop-
ulation parameters. In contrast, if the sampling preci-
sion of social identity research is poor, it would imply 
that the sample statistics are not good estimates of the 
corresponding population parameters. A further im-
ȒǹǩǉƺȠǩȅǿ�ΛȅȣǹǏ�ǈǓ�ȠǦƺȠ�ȠǦǓ�ЙǿǏǩǿǠș�ǉƺǿǿȅȠ�ǈǓ�ȠȖȣșȠǓǏॹ�
which would be a preliminary problem that future re-



115

SOCIAL IDENTITY PRECISION

search would have to solve before addressing the more 
ǉȅǿǉǓȒȠȣƺǹ�ǩșșȣǓș�ǩǏǓǿȠǩЙǓǏ�ǩǿ�ȠǦǓ�ǟȅȖǓǠȅǩǿǠ�ȒƺȖƺǠȖƺȒǦঀ
 To summarize the present thinking, we believe 
that getting the empirical facts straight is vital both 
for theorizing and for evaluating theories. If a theory 
is unable to explain human behavior reliably and val-
idly, then it is not a strong psychological theory. By 
ensuring that sample statistics are good estimators of 
population parameters, the reliability and validity of 
theoretical conclusions related to social identity theory 
ǉƺǿ�ǩǿșȒǩȖǓ�ǠȖǓƺȠǓȖ�ǉȅǿЙǏǓǿǉǓঀ�'ȣȖȠǦǓȖॹ�ȠǦǓ�ǠǓǿǓȖƺǹǩΦƺ-
tion of these theories would also be improved. Thus, 
for the purpose of this article, the actual content of 
social identity theory is unimportant. What is most 
important, is the sampling practices of that research. 
To examine this issue, we use the a priori procedure.
The A Priori Procedure
 The a priori procedure (APP) assumes the cru-
ciality of obtaining sample statistics that are good 
estimators of corresponding population parameters 
শeȖƺЙǾȅΛ� ǓȠ� ƺǹঀॹ� �ষঀࢱࢳࢱࢳ @ǓșȠ� ȠǦǓ� ȖǓƺǏǓȖ� ǏȅȣǈȠș� ȠǦǩșॹ�
imagine a fanciful scenario where Laplace’s omni-
scient demon appears and informs us that there is no 
relationship between sample statistics and correspond-
ing population parameters. In that case, no empirical 
reports would be trusted, nor would sample statis-
tics be taken to provide good tests of hypotheses. Of 
course, there is no demon, but considering the fanciful 
scenario renders salient the importance of estimation.
 Given that estimation is crucial, there are two re-
lated questions. First, there is the precision question: 
How close do we desire that sample statistics be to 
their corresponding population parameters? Second, 
ȠǦǓȖǓ� ǩș� ȠǦǓ� ǉȅǿЙǏǓǿǉǓ� ȕȣǓșȠǩȅǿॸ� vǦƺȠ� ȒȖȅǈƺǈǩǹǩȠΡ�
do we insist on of being that close? The basic idea of 
ȠǦǓ��XX�ǩș�ȠǦƺȠ�ȠǦǓ�ȖǓșǓƺȖǉǦǓȖ�ǾƺǷǓș�șȒǓǉǩЙǉƺȠǩȅǿș�ǟȅȖ�
ȒȖǓǉǩșǩȅǿ�ƺǿǏ�ǉȅǿЙǏǓǿǉǓॹ�ƺǿǏ�ȠǦǓǿ�ƺǿ��XX�ǓȕȣƺȠǩȅǿ�
ȒȖȅΚǩǏǓș�ȠǦǓ�ǿǓǉǓșșƺȖΡ�șƺǾȒǹǓ�șǩΦǓ�Ƞȅ�ǾǓǓȠ�ȠǦǓ�șȒǓǉǩЙ-
cations. If the researcher collects the necessary sample 
size, or a larger one, then the researcher can be assured 
ȅǟ�ǾǓǓȠǩǿǠ�ȠǦǓ�șȒǓǉǩЙǉƺȠǩȅǿș�শeȖƺЙǾȅΛ�ǓȠ�ƺǹঀॹࢱࢳࢱࢳ�ষঀ
 Consider an example. Suppose that a researcher 
intends to collect a single sample and is interested in 
ЙǿǏǩǿǠ� ȅȣȠ� ȠǦǓ� șƺǾȒǹǓ� șǩΦǓ� ǿǓǓǏǓǏ� Ƞȅ� ǈǓ� �ઔࢶࢺ ǉȅǿЙ-
dent of obtaining a sample mean within one-tenth 
of a standard deviation of the population mean. Us-
ǩǿǠ�ƺǿ�ǓȕȣƺȠǩȅǿ�ǈΡ�eȖƺЙǾȅΛ�শࢸࢲࢱࢳআࢺࢲࢱࢳ�ষॹ�� � � � � � � � � � � � ॹ
 

where n is the sample size, f is the desired precision, 
and z(1-c)/2 is the z-score that corresponds to the de-
șǩȖǓǏ� ǏǓǠȖǓǓ� ȅǟ� ǉȅǿЙǏǓǿǉǓঀ� 2ǿșȠƺǿȠǩƺȠǩǿǠ� ΚƺǹȣǓș� ǩǿȠȅ�
the equation indicates the following: n=(1.96/0.1)2 

