**
**
This is *an analysis of analyses*. The Rind et al. team did not
add a new study of a new sample to the existing ones. Meta-analysis is a method to review
the data and the results of existing studies. The method makes it possible to compare the
data and the results of many other studies and to 'add' the data and the results together,
so to speak. By this method, all samples together form a 'new' big sample. This is the
strength of a meta-analysis. A statistical rule is: the greater the sample, the more the
results can be trusted.

**
**
*
**Correlation* is the central concept in the study. Correlation is the
association between two or more factors. A *factor *or a *moderator *is a force
that may have some influence (e.g., intelligence can influence school results). A factor
has to be measured by some method. The outcome of the measurement is a *variable *(e.g.,
an intelligence quotient).

If a researcher measures the I.Q. of a sample of children, the I.Q.
figures will *vary *among the children. The result of the measurement will show the *variability
*of the *sample. *

With some methods, one can estimate the variability of the *population
*(e.g. all children of a given age in a given country). Then it's called *the
population variance. *

*
**Analysis of variance *or *ANOVA*, like correlation, measures
the association between two or more factors. Put another way, correlation and ANOVA
measure how variability in one variable is related to variability in another variable.

The level of correlation is reflected in a *correlation coefficient*,
noted as *r, *a figure between +1.00 (the longer it rains, the more water in a bin)
and -1.00 (the more it rains, the lower the amount of children playing on the streets).
The significance (credibility) of this figure depends on the size of the sample, thus on
the amount of observations or participants. The more observations for a given value of *r*,
the more significance. Therefore, the number of participants is usually given after the *r
*with the letter *n *or *N.*

Note that the size of the association between two variables (i.e., *r*)
is a different concept than *statistical significance*, which addresses the question
of whether or not the two variables are really related to one another. For the
meta-analysis, *r* is used as a measure of *effect size*.

In a meta-analysis, most of the correlation coefficients are given
after a correction in which the size of the sample is included in the calculation. After
doing so, a more *unbiased r *appears: the *r*_{u. }This figure reflects
the best estimate of the level of the correlation *within the population.*

One useful property of *r* is that the figure *r* or *r*_{u}
_{
}
can be squared. This figure is named the *‘coefficient of determination’
or ‘percentage of variance accounted for’*. If some variable V1 predicts 50%
of the variability in some variable V2, then the coefficient of determination would be .50
(which corresponds to an *r* of about .7). Note, that 0.9 x 0.9 = 0.81 and that 0.4 x
0.4 = 0.16. The squared figure *r*_{u}^{2} is lower than the *r*_{u.}

To interpret the *effect size*, the Rind team calls an *r*=.50
large, .30 medium, and .10 small. Thus a coefficient of determination of 1% is small, 9%
is medium, and 25% is large.

The main factor in the meta-analysis is the experience of CSA. This
main factor is compared with many other factors, for example adjustment and many
psychological factors. If there appeared to be a high percentage of variance between CSA
and, say, adjustment, one supposes that the CSA experience had a (small, medium, or large)
*effect *on the adjustment*. *If the degree of consent or the gender appears to
have effect on the adjustment, than the degree of consent or the gender can be seen as *a
moderator. *

Because the studies gave one effect size for each sample, the number of
effect sizes is the same as the number of samples, mentioned in the tables as *k.*

**
**
As it has been said: the greater the sample, the more reliable is the
correlation. To give a measure for the reliability, usually two figures are given; the one
lower and the other higher than the computed correlation coefficient. Between these two
figures, the correlation is reliable with a chance of 95% - or a chance of 2.5% that the
correlation is lower than the lowest figure and 2.5% that it's higher than the highest
figure.

Note that, if the first figure is below zero and the latter above zero,
the correlation can be negative as well as positive. If both figures are above zero, we
know (with a confidence of 95%) that there is a positive correlation between the given
figures, but if one of the figures is zero or negative, we can’t even say with
sufficient confidence wether the correlation is negative or positive. This, to cite page
29 of the meta-analysis, "an interval not including zero indicated an effect size
estimate was significant."

**
****One- and two-tailed
tests**

If the researcher is quite sure that the correlation will be a positive
one (as in the example of the wet streets and the rain), he tests only at the positive
side of the possible correlation coefficients. This is *a one-tailed test. *If the
researcher is not sure of how two variables are related, or if he wants to know the size
of the correlation rather than just its existence or non-existence, he should test at both
ends of the possible correlation coefficients: he does *a two-tailed test. *

**
**
This is the correlation between several *symptoms* (for example,
depression) and the CSA factor, as it appeared in all samples in which these symptoms are
measured. The CSA factor usually has two *levels*: with or without CSA experience. In
other studies, more levels are used, e.g. contact CSA, non-contact CSA, no CSA. The
‘without-group’ is the control group. If, say, 50% of the CSA group had
depressive symptoms and also 50% of the control group had depressive symptoms, the effect
size of CSA will be zero. If 100% of the CSA group had these symptoms and 0% of the
control group, the correlation and the effect size would be 1.00.

