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I am working on a project estimating salmon escapement through visual spawner surveys. We conducted weekly surveys and counted the number of individuals we observed. These numbers were used in an Area-under-the-curve model to estimate the number of salmon present across the entire survey period. This model provides a cumulative estimate (single value) with no mean or sd.

I want to compare the current year's estimate (374.43) to the average escapement across previous years' estimates (n=19, mean=432.2179, sd=632.0642) to determine if my escapement estimate for this year significantly differed from historical data for a given stream.

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    $\begingroup$ I can tell you right now, if your mean is 400 and the sd is 600, 374 is not "out of the ordinary" :) $\endgroup$
    – Alex J
    Commented Mar 20 at 4:04
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    $\begingroup$ Are you perhaps interested in a prediction interval? So given the data you've already collected, it's an interval for which 95% of "new" values should be contained in. $\endgroup$
    – Alex J
    Commented Mar 20 at 4:05

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You cannot test whether your current estimate is "significantly different" statistically. You can however say that you current year's estimate is lower and falls outside of the confidence intervals obtained from 19 years before.

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    $\begingroup$ This isn't true, you can very well compare this value against the historical mean/variance -- and how is a confidence interval not a (more informative) test for significance expressed in another form? $\endgroup$
    – PBulls
    Commented Mar 20 at 11:58
  • $\begingroup$ @PBulls I agree but only in case the variance has not changed through the years $\endgroup$
    – BenP
    Commented Mar 22 at 6:58
  • $\begingroup$ It is meaningless to compare an observation to a confidence interval. Perhaps you mean a prediction interval? $\endgroup$
    – whuber ♦
    Commented Mar 22 at 17:47

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