Standard error and 95% confidence interval question

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Kara1617
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I have attempted this question but my answer doesn't seem right to me.
This is the data table:
Mean number of spotted knapweed plants per m^2
Chemical Control
2
15
3
20
3
16
2
Biological Control
2
3
3
5
4
3
2

Clearly biological control is more effective. But after doing my calculations using this formula:
Standard error = standard deviation / square root of n
and then 1.96xSE
mean + 1.96xSE and mean -1.96xSE, and drawing error bars, they overlap meaning that supposedly there is no difference between the means. Can anyone explain to me what I'm doing wrong here?
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QuentinM
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Well at a first glance, the variation in the chemical control is going to be huge. in half the data its as effective as the biological control, in half, not so much. If, say, all the values were over 10, the variation would be less and hence you could say they might overlap.


Now im doing the calculation, I have the SD of the chemical control group as 7.32, and its mean as 8.714. Its SD is almost as large as the mean! Therefore its highly likely they will overlap anyway. Calculating to the SE from those numbers, thats 2.77 for the chemical and 0.37 for the biological. Again, large differences there. And finally with the CI's, its 5.425 that I get for chemical, and 0.733 for biological-again, big differences.

These big differences are all because of the huge differences in values among the data.


And also you said "no difference". You can clearly see there is a difference in the means....8.714 average for chemical, 3.14 for biological. The correct term is "statistically significant" difference. This is a difference that statistics suggests is iron clad, based on reproducibility. You can see that for the chemical control, the results arent reproducible-they are either high or low, no real middle ground. The way to test if this is the case would be to do more samples...this would mean you divide by a larger number for SE (square root of N would be larger because N is) and hence SE would be reduced, and so would....hopefully you get the point.
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