# Is it reasonable to calculate a T-test or Cohen's d with one group's sample size, mean and standard deviation being averaged or pooled?

This is my data:

• year 1: n, mean, sd
• year 2: n, mean, sd
• year 3: n, mean, sd
• year 4: n, mean, sd
• year 5: no data
• year 6: n, mean, sd (special event happened)

Sample sizes, means and standard deviations were different from year to year, but always on a similar level.

What I want to know: I want to compare the mean of year 6 to the means of year 1-4, since i want to know if the event that happened in year 6 might be a cause for the mean in year 6. I would use the event as an explanation for any statistically meaningful difference of the means.

What I did until now: I averaged ((year 1 + year 2 + year 3 + year 4) / 4) the sample sizes, means and standard deviations of years 1-4 to get an average n, an average mean, an average sd. With that information and the n, mean and sd from year 6, i calculated Cohen's d and a T-Test by using an excel effect size calculator (https://www.cem.org/effect-size-calculator).

What I am aware of: Calculating the mere average of n, mean, sd for years 1-4 is probably not accurate enough. I know about pooled standard deviation, which could be better suited for averaging SD (e.g. https://www.polyu.edu.hk/mm/effectsizefaqs/effect_size_equations2.html). I guess that in a similar way I could pool the means of years 1-4. And for the sample sizes, just using the average should suffice. This way, my calculations would be probably more accurate and more reasonable.

What my main question is: Is it reasonable at all, to average and/or pool the n, mean and sd of year 1-4 and use this pooled values for a calculation of T-Test and Cohen's d for a comparison with year 6?

More specific questions are:

• Is it reasonable to just average n, means and sds for what I want to know? (It would be I imagine, if the results would be approximate enough, and not outright wrong.)
• Is it reasonable to pool the means and sds for what I want to know? (I guess it would be more accurate than using the average because of the different sample sizes.)
• Which other ways of calculating/methods are possible to achieve what I want to know (see above)?