઀ࢵࢹࢴঀࢷࢲઇࢶࢹࢴঀ�eǦȣșॹ�ȠǦǓ�ȖǓșǓƺȖǉǦǓȖ�ΛȅȣǹǏ�ǦƺΚǓ�Ƞȅ�ǉȅǹ-
ǹǓǉȠ� ��ȒƺȖȠǩǉǩȒƺǿȠșࢶࢹࢴ Ƞȅ�ǾǓǓȠ� șȒǓǉǩЙǉƺȠǩȅǿșঀ� 2ǿșǩșȠǩǿǠ�
on 385 participants may seem extreme compared to the 
much smaller sample sizes in most research, however, 
this provides a much greater level of precision than in 
ȠΡȒǩǉƺǹ�ȒșΡǉǦȅǹȅǠΡ�ȅȖ�ǾƺȖǷǓȠǩǿǠ�ȖǓșǓƺȖǉǦ�শeȖƺЙǾȅΛ�૭�
EΡȧΦॹࢺࢲࢱࢳ�আ�eȖƺЙǾȅΛॹ�/ΡǾƺǿॹ�૭�?ȅșȠΡǷॹࢱࢳࢱࢳ�ষঀ�2ǟ�
the researcher is willing to settle for less precision, such 
as precision at the 0.3 or 0.4 level typical in much social 
psychology research, the necessary sample size would 
drop dramatically. This precision can be treated much 
ǹǩǷǓ�ǉȅǿЙǏǓǿǉǓ�ǹǓΚǓǹॹ�ΛǦǓȖǓ�ΛǓ�ΛƺǿȠ�Ƞȅ�șǦȅȅȠ�ǟȅȖ�ƺࢶࢺ�ઔ�
ǉȅǿЙǏǓǿǉǓ�ǹǓΚǓǹ�ǈȣȠ�ǾƺΡ�ǦƺΚǓ�Ƞȅ�șǓȠȠǹǓ�ǟȅȖࢱࢺ�ઔॹ�ǟȅȖ�ȒȖǓ-
cision we can shoot for .1 but may have to settle for .3 
or.4, depending on the circumstances of the research. 
 Although the APP was designed to be used 
pre-data, it can be used post-data too, which is a neces-
sary condition for the present work. Remaining with 
the foregoing example, suppose the researcher wanted 
to collect 385 participants but only succeeded in ob-
ȠƺǩǿǩǿǠࢱࢱࢲ��ȅǟ�ȠǦǓǾঀ�hșǩǿǠࢶࢺ�ઔ�ǉȅǿЙǏǓǿǉǓ�ƺș�ƺ�ǉȅǿ-
ventional value, what is the precision entailed by 100 
participants? To answer, the foregoing equation can 
be algebraically manipulated to yield f as opposed to  
   

Thus, if the sample size is 100, rather than 385, 
the actual precision would be 0.196 rather than 
ȠǦǓ� ǏǓșǩȖǓǏ� ΚƺǹȣǓ� ȅǟ� �ࢱࢲঀࢱ শeȖƺЙǾȅΛ� ǓȠ� ƺǹঀॹ� ষঀࢹࢲࢱࢳ
 Researchers are usually interested in more com-
ȒǹǓΠ� ǉƺșǓș� șȣǉǦ� ƺș� ǏǩАǓȖǓǿǉǓș� ǈǓȠΛǓǓǿ� ǠȖȅȣȒșॹ� ǉȅȖ-
ȖǓǹƺȠǩȅǿ� ǉȅǓГǉǩǓǿȠș� ȅȖ� ǟȣǿǉȠǩȅǿș� ȅǟ� ȠǦǓǾ� শǓঀǠঀॹ� ȖǓ-
ǠȖǓșșǩȅǿ� ΛǓǩǠǦȠșষॹ� ƺǿǏ� șȅ� ȅǿ� শeȖƺЙǾȅΛॹ� �ষঀࢺࢲࢱࢳ 2ǿ�
more complex cases, the mathematics can become 
extremely complex; but it is not necessary to address 
that complexity here because Hui et al. (2020) pub-
lished links to programs for rendering the computa-
tions and these are free and user-friendly. However, 
ȠǦȅșǓ�ǩǿȠǓȖǓșȠǓǏ�ǩǿ�ȠǦǓ�ǾƺȠǦǓǾƺȠǩǉș�ǉƺǿ�ǉȅǿșȣǹȠ�eȖƺЙ-
mow and MacDonald (2017) for multiple groups, 
eȖƺЙǾȅΛॹ�vƺǿǠॹ�ƺǿǏ�vƺǿǠ�শࢱࢳࢱࢳষ�ǟȅȖ�ǏǩАǓȖǓǿǉǓș� ǩǿ�
means for independent samples or dependent samples, 
ƺǿǏ� vƺǿǠ� ǓȠ� ƺǹঀ� শࢲࢳࢱࢳষ� ǟȅȖ� ǉȅȖȖǓǹƺȠǩȅǿ� ǉȅǓГǉǩǓǿȠșঀ
 To place into perspective the importance of preci-



