Once this data has been collected,
confidence intervals (CI) for each study are calculated, as 1.96 times the standard error (SE) if the data are assumed to be normally distributed.
in univariate analysis, the data also need to be weighted so the more reliable studies carry more importance than the less reliable ones. This can be done in a number of ways: weighting by sample size- those with bigger samples are more weighted, by qualitative estimates- where the researcher assigns weights by how valid they see the study, however this is subjective to the researcher, or more commonly by a measure of variance- most commonly 1 divided by the standard deviation squared, which would give small values when the data were noisy and larger values when the data were more precise. The weighted mean of the effect sizes are then calculated, along with the weighted mean confidence intervals.
the choice of meta-analysis can be considered. Univariate meta analysis reports weighted mean effect sizes for the relationship and provides information on the magnitude of variance among primary studies (Borenstein et al. 2009). There are other techniques such as meta-regression analysis, that investigates the heterogeneity of observed effect sizes (Hedges & Olkin, 1985), and qualitative meta analysis that focus on descriptive rather than numerical data (Hoon 2013).
This information is then added into a forest plot, where each study is represented as a square with its error bars (CI or SE) on either side, and at the bottom of the plot, a diamond reflects the grand mean of all of the studies. the middle of the diamond represents the mean and the left and right corners represent the mean CI of all the studies. If these corners do not overlap the line of no effect, which is the line where there is no difference between participants that did and didn't have COVID, then there is a true effect of COVID on cognitve function.