[Note for bibliographic reference: Melberg, Hans O. (1997), True and False at the
same time? Russian religiousness and statistical theory , http://www.oocities.org/hmelberg/papers/970409.htm]
True and False at the same time?
Russian religiousness and statistical theory
by Hans O. Melberg
Consider a researcher who wants to examine whether the Russians on average are more or
less religious than, say, the Norwegians. The null hypothesis would be that there is no
significant difference between Russia and Norway. The alternative hypothesis would be that
there is a significant difference. Before I proceed, I should note that this is not phoney
debate as there are real people who hold each view. For example, Gogol and Tarsis have
argued that the typical Russian is deeply religious. The opposite view - that the average
Russian is only superficially religious - can be exemplified by the writings of Belinsky
and Gorky. (Source: R. Hingley The Russian Mind, around p. 110). So, the question
is: Who is right?
The problem is that both the null and the alternative hypothesis could be true at
the same time. The Russians could be both more and less religious than the
Norwegians. This sounds contradictory. A person may exhibit contradictory opinions at
different times, but when we take the average over time and persons for a country (as
implied in the word "typical") the result cannot be that two mutually
incompatible attitudes are typically Russian?
In fact, it is sometimes possible to solve the apparent contradiction. (Sometimes, not
always, because it would not work, for example, if the discussion was whether there were
more or fewer pregnant women in Russian than Norway). Consider the case of country A with
10% atheists, 80% agnostics and 10% Christians. Compare this to country B which has 40%
atheists, 20% agnostics and 40% Christians. Clearly, country B exhibit both stronger
religious feelings and stronger anti-religious feelings than country A. One may call this
the bipolar theory - that the Russians have a more extreme belief and value system than
other ethnic groups.
What are the implications of this example? To be honest, I am not quite sure - but I
have some thoughts. First, I believe, the example shows the importance of always including
a third alternative for the respondents (the "I do not know" box) when we design
questionnaires - not just the two alternatives yes or no. Second, I believe the example
highlights the danger of thinking in terms of averages. When dealing with data about
income, religiousness, number of children (to mention a few), a simple average is not a
very good descriptive statistics. We all know that nobody has 2.3 children. Maybe the
median in many cases is a better statistic, but even the median would not solve the
problem related to Russian religiousness. To solve this problem we have to get information
about the distribution of the answers.
A final comment relates to the problem people have in distinguishing between internal
and external negation (for more on this see Elster's chapter on Zinoviev in his book Political
Psychology). Consider the statement: "I believe in God". What is the
opposite of this? In logic the opposite is found by negating the statement - in short by
inserting a "not." So, the opposite of "I believe in God" would be
"Not, I believe in God" - or in more grammatically correct English "It is
not true that I believe in God." This is called external negation.
However, the "not" may also be inserted in another position. On this account
the opposite of "I believe in God" would be "I believe in not-God" or,
in more elegant language "It is true that I do not believe in God." This is
called internal negation. [Note: a more accurate account of both internal and external
negation can be found in Jon Elster's Political Psychology , p. 73ff]
Now, the reader may well think that this logical exercise is abstract and irrelevant
pedantry. However, I believe it has great relevance, for example, in the debate about
Russian religiousness. Essentially there are three types of attitudes to religion: The
believer, the agnostic and the atheist. The agnostic represents the external negation of
the statement "I believe in God". About him it would be true to say "It is
not true that he believes in God", but it would be false to say "It is true that
he does not believe in God." (since he simply does not know whether to believe or
not). However, the last statement would be true about the atheist, who represents the
internal negation of the statement "I believe in God."
Now, the relevance of all this is this: Many people have problems in distinguishing
between the external and internal negation of a statement. This means that they may easily
misinterpret statistical evidence, such as in the example from Russia. If you believe
there are only two alternatives - that you either are or are not religious - and you are
given data which shows that a higher percentage of Russians than Norwegians are religious,
then you will infer that the opposite is also true: that the Norwegians are more
anti-religious than the Russians. This, as I have tried to argue, would be a false
inference. Moreover, if you ignore the distinction between internal and external negation,
you may well design a questionnaire which is misleading (since you might only provide two
alternatives (yes, no) when three would be appropriate (yes, no, do not know))
In conclusion, the example convinced me that the average is a poor statistical
descriptor, and that we should be much more interested in measures of distribution, or
maybe even better, measures of the shape of the population. There are probably some
other lessons to draw from this example which I have not fully understood yet. Any
suggestions?
[Note for bibliographic reference: Melberg, Hans O. (1997), True and False at the
same time? Russian religiousness and statistical theory , http://www.oocities.org/hmelberg/papers/970409.htm]