116

WILSON, TRAFIMOW, WANG, WANG

șǩȅǿ�ΚƺǹȣǓșॹ�ΛǓ�ȠȣȖǿ�Ƞȅ�eȖƺЙǾȅΛ�ǓȠ�ƺǹ�শࢹࢲࢱࢳষঀ�vǩȠǦǩǿ�
șǉǩǓǿȠǩЙǉ�ǩǿȕȣǩȖΡॹ�ȖǓȒǹǩǉƺȠǩȅǿ�ǩș�ƺ�ΚǩȠƺǹ�Ƞȅȅǹ�ǟȅȖ�ȠǦǓ�Κƺ-
lidity and reliability of a theory. If the results based on 
a theory cannot be replicated, then that theory lacks 
șȣГǉǩǓǿȠ�șȣȒȒȅȖȠঀ�2ǿ�ƺ�șǩǿǠǹǓেșƺǾȒǹǓ�șȠȣǏΡॹ� ǩǟ�ΛǓ�ǏǓ-
sire a precision value of .1, and we only have a sample 
size of 10, then the probability of replicating would 
only be .06! However, with 111 participants, that 
probability becomes .5, and so on as the sample size in-
creases. The bottom line, then, is that the APP can be 
used, in a post-data fashion, to determine the sampling 
precision of varied published social identity research, 
where the sample sizes are reported. And this in turn 
can be used to draw conclusions about the possible 
replicability, validity, etc. of that published research.
 One question that often comes up is why sam-
ȒǹǩǿǠ�ȒȖǓǉǩșǩȅǿ�ǾƺȠȠǓȖș�ƺȠ�ƺǹǹঁ�2ǟ�ΛǓ�ǦƺΚǓ�ƺ�ǠȅȅǏ�ǓАǓǉȠ�
size, then what is the point of the APP? Well, think 
ƺǈȅȣȠ�ǓАǓǉȠ�șǩΦǓঀ�2ǟ�ΛǓ�ƺȖǓ�ǹȅȅǷǩǿǠ�ǟȅȖ�ƺ�șȒǓǉǩЙǉ�ǓΠȒǓȖ-
ǩǾǓǿȠƺǹ�ǓАǓǉȠॹ�ƺǿǏ�ȅȣȖ�ǓАǓǉȠ�șǩΦǓ� ǩș� ǹƺȖǠǓ�ǓǿȅȣǠǦॹ�ǿȅ�
matter how small a sample we have, we will be able to 
șǓǓ�ȠǦǓ�ǓАǓǉȠঀ�/ȅΛǓΚǓȖॹ�ǏȅǓș�ȠǦƺȠ�ǾǓƺǿ�ȠǦƺȠ�ȠǦǓ�ΛǦȅǹǓ�
population of the world will also undergo that same 
ǓАǓǉȠঁ�[ǓƺǹǩșȠǩǉƺǹǹΡ�ǿȅȠঀ�eǦƺȠ� ǩșॹ� ǿȅ�ǾƺȠȠǓȖ�ΛǦƺȠ� ȠǦǓ�
ȅǈȠƺǩǿǓǏ� ǓАǓǉȠ� șǩΦǓ� ǟȅȖ� ȅȣȖ� șƺǾȒǹǓॹ�ΛǓ� ǦƺΚǓ� ǿȅ� ǩǏǓƺ�
ǩǟ� ȠǦƺȠ�ǓАǓǉȠ�șǩΦǓ� ǩș�ǉǹȅșǓ�Ƞȅ�ȠǦǓ�ȒȅȒȣǹƺȠǩȅǿ�ǓАǓǉȠ�șǩΦǓ�
unless there has been some sort of APP calculation. 
Therefore, there is no way to know how well the ob-
ȠƺǩǿǓǏ�ǓАǓǉȠ�șȣȒȒȅȖȠș�ȅȖ�ǏǩșǉȅǿЙȖǾș�ȠǦǓ�ǦΡȒȅȠǦǓșǩș�ȅȖ�
theory from which the hypothesis was derived. This 
is the strength of the APP and sampling precision. 
Sampling precision values, and the APP, can be used 
Ƞȅ�ȒȖȅΚǩǏǓ� ǩǿǉȖǓƺșǓǏ�ǉȅǿЙǏǓǿǉǓ� ǩǿ�ȅȣȖ� șƺǾȒǹǓ� șȠƺȠǩș-
Ƞǩǉșॹ�ƺǿǏ�ȠǦȣș� ǩǿǉȖǓƺșǓǏ�ǉȅǿЙǏǓǿǉǓ�ȠǦƺȠ� ȠǦǓ�ǓАǓǉȠ�ΛǓ�
are seeing is representative of the overall population, 
ǿȅȠ�ǴȣșȠ�ȠǦƺȠ�ȠǦǓ�ǓАǓǉȠ�ǩș�ȒȖǓșǓǿȠ�ǩǿ�ȅȣȖ�șƺǾȒǹǓঀ�KΚǓȖ-
all, the APP sampling precision values can be viewed 
ƺș� ƺ� ǉǹȅșǓǿǓșș� șȠƺȠǩșȠǩǉ� șǩǾǩǹƺȖ� Ƞȅ� ǉȅǿЙǏǓǿǉǓ� ǹǓΚǓǹș� ǩǿ�
that the more stringent criteria we use, the more con-
ЙǏǓǿȠ� ΛǓ� ǉƺǿ� ǈǓ� ǩǿ� ȅȣȖ� ǩǿǟǓȖǓǿǉǓș� ƺǿǏ� ǉȅǿǉǹȣșǩȅǿșঀ
 In this study, we tested competing hypotheses from 
optimistic versus pessimistic viewpoints. From an opti-
mistic viewpoint, the expectations would be as follows.
 H1: The precision of research in the social identi-
ty area should be hopefully below the 0.10 level or at 
ǹǓƺșȠ�ȠǦǓࢱ�ঀࢱࢳ�ǹǓΚǓǹ�ǟȅȖ�ȠȖȣǓ�ǓΠȒǓȖǩǾǓǿȠƺǹ�ǏǓșǩǠǿș�শeȖƺЙ-
mow, 2018). 
 H2: Precision in the social identity area should be 

