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From |
"FEIVESON, ALAN H. (AL) (JSC-SK) (NASA)" <alan.h.feiveson@nasa.gov> |

To |
"'statalist@hsphsun2.harvard.edu'" <statalist@hsphsun2.harvard.edu> |

Subject |
st: RE: Statistics Question. |

Date |
Thu, 7 Apr 2005 08:28:45 -0500 |

You could simply do a t-test on the ratios to see if their mean is one - or do a t-test on the log ratios to see if their mean is zero. Which is "better" depends on whether the ratios or log ratios are more likely to be normally distributed. Doing a t-test on the log ratios is the same as doing a paired t on the log of the original variable. Al Feiveson t-test on the ratios: . ttest r=1 One-sample t test ---------------------------------------------------------------------------- -- Variable | Obs Mean Std. Err. Std. Dev. [95% Conf. Interval] ---------+------------------------------------------------------------------ -- r | 6 .8761667 .0484282 .1186245 .7516779 1.000655 ---------------------------------------------------------------------------- -- Degrees of freedom: 5 Ho: mean(r) = 1 Ha: mean < 1 Ha: mean != 1 Ha: mean > 1 t = -2.5570 t = -2.5570 t = -2.5570 P < t = 0.0254 P > |t| = 0.0508 P > t = 0.9746 t-test on the log ratios: . ttest z=0 One-sample t test ---------------------------------------------------------------------------- -- Variable | Obs Mean Std. Err. Std. Dev. [95% Conf. Interval] ---------+------------------------------------------------------------------ -- z | 6 -.1399694 .0559768 .1371145 -.2838622 .0039235 ---------------------------------------------------------------------------- -- Degrees of freedom: 5 Ho: mean(z) = 0 Ha: mean < 0 Ha: mean != 0 Ha: mean > 0 t = -2.5005 t = -2.5005 t = -2.5005 P < t = 0.0272 P > |t| = 0.0545 P > t = 0.9728 . -----Original Message----- From: owner-statalist@hsphsun2.harvard.edu [mailto:owner-statalist@hsphsun2.harvard.edu]On Behalf Of Thomas J. Flanagan Sent: Wednesday, April 06, 2005 10:25 AM To: statalist@hsphsun2.harvard.edu Subject: st: Statistics Question. Listhost: is there any way to run a paired t-test for data values if one ONLY has the ratios of the values, and not the actual values. The specific problem I am trying to work out is: McElhoe and Conner (1986) use an instrument called VISIPLUME to measure UV light. By comparing absorption in clear air and absorption in polluted air, the concentration of SO2 in the polluted air can be estimated. The EPA has a standard method for measuring So2 in air, and we wish to compare the two methods across a range of air samples. The recorded response is the ratio of the Visiplume reading to the EPA standard reading. The six observations on coal plant number X are: .950, .978, .762, .733, .823, 1.011. If we make the NULL HYPOTHESIS be that the Visiplume and standard measurements are equivalent, then the ratios could, with equal probability, have been observed as their reciprocals. That is, the ratio of .950, could equally have been 1/.950= 1.053, since the labels are equivalent and assigned at random. Supposed we take as our summary of the data the sum of the ratios. We observer .95âEUR¦+1.011= 5.257. Test (using randomization methods) the null hypothesis of equivalent measurement procedures AGAINST the alternative that Visiplume reads higher than the standard. Report a P Value. My current work thus far is this>. I am using a paired t-test. Ho is the mean of the difference between the Visiplume and the Standard is 0. To test this, I use the T statistic, with 5 degrees of freedom, d âEUR" U/ OâEUR"(n)^1/2 D represents the mean of the differences between the two treatments, and u is zero, per the null hypothesis. N is 6, and the 0 is the pooled variance estimator. This provides a p value nearby .30 Do you believe this method is accurate, and do you replicate this p value? I am attempting next to work it out in STATA. * * For searches and help try: * http://www.stata.com/support/faqs/res/findit.html * http://www.stata.com/support/statalist/faq * http://www.ats.ucla.edu/stat/stata/ * * For searches and help try: * http://www.stata.com/support/faqs/res/findit.html * http://www.stata.com/support/statalist/faq * http://www.ats.ucla.edu/stat/stata/

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