On 09-Aug-08 20:31:33, Felipe Carrillo wrote: ># Hi all: > #I got a vector with fish lengths(mm) > # Can someone help me interpret the output of > # a t.test in plain english? > # Based on the t.test below I can say that > # I reject the null hypothesis because > # the p-value is smaller than the the significance > # level(alpha=0.05). What else can I conclude here? > Ho = 36 mm > Ha <> 36 mm > fishlength <- c(35,32,37,39,42,45,37,36,35,34,40,42,41,50) > t.test(fishlength,mu=36) > One Sample t-test > > data: fishlength > t = 2.27, df = 13, p-value = 0.04087 > alternative hypothesis: true mean is not equal to 36 > 95 percent confidence interval: > 36.14141 41.71573 > sample estimates: > mean of x > 38.92857
The standard interpretation of the above is that, on the hypothesis that the fish were sampled from a population in which the mean length was 36 (and the distribution of length is sufficiently close to Normal for the t-test to be adequately applicable), then the value of t differs from 0 by an amount which has probability less than 0.05 of being attained if that hypothesis were true. Therefore the result is evidence of some strength that the hypotesis is not true, and the mean length of fish in the population is different from 36. However, it is on the borderline of the mildest criterion of "significant difference" usually adopted, namely 0.05. A more stringent criterion could be, for instance, 0.01; and then you would not be "rejecting this null hypothesis". As for the following: > # I also would like to know how to interpret the output > # when mu=0? Notice that the p-value from the t.test above > #is different from this t.test. Are we trying to reject the null > # hypothesis here too? > > t.test(fishlength) > One Sample t-test > > data: fishlength > t = 30.1741, df = 13, p-value = 2.017e-13 > alternative hypothesis: true mean is not equal to 0 > 95 percent confidence interval: > 36.14141 41.71573 > sample estimates: > mean of x > 38.92857 > > Thanks in advance for your help. In terms of interpreting a statistical test, using your data, of the hypothesis that the mean length in the population is 0, the P-value of 0.0000000000002017 is very strong evidence indeed that the mean is not 0. However, I do not know why you are asking the question. No test is needed. The length of any living fish, even while it is still in the egg, is greater than 0; and whatever population you have taken your sample from will have a mean length which is greater than 0. That is not to say that the result of a t-test on any sample will necessarily give a significant result. You could have a small catch with lengths, say, fishlengths <- c(2,4,9,20,50) t.test(fishlengths,mu=0) # One Sample t-test # data: fishlengths # t = 1.9273, df = 4, p-value = 0.1262 # alternative hypothesis: true mean is not equal to 0 # 95 percent confidence interval: # -7.489442 41.489442 # sample estimates: # mean of x # 17 And all you can conlude from that is that the sample, *in itself*, does not carry sufficient information to confirm what you know is true (i.e. mu > 0). Even the one-sided test of mu=0 with alternative alt="greater" does not give a result significant at 5%: t.test(fishlengths,mu=0,alt="greater") # One Sample t-test # data: fishlengths # t = 1.9273, df = 4, p-value = 0.0631 # alternative hypothesis: true mean is greater than 0 # 95 percent confidence interval: # -1.803807 Inf # sample estimates: # mean of x # 17 Hoping this helps! Ted. -------------------------------------------------------------------- E-Mail: (Ted Harding) <[EMAIL PROTECTED]> Fax-to-email: +44 (0)870 094 0861 Date: 09-Aug-08 Time: 22:28:34 ------------------------------ XFMail ------------------------------ ______________________________________________ R-help@r-project.org mailing list https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide http://www.R-project.org/posting-guide.html and provide commented, minimal, self-contained, reproducible code.