**
**
This correlation reflects the overall association between CSA and those
types of adjustment measured in the several samples, corrected for the sample size. If a
study measured four symptoms in one sample, these four symptom-level effect sizes in the
study are averaged into one sample-level effect size in the meta-analysis.

**
**
A meta-analysis combines the data from several studies about the same
subject. *Homogeneity *measures the differences or similarities between the several
studies. If several studies reach nearly the same conclusion, one can combine the data
with reasonable confidence. If the studies differ greatly in their outcomes, one should be
more cautious about combining the data. The statistical measure of homogeneity between the
outcomes of the studies has been given in the tables as *H. *

This *H *is calculated by a test, named "Chi-square"
that compares the differences between groups of data. The more groups of data, the higher
the Chi square will be. The statistical way of saying this is "*df *(degrees of
freedom) *= k *(number of choices or groups) – *1". *To know the
significance of the chi-square, one has to look at a table. Usually, the significance is
mentioned as an (*) in the tables. An asterisk means that the groups of data were
different, a non-significant *H* suggusts that there was a great deal of homogeneity
amongst the several studies. The asterix is explained in the tables as "*p <*
.05 in chi-square test." This means that the cance that such great differences
between homologous data would occur is smaller than 5%. To reach homogeneity, the authors
removed the most extreme effect sizes, irrespective of wether they were extremely high or
extremely low, until homogeneity was reached – if possible. Otherwise, the studies
could not be compared with on another with confidence.

**
**
Suppose that five studies resulted in the following effect sizes: 0.14,
0.17, 0.23, 0.25 and 0.27. The mean effect size (neglecting the sample size in this
example) is 0.21. Now suppose a sixth study resulted in an effect size of 0.70. Then, the
mean will be 0.29. The one high effect size will raise the mean and the sixth study would
have great influence on the results. It is better to expel this sixth study from the
meta-analysis since it seems to be an aberration. These kinds of studied are called
"outliers".

Factually, three studies were outliers: two studies with very high
positive effect sizes (having many incest cases in the samples) and one with a negative
effect size. "Positive" should be read as: "the more CSA, the more *problems
with *adjustment – see page 31 of the meta-analysis.

**
**
If one has a set of effect sizes, one can compute the mean effect size.
It is better to include the size of the sample in the computation. Doing so, the larger
samples have more influence on the mean than the smaller samples. This mean is called a *weighted
mean.*

**
**
A correlation coefficient *r *or *r*_{u }is not an
interval measure: i.e. the distance between *r *= 0.1 to *r *=0.2 is not the
same as the distance from *r *= 0.8 to *r *= 0.9. A transformation to Fisher's Z
gives each correlation coefficient a figure that better reflects its position in the
collection of all coefficients when performing meta-analyses. It makes it possible to use
the correlation coefficient and the sample size in a calculation of the weighted mean.
This weighted mean can then be transformed back into a correlation coefficient.

BTW, the *r*_{u}^{2 }or *% of variance *is an
interval measure.

**
**
The *standard deviation *is a figure, mostly between – 2.0
and 2.0, that shows the position of each of the data in the total collection of data. Data
with a SD of 0.0 are the mean data. About half of the data have positions between SD
– 0.1 and 0.1. Data with positions like – 1.9 or 1.9 are at the extremes of the
data collection.

**
****Multiple regression analysis and (semi) partial correlation**

This is a method to compare several ('multiple') factors and to compute
the strength of the influence of each of them on another factor. This kind of analysis is
better than the 'simple correlation' between only two variables.

Take for example the learning process at school. We can suppose that
several factors have influence: the intelligence of the children, the method of teaching,
the size of the classes and the personality of the teacher. If you have enough data, you
can take the data of the children of the same teacher, the same intelligence and the same
class size but with a different method of teaching. Then you '*regress' *all factors
except one. So you can see if the method of teaching has any influence by computing the
correlation between that one factor and the regressed other factors. This correlation is
called a *partial correlation. *With the regression of fewer other factors, it's
called a *semi partial correlation. *By making many of these comparisons, you're
doing *multiple analysis *to compute the strength of each factor. Remember that in
the meta-analysis, the factor 'family environment' and 'CSA experience' *together *had
influence on the adjustment, but that 'family environment' appeared to have 10 times more
influence than the factor "CSA experience".