improving, with recent social identity research enjoy-
ing a precision advantage over less recent social identi-
ty research. 
 Of course, from a pessimistic perspective, the 
foregoing hypotheses should not be supported. If the 
precision of social identity research is worse than 0.30 
শȠǦƺȠ� ǩș� ǹƺȖǠǓȖষॹ� ȠǦƺȠ�ΛȅȣǹǏ�șȣȒȒȅȖȠ�ȒǓșșǩǾǩșǾ�শeȖƺЙ-
ǾȅΛॹࢹࢲࢱࢳ�ষঀ�'ȣȖȠǦǓȖॹ�ǩȠ�ΛȅȣǹǏ�ǈǓ�ȣǿǏǓșǩȖƺǈǹǓ�Ƞȅ�ЙǿǏ�
that precision is not improving, as an increase in preci-
sion is related to an increase in replicability and stron-
ger generalization of theory, and as research methods 
have supposedly improved as time passes, we should 
hope to see an improvement in sampling precision 
as well. Finally, because the APP has never been used 
systematically to analyze correlational research, the 
relevant correlational analyses to be presented can be 
ǉȅǿșǩǏǓȖǓǏ�ǓΠȒǹȅȖƺȠȅȖΡ�ƺș� ƺ�ЙȖșȠ� șȠǓȒ� ȠȅΛƺȖǏș�ƺ�ǾȅȖǓ�
integral use of the APP in sampling analysis.

Method
 The goal of this research was to investigate the pre-
cision (how close a sample statistic would be to its pop-
ulation parameter) of a sample of published social iden-
tity research. To investigate the question of whether 
șȅǉǩƺǹ�ǩǏǓǿȠǩȠΡ�ȖǓșǓƺȖǉǦ�ЙǿǏǩǿǠș�ƺȖǓ�ȒȖǓǉǩșǓ�ǓǿȅȣǠǦ�Ƞȅ�
be trusted, we applied the APP programs presented by 
Hui et al. (2020) to test the precision of the studies in-
cluded in a sample of published social identity research. 
The present a posteriori use of the APP has been sys-
ȠǓǾƺȠǩǉƺǹǹΡ�ǓǾȒǹȅΡǓǏ�ǈΡ�eȖƺЙǾȅΛ�ƺǿǏ�EΡȧΦ�শࢺࢲࢱࢳষ�
ƺǿǏ�eȖƺЙǾȅΛॹ�/ΡǾƺǿॹ�ƺǿǏ�?ȅșȠΡǷ�শࢱࢳࢱࢳষ�ǟȅȖ�ǓΠȒǓȖ-
imental research but not for correlational research.

Procedure
 A total sample of 75 academic papers (see Table 
1) was collected, prior to data analysis, broken down 
into 25 papers per time period across three time peri-
ods: 2014 to 2021, 1995 to 2001, and 1975 to 1981. 
2Ƞ�Λƺș� ǩǾȒȅȖȠƺǿȠ� Ƞȅ� ǩǿǉǹȣǏǓ� ƺ� șƺǾȒǹǓ� șȣГǉǩǓǿȠǹΡ� Ǐǩ-
verse to be representative of the existing literature, 
while also ensuring that the sample broke into equal 
portions. The sample included articles from 46 dif-
ferent journals, randomly selected from the set of ar-
ticles that met our criteria, from multiple academic 
disciplines (i.e., psychology, advertising, business, so-
ciology, etc.). The primary criteria for selection were:
1. Must include social identity as a primary tar-

get of interest for investigation. This may be as 



117

a theoretical concept, an applied concept, etc. 
This was checked via the mention of social iden-
tity in subject terms, titles, or the paper itself.

2. Must directly specify the methodology (cor-
relational, between-subjects, etc.). This is im-
portant, as determining the method of anal-
ysis is vital to understanding the precision of 
particular samples using the APP equations.

3. Must have a publication date within one of the three 
date ranges (1975-1981, 1995-2001, 2014-2021). 
These date ranges were chosen as an exploratory (not 
exhaustive) representation of research across time.

