Safa's link is a large-sample version. It's not suited for your tiny sample sizes (3 and 4). It's also abbout the case when the given CI refers to the mean difference, but your CIs refer to the two individual samples.

Assuming the data is normal distributed, and for small sample sizes, the t-distribution should be used.

The calculations can be done by hand, all you need is to look up the critical values of the t-distribution. For 95% confidence the critical t-values are

t1 = 4.3 your first sample (n1=3) and

t2 = 3.2 for your second sample (n2=4).

These values could be obtained e.g. in Excel with T.INV.2S.

The standard errors can be obtained from the CI half-widths (w):

w1 = (0.8744 - 0.7086)/2

w2 = (1.4780 - 1.2930)/2

se1 = w1/t1

se2 = w2/t2

The standard deviations (s) of the samples are then

s1 = se1 * sqrt(n1)

s2 = se2 * sqrt(n2)

Getting the pooled se for the two-sample t-test

seP

Thanks Jochen Wilhelm .

Hi Dr Jochen Wilhelm,

I am hoping you could help with a similar problem involving calculating a p-value for the difference in pooled prevalence between two subgroups in the context of a meta-analysis:

Prevalence Subgroup 1: 18.58% [95%CI 12.26-25.8] (n=699)

Prevalence Subgroup 2: 20.18% [95%CI 16.64-23.96] (n=6453)

I have tried following the same logic as your previous answer but unfortunately wasn't able to work it out.

Additionally, is it possibile to calculate a single p-value for subgroup differences when there are 3 or more subgroups (similar to the 'test for subgroup differences' used for an meta-analysis of treatment effect)

Thank you

Dear Mark Chia , what's the concrete problem with the analysis? It works straight out, giving p = 0.99 (such a high p-value is expected since the CIs are rather huuuuge given the very large sample sizes; there is nothing significant in the differences of less than 2 %-points in front of this terribly high uncertainty). The only thing one might consider here is that %-values should not be analyzed with a t-test. Better use logit-tranformed values (but in this particular example it doen't matter, because the uncertainty is simply overwhelming).

You can always compare models that differ in more than a single coefficient, and when the models are nested and the response is approximately normal distributed, the ANOVA F-test would be the correct test.

Thanks Jochen Wilhelm . I was trying to replicate the calculation from this paper so that I can do something similar for my own study.

I was getting the same result of p=0.99 rather than p=0.71, but perhaps it's because I failed to do the transformation (double arcsine transformation was used in this case)

"Subgroup analysis showed that PTSD prevalence as measured by screening instruments alone was 20.18% (95% CI, 16.64–23.96; I2 = 91%). When the diagnosis was based on clinical assessment, PTSD prevalence was 18.58% (95% CI, 12.26–25.80; I2 = 80%) (Fig. 4). The difference between these two subgroups was not statistically significant (p = 0.71)."

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