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I am doing a research and I need to determine the effect of adapting to climate change on farm productivity and income. My methodology is to compare the productivity and net farm income of farms that adapt to climate change with farms that do not adapt. What I did was from 37 respondents that adapts to CC and from 23 respondents that do not adapt, I randomly selected 5 respondents from each category with almost the same farm characteristics (farm size and tenure status). I want to test if the mean difference in productivity and income between farms that adapt and farms that do not is statistically significant. I am going to use a t-test. My question is, is it okay if my sample size is just 5 from each category(farms with adaptation and farms without)?

chimj
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  • https://stats.stackexchange.com/questions/37993/is-there-a-minimum-sample-size-required-for-the-t-test-to-be-valid – SmallChess Apr 30 '17 at 12:22

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Your confidence intervals would be so large as to make it unlikely you would find a significant difference. As you have 60 respondents, which isn't an enormous sample size, it would be better to take as many of them as you can with similar farm characteristics and not worry if the numbers from each group are different.

Robert Jones
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  • I followed your suggestion, and based on my data, there is a total of 16 respondents with the same farm characteristics. would that be enough? – chimj May 02 '17 at 02:03
  • It is a bit small, but a definite improvement. How many do you have in each group? – Robert Jones May 03 '17 at 18:03
  • You can use the formula ABS(P2-P1)+/-F*SQRT((P1*(100-P1)/n1)+(P2*(100-P2)/n2)) to get the +/- range - where P1 = observed percentage achieved and n1 = sample size for sample 1 and and P2 = observed percentage achieved and n2 = sample size for sample 2 and and F = confidence level factor (use 1.96 for 95% confidence) - the formatting here is awful !! this explanation should have been on separate lines – Robert Jones May 03 '17 at 18:04
  • Trying out improved formatting You can use the formula ABS(P2-P1)+/-F*SQRT((P1*(100-P1)/n1)+(P2*(100-P2)/n2)) to get the +/- range - where P1 = observed percentage achieved and n1 = sample size for sample 1 and and P2 = observed percentage achieved and n2 = sample size for sample 2 and and F = confidence level factor (use 1.96 for 95% confidence) – Robert Jones May 03 '17 at 21:01
  • Trying out improved formatting You can use the formula ABS(P2-P1)+/-F*SQRT((P1*(100-P1)/n1)+(P2*(100-P2)/n2)) to get the +/- range - where P1 = observed percentage achieved and n1 = sample size for sample 1 and and P2 = observed percentage achieved and n2 = sample size for sample 2 and and F = confidence level factor (use 1.96 for 95% confidence) – Robert Jones May 03 '17 at 21:04