 The articles were picked using the institution-
ƺǹ� ǹǩǈȖƺȖΡ� șǓƺȖǉǦ� Ƞȅȅǹঀ�?ǓΡΛȅȖǏș�ȣșǓǏ� Ƞȅ�ЙǹȠǓȖ� ȖǓșȣǹȠș�
were as follows: social identity, social identity theory, 
SIT, experimental, correlational, and research. Arti-
cles were picked using a random method of 2 articles 
per results page starting from the top. If the article 
did not specify social identity, the research method, 
or was outside of the appropriate date ranges, then 
it was skipped, and the next article was picked. Once 
two articles on the page were selected, we moved 
to the next results page and began selection again. 
All studies picked in this sample were quantita-
tive leaning (i.e., analysis was done quantitatively).
 Once the articles were collected, the relevant in-
formation was cataloged via an Excel spreadsheet 
শǏƺȠƺ� ƺΚƺǩǹƺǈǹǓ� ǟȖȅǾ� vǩǹșȅǿॹ� eȖƺЙǾȅΛॹ� vƺǿǠॹ� ૭�
Wang, 2021 via the OSF open-access database). The 
information cataloged included the citation for the 
paper, journal, publication year, number of studies 
included in the paper, sample sizes, and number of 
conditions. While some of this information is not 
pertinent for the actual precision analysis, examin-
ǩǿǠ� ǏǩАǓȖǓǿǉǓș� ǩǿ� ȠǦǓ� ǾǓƺǿș� ƺǿǏ� ǾǓǏǩƺǿș� ǈΡ� Ȓȣǈ-
lication year and methodology type is of interest for 
potential broader investigations and conclusions.
 To determine the precision of each study, we used 
the APP programs listed in Hui et al. (2020). Given sam-
ple sizes reported in the articles, and assuming a conven-
Ƞǩȅǿƺǹࢶࢺ�ઔ�ǉȅǿЙǏǓǿǉǓ�ǹǓΚǓǹॹ�ȠǦǓ�ȒȖȅǠȖƺǾș�ȒȖȅΚǩǏǓ�ȠǦǓ�
ȒȖǓǉǩșǩȅǿ� ǹǓΚǓǹॹ� ǈȣȠ�ΛǩȠǦ� ƺ� ǉȅǾȒǹǩǉƺȠǩȅǿঀ� ^ȒǓǉǩЙǉƺǹǹΡॹ�
because some studies were experimental whereas oth-
ers were correlational, there are mathematical reasons 
why the precision of the correlational studies cannot be 
compared directly to the precision of the experimental 

studies (Wang et al., 2021)1. Consequently, results per-
taining to experimental studies and results pertaining 
to correlational studies will be presented separately.

Results
 There were too few mixed designs for analysis 
and so we focused on between-participants experi-
mental studies and correlational studies. For experi-
mental studies, the mean precision level was 0.51 (SD 
= .25) and the median precision level was 0.50 (n = 
�ষঀ�eǦǓșǓ�ЙǿǏǩǿǠșࢺࢴ șȣȒȒȅȖȠ�ƺ�ȒǓșșǩǾǩșȠǩǉ�ΚǩǓΛ�ȅǟ�ǓΠ-
perimental social identity research. For correlational 
studies, the mean precision level was 0.24 (SD = .16) 
and the median precision level was 0.20 (n = 55). How-
ever, we reiterate that the precision of correlational 
research cannot be compared to the precision of ex-
perimental research. As correlations range from -1 to 
+1, and the precision value pertains to the fraction of 
a variance (not a fraction of a standard deviation), the 
degree to which this level of precision in correlation-
al research is pessimistic or optimistic is a judgment 
call. Certain theories and paradigms may require more 
șȠȖǩǿǠǓǿȠ�ǉȣȠȅАș�ǟȅȖ�ΛǦƺȠ� ǩș�ǉȅǿșǩǏǓȖǓǏ�ȅȒȠǩǾǩșȠǩǉ�ȅȖ�
pessimistic, and since correlational APP equations 
use variance instead of standard deviation in analy-
șǩșॹ� ȠǦǓ� ǉȣȠȅАș� ƺȖǓ� ƺ� ǴȣǏǠǾǓǿȠ� ǉƺǹǹ� ȅǟ� ȠǦǓ� ȖǓșǓƺȖǉǦǓȖঀ
� eȅ�ǓΚƺǹȣƺȠǓ�ȠǦǓ�ǓАǓǉȠ�ȅǟ�ȠǦǓ�ΡǓƺȖ�ȅǟ�ȒȣǈǹǩǉƺȠǩȅǿ�ȅǿ�
precision, we performed multiple correlational anal-
yses. First, we obtained mean and median precision 
levels across the three time periods for the experimen-
tal research. The mean precision levels were 0.59 (n = 
17, SD = .20), 0.64 (n = 10, SD = .24), and 0.29 (n 
= 12, SD = .16) for the most distant to most recent 
time periods, respectively. The corresponding median 
precision levels were 0.59 (n = 17), 0.71 (n = 10), and 
0.23 (n = 12). With respect to correlational research, 
the mean precision levels were 0.23 (n = 11, SD = .09), 
0.27 (n = 24, SD = .19), and 0.21 (n = 20, SD = .15) 
for the most distant to most recent time periods, re-
spectively. The corresponding median precision levels 
for correlational studies were 0.25 (n = 11), 0.23 (n 
= 24), and 0.18 (n = 20). Overall, both correlational 
and experimental precisions have shown improve-
ment over time, with experimental studies showing 
much more improvement than correlational studies. 
 Second, we correlated precision with the year of 

 1 1 These include that correlations are bounded (-1, +1) and that the precision level refers to a squared standard deviation (variance) as opposed to a stan- These include that correlations are bounded (-1, +1) and that the precision level refers to a squared standard deviation (variance) as opposed to a stan-
dard deviation. dard deviation. 

SOCIAL IDENTITY PRECISION



118118

publication. Because smaller values indicate better 
precision, an optimistic perspective suggests a negative 
correlation whereas a pessimistic perspective suggests 
no correlation or a positive correlation. The correla-
tion was -0.445 (n = 39, p = .004) for experimental 
research and -0.056 (n = 55, p = .687) for correlational 
research. Figure 1 contains a scatterplot pertaining to 
experimental research and Figure 2 contains a scatter-
plot pertaining to correlational research, both with the 
ǈǓșȠ�ЙȠ�ȠȖǓǿǏǹǩǿǓ�Ƞȅ�ǓΠƺǾǩǿǓ�ȠǦǓ�ȒȖȅǠȖǓșșǩȅǿ�ȅǟ�ȠǦǓ�ǏƺȠƺঀ

 From the data presented in Figure 1, we can see 
a clear negative trend across time. As the publica-
tion year becomes more recent, the precision level 

Figure 1. Scatterplot representing precision of experimental social 
identity research along the vertical axis as a function of year of 
publication along the horizontal axis.  

