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enter image description hereI have datasets (one 1997-2001, another 2020, 2021) with means and standard deviations that I need to compare. Two different dats information (mass and total number). It is expected that I compare the two data sets using statistical analyses.

A t-test was suggested. However I am unsure how to go about this when there are no original data on the individuals themselves for 2001 data set (only have full original data for 2021). I was able to do a manual hypothesis testing using the two means and standard deviations. I cannot think of any statistical analyses to represent an appropriate comparison without the original data from the 2001 data set. I really would appreciate any kind of help or recommendations.

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    $\begingroup$ t tests depend only on means, SDs and sample sizes; Otherwise you can plot say means and confidence intervals. $\endgroup$
    – Nick Cox
    Sep 26, 2021 at 15:43

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To follow on what Nick Cox wrote, your situation is you have two populations (1997-2001 vs 2020-2021) with (probably) different variances, and you want to check whether they have the same mean. That's the situation where you would use Welch's t-test.

You have all the numbers to plug into the first formula on the Wikipedia page for Welch's t- test: https://en.wikipedia.org/wiki/Welch%27s_t-test

The thing to be careful of is that with a t-test you're assuming the means are normally distributed. That's not an issue for the 1997-2001 data since the sample size is quite large. For the 2020-2021 data, you'll want to check for normality by looking at the Q-Q plot and seeing if it looks like a straight line.

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    $\begingroup$ (+1) There is an important detail to flag. As not all birds are found to contain plastic, the mean plastic content is a mean over several zeros and several positive weights. That bimodal distribution is going to be a little awkward as underlying the sampling distribution of the mean. You could do simulations on the conditional distribution or use bootstrapping to get a handle on the consequences. $\endgroup$
    – Nick Cox
    Sep 26, 2021 at 16:18
  • $\begingroup$ You guys have no idea how thankful I am for your input! Your suggestions helped me big time. Thank you both so much :) $\endgroup$
    – Cassandra Woods
    Sep 27, 2021 at 2:57

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