I would like to test whether the job satisfaction score I’ve observed in a new dataset is significantly different from scores reported in previous studies that use the same job satisfaction scale. Although I don’t have the raw data from these previous studies, I do have scale means and sample sizes from each study. Could I use these previous studies to create a 95% confidence interval (CI) and then examine whether the mean of my new sample falls within that CI? And what standard deviation would I use to compute this CI—the mean of the SDs of the individual studies or the SD of means across the studies? And should I somehow weight the previous studies by sample size when computing the CI?
If you have the mean, sample size and SD of the previous studies, you can easily calculate the CI for each study (in the statistic programm Stata it is the "cii means" command). The definition of the 95% CI is that of 100 calculated CIs the "true mean" should be covered 95 times (e.g. https://mda.gesis.org/index.php/mda/article/download/2014.001/34 ). So, if you have for example 20 previous studies (with random samples!), the mean of your study should be covered by 19 of them.
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