Figure 1. Scatterplot representing precision of correlational social 
identity research along the vertical axis as a function of year of 
publication along the horizontal axis. 

moves further towards zero, indicating a promising 
improvement in experimental precision. In contrast, 
'ǩǠȣȖǓࢳ��ǏȅǓș�ǿȅȠ�șǦȅΛ�ǾȣǉǦ�ȅǟ�ƺǿ�ǓАǓǉȠ�ȅǟ�ȠǩǾǓ�ȅǿ�
correlational precision. These time-period correla-
tions should be taken as exploratory however due 
to the small sample sizes within each time period.

Discussion
 Social identity research composes an important 
domain within social psychology that is relevant to oth-
ǓȖ�ЙǓǹǏș�Ƞȅȅ�șȣǉǦ�ƺș�ǾƺȖǷǓȠǩǿǠॹ�șȅǉǩȅǹȅǠΡॹ�ƺǿǏ�ȅȠǦǓȖșঀ�
Hence, it is unsurprising that there is a large literature 
and many arguments both praising and criticizing so-
cial identity theory. The present work is agnostic about 
ȠǦǓ�ǹƺȖǠǓȖ�șȅǉǩƺǹ�ǩǏǓǿȠǩȠΡ�ǩșșȣǓș�ǈȖǩǓМΡ�ǾǓǿȠǩȅǿǓǏ�ǓƺȖǹǩ-
er. This is not to say that these issues are unimportant; 
in contrast, we believe they are very important. How-
ever, we also believe that if empirical facts are going to 
be used either to test theories or to provide the founda-
tion for theory formation, it is crucial to be clear that 
the empirical facts really are factual. That is, it is a pre-
requisite that researchers have good reason to believe 
that the sample statistics researchers report are rea-
sonably good estimates of corresponding population 
parameters. Our goal was to test whether this prereq-
uisite has been met in a sample of published research.
 The picture is very clear with respect to experi-
ǾǓǿȠƺǹ� ȖǓșǓƺȖǉǦঀ� ^ƺǾȒǹǓ� șǩΦǓș� ƺȖǓ� șǩǾȒǹΡ� ǩǿșȣГǉǩǓǿȠॹ�
thereby resulting in precision levels that one would 
consider untrustworthy. It is true that there are many 
ǟƺǉȠȅȖș�ȠǦƺȠ�ǉƺǿ�ǉȖǓƺȠǓ�ȠǦǓșǓ�ǩǿșȣГǉǩǓǿȠ�ǿȣǾǈǓȖș�șȣǉǦ�
as funding constraints, time, feasibility, and more. 
However, this does not disqualify the conclusion of 
ǩǿșȣГǉǩǓǿȠ� șƺǾȒǹǓ� șǩΦǓșॹ� ǈȣȠ� ȅǿǹΡ� ǩǿǉȖǓƺșǓș� ȠǦǓ�ǿǓǓǏ�
for more detailed and stringent research practices. It 
is important to note that quality research with smaller 
sample sizes is still very much alive and is in no way dis-
ȕȣƺǹǩЙǓǏ�ǏȣǓ�Ƞȅ�șƺǾȒǹǩǿǠ�ȒȖǓǉǩșǩȅǿঀ�2ǿșȠǓƺǏॹ�șƺǾȒǹǩǿǠ�
precision should be taken as an additional tool to assist 
researchers, in an a priori fashion, to determine a sam-
ple size needed for sample statistics that meet their cor-
responding population parameters, in essence giving 
researchers a goal for their eventual work to shoot for.
 There is some good news, which is that precision 
is improving, with research in the most recent period 
of research exhibiting more precision than research 
in previous periods. But even with the improvement, 
ǩȠ�ΛȅȣǹǏ�ǈǓ� ǏǩГǉȣǹȠ� Ƞȅ� ƺȖǠȣǓ� ȠǦƺȠ� ȠǦǓ� ǹǓΚǓǹ� ȅǟ� ȒȖǓǉǩ-

WILSON, TRAFIMOW, WANG, WANG



119

SOCIAL IDENTITY PRECISION

șǩȅǿ� ǩș� șȣГǉǩǓǿȠঀ�/ȅΛǓΚǓȖॹ� �eȖƺЙǾȅΛ�ƺǿǏ�EΡȧΦ� শࢺࢲࢱࢳষ�
ǏǓǾȅǿșȠȖƺȠǓǏ� ǩǾȒȖǓǉǩșǩȅǿ� ΛǩȠǦ� ȖǓșȒǓǉȠ� Ƞȅ� ЙΚǓ� ƺȖǓƺș� ȅǟ�
psychology (social, developmental, clinical, cognitive, 
ƺǿǏ� ǿǓȣȖȅষॹ� ƺǿǏ� eȖƺЙǾȅΛॹ�/ΡǾƺǿॹ� ƺǿǏ� ?ȅșȠΡǷ� শࢱࢳࢱࢳষ�
demonstrated imprecision with respect to marketing, 
there is no reason to be more pessimistic with respect to so-
cial identity research than other social science research. It 
is perhaps better to view social identity research as anoth-
er domain in which researchers should devote increased 
ȖǓșǓƺȖǉǦ� ǓАȅȖȠș� ǩǿ� ȠǦǓ� ǏǩȖǓǉȠǩȅǿ� ȅǟ� ǩǾȒȖȅΚǓǏ� ȒȖǓǉǩșǩȅǿঀ
� �ș� ȠǦǓ� ȒȖǓșǓǿȠ� ΛȅȖǷ� ǉȅǿșȠǩȠȣȠǓș� ȠǦǓ� ЙȖșȠ� șΡșȠǓǾƺȠ-
ic application of the APP to correlational research, the 
correlational analyses are better considered exploratory 
ȠǦƺǿ�ǏǓЙǿǩȠǩΚǓঀ��ȅȖȖǓǹƺȠǩȅǿƺǹ� ȖǓșǓƺȖǉǦ�ȅАǓȖș�ǈȅȠǦ�ƺǏΚƺǿ-
tages and disadvantages relative to experimental research. 
From an APP perspective, an advantage of correlation-
al research is that there is only one group, thereby ren-
dering precision easier to obtain. Going beyond an APP 
perspective, correlational research can be argued to be 
more representative of reality because of a lack of po-
ȠǓǿȠǩƺǹǹΡ� ƺȖȠǩЙǉǩƺǹ� ǹƺǈȅȖƺȠȅȖΡেǩǿǏȣǉǓǏ� ǾƺǿǩȒȣǹƺȠǩȅǿঀ� 2ǿ�
addition, it is easier to obtain diverse samples in cor-
relational contexts, though the recent proliferation of 
ΛǓǈেȒǓȖǟȅȖǾǓǏ� ǓΠȒǓȖǩǾǓǿȠș� ǩș� ȖǓǏȣǉǩǿǠ� ȠǦǩș� ǏǩАǓȖǓǿǉǓঀ
 But there are disadvantages too. From an APP perspec-
tive, a disadvantage is the lack of previous systematic APP 
ƺȒȒǹǩǉƺȠǩȅǿș�Ƞȅ�ǉȅȖȖǓǹƺȠǩȅǿ�ǉȅǓГǉǩǓǿȠșॹ�ȠǦǓȖǓǈΡ�ȖǓǿǏǓȖǩǿǠ�
ǉȅǾȒƺȖǩșȅǿ�ǏǩГǉȣǹȠঀ�eǦǩș�ǩș�ǿȅȠ�ƺ�ǟƺȣǹȠ�ȅǟ�ȠǦǓ�ǉȅȖȖǓǹƺȠǩȅǿƺǹ�
research itself, but rather due to the historical fact that APP 
equations applicable to experimental data were developed 
prior to APP equations applicable to correlational data, 
and thus the basic assumptions underlying the equations 
cannot be directly compared on an “A = B” comparison. 
More generally, it is well-known that correlational research 
provides a less convincing case for causal mechanisms than 
experimental research. On the other hand, however, given 
the present demonstration of the lack of precision of ex-
perimental social identity research, it is not clear that even 
ȠǦǓ�ǓΠȒǓȖǩǾǓǿȠƺǹ�ЙǿǏǩǿǠș�ȒȖȅΚǩǏǓ�șȠȖȅǿǠ�ǉƺȣșƺǹ�ǓΚǩǏǓǿǉǓঀ�
2ǟ�ƺ�șƺǾȒǹǓ�ǾǓƺǿ�ǏǩАǓȖǓǿǉǓ�ǉƺǿǿȅȠ�ǈǓ�ȠȖȣșȠǓǏ�Ƞȅ�ȖǓƺșȅǿƺǈǹΡ�
ǓșȠǩǾƺȠǓ� ȠǦǓ�ȒȅȒȣǹƺȠǩȅǿ�ǾǓƺǿ�ǏǩАǓȖǓǿǉǓॹ� ƺ� șȠȖȅǿǠ� ǉƺȣșƺǹ�
conclusion is contraindicated. Therefore, the disadvan-
tage of correlational research paradigms relative to exper-
imental research paradigms might be considered decreased 
in the context of small sample experimental research.
 Major implications can be discussed surrounding 
șƺǾȒǹǩǿǠ� ȒȖǓǉǩșǩȅǿ� ƺǿǏ� ǦȅΛ� ǩȠ� ǾǩǠǦȠ� ƺАǓǉȠ� șȅǉǩƺǹ� ǩǏǓǿ-
ȠǩȠΡ� ȖǓșǓƺȖǉǦ� ƺǿǏ� ȠǦǓȅȖǓȠǩǉƺǹ� ЙǿǏǩǿǠș� ȅǟ� șȅǉǩƺǹ� ǩǏǓǿȠǩȠΡ�

theory. It is important, as mentioned previously, 
to have sample statistics that are good estimates of 
corresponding population parameters. Without 
this, basic assumptions of the applicability of the-
ȅȖǩǓș� ƺǿǏ� șƺǾȒǹǓ�ЙǿǏǩǿǠș� ƺȖǓ�ǿȅȠ�ǾǓȠঀ� 2ǟ� șƺǾȒǹǩǿǠ�
precision for research in social identity work is con-
sistently low across the board, with no real attempt 
Ƞȅ� ǩǾȒȖȅΚǓॹ� ȠǦǓǿ� ȠǦǓ� ȖǓȒǹǩǉƺǈǩǹǩȠΡ�ȅǟ� ȠǦȅșǓ�ЙǿǏǩǿǠș�
ǩș� ǩǿ� ǴǓȅȒƺȖǏΡঀ� (ǩΚǓǿ� ȠǦǓ� ǾƺǴȅȖ� ȒȣșǦ� ǈΡ� șǉǩǓǿȠǩЙǉ�
ƺǏΚȅǉƺȠǓș� ǟȅȖ� ǠȖǓƺȠǓȖ� ȖǓȒǹǩǉƺǈǩǹǩȠΡ� ǩǿ� șǉǩǓǿȠǩЙǉ� ȖǓ-
search, especially in social sciences, this means that 
sampling precision is a vital step towards a more 
ȅȒǓǿ� ƺǿǏ� ȠȖȣȠǦǟȣǹ� șǉǩǓǿȠǩЙǉ�ǏǩșǉǩȒǹǩǿǓঀ� 2ǟ� șƺǾȒǹǩǿǠ�
ȒȖǓǉǩșǩȅǿ�ΛǓȖǓ�Ƞȅ�ȖǓǾƺǩǿ�ǹȅΛॹ�ȠǦǓ�ЙǿǏǩǿǠș�ȅǟ�șȅǉǩƺǹ�
research and the applicability of theories developed 
ǟȖȅǾ�ȠǦȅșǓ�ЙǿǏǩǿǠș�ΛȅȣǹǏ�ǈǓ�ȕȣǓșȠǩȅǿƺǈǹǓ�ƺȠ�ǈǓșȠঀ
� �ș� ƺǹΛƺΡș� ΛǩȠǦ� șǉǩǓǿȠǩЙǉ� ȖǓșǓƺȖǉǦॹ� ȠǦǓȖǓ� ƺȖǓ�
some limitations. One limitation is that we only 
tested three time periods. This of course was done 
due to time constraints as well as the exploratory 
শȖƺȠǦǓȖ�ȠǦƺǿ�Йǿƺǹষ�ǿƺȠȣȖǓ�ȅǟ�ȠǦǓ�ȖǓșǓƺȖǉǦঀ���șǓǉȅǿǏ�
limitation is that the sample size of the studies in-
cluded was limited (again due to time constraints). 
Thus, conclusions may be clear, but a more com-
prehensive analysis with a much larger sample size 
would provide a more detailed and stringent review 
of sampling precision in a posteriori fashion. Unfor-
tunately, no APP techniques have yet been devel-
oped to estimate the number of studies that should 
be included in an analysis such as that conducted 
here, and so traditional APP techniques are invalid 
to determine the sample size for a meta-style analysis 
of this kind. A third limitation is that, even within 
social identity research, there are research catego-
ries not addressed here. For example, there is social 
identity research with a basic or applied focus, a fo-
cus on integrating other literature, and many others.
 Of course, one potential avenue for future re-
search is to address the foregoing limitations. A sec-
ond potential avenue is to expand to domains that 
are not precisely about social identity but are related. 
These could include work in attachment, aggression, 
or stereotyping. A third avenue is to pursue non nor-
mal distributions. Because the researchers in the ex-
perimental papers all performed statistics based on 
the assumption of normality, we used that assump-
tion too in the present analyses for the sake of con-
sistency. However, this assumption is likely wrong, 



120

WILSON, TRAFIMOW, WANG, WANG

as most distributions are skewed (Blanca et al., 2013; 
Ho & Yu, 2015; Micceri, 1989). The usual counter to 
skewness arguments is that the Central Limit Theorem 
renders deviations from normality unimportant, but 
that depends on the goal of the research. For example, 
ǟȅȖ�ȠǦǓ�ǟƺǾǩǹΡ�ȅǟ�șǷǓΛ�ǿȅȖǾƺǹ�ǏǩșȠȖǩǈȣȠǩȅǿșॹ�eȖƺЙǾȅΛॹ�
Wang, and Wang (2019; 2021) have demonstrated that 
there are important precision gains to be had for analy-
ses analogous to those conducted here, even under low 
levels of skewness, provided that the researcher focuses 
on locations as opposed to means. Because locations 
are a parameter of skew normal distributions, whereas 
means are not, it makes sense to use locations rather 
than means anyway as locations are the more generally 
applicable parameter. And because the location equals 
the mean when there is normality, nothing is lost by 
including locations in APP analyses, even in the rare 
cases where the normality assumption is true. It is also 
important to note again that this research is not an 
examination of the accuracy of social identity theory 
itself and is not limited to “social identity researchers’’ 
in the traditional sense (that is those who test the the-
ory of SIT). The goal of this research was to examine a 
broad and eclectic mix of social identity applications.
 In conclusion, the notion that theory should be 
checked against reality is a staple of science, including 
the social sciences. But the reality in the social sciences 
tends to be characterized by summary statistics such 
ƺș�ǾǓƺǿșॹ�șȠƺǿǏƺȖǏ�ǏǓΚǩƺȠǩȅǿșॹ�ǉȅȖȖǓǹƺȠǩȅǿ�ǉȅǓГǉǩǓǿȠșॹ�
etcetera. Social scientists do not obtain such sample 
summary statistics as ends in themselves. Rather, social 
scientists obtain sample summary statistics because of 
the faith they have that these provide good estimates of 
corresponding population parameters. In contrast, the 
foregoing analyses demonstrate that the sample statis-
tics on which research involving social identity depends 
cannot be trusted as accurate estimators of correspond-
ing population parameters. We hope and expect that 
the present work will stimulate social identity research 
to focus on the preliminary issue of obtaining trust-
worthy empirical facts, as a prerequisite to resolving 
the important conceptual issues of consuming interest.

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