So far all responses have appeared to assume that the data represent left and right ovaries on the SAME women. But this cannot be the case, because the total number of left ovaries in the data is 132, and of right ovaries 103. So: before we can offer useful advice, we need to know whether the pathology being documented occurs, when it occurs, only in one of a woman's ovaries (for these data, anyway), or whether some of the 235 instances of pathology represent both ovaries for some of the women. If there are any of these last, those are the only cases for which one has paired data. See other comments to Paige, embedded in the post below:
On Wed, 10 Dec 2003, Paige Miller wrote: > Ray Koopman wrote: > > [EMAIL PROTECTED] (Jan) wrote (edited): > > > >>[Problem about the occurrence of] pathology at female ovaries, > >>and graded them according to the severity. > >>Left: 1: 91, 2: 31, 3: 7, 4:3; > >>Right: 1:66, 2:28, 3:6, 4:3; totals: left: 132, right: 103. > >>... [snip] ... > >>Q: 1/Which test should I use to compare left vs right againsi > >>grading (if i can due to the difference in spread among grades?!)? > >>2/Can I say that left is significantly more affected than right? > >>(which test, based on which presumptions)? Thanks a lot!! > > > > The data should be organized in a 5 by 5 contingency table F in > > which F_ij, i,j = 0...4, is the number of women whose left and right > > ovaries had severity scores i and j, respectively, where 0 indicates > > no pathology. It is not clear what the given values > > 1 2 3 4 > > L 91 31 7 3 > > R 66 28 6 3 > > are. Are they the leftmost column F_i0 and the topmost row F_0j, > > omitting F_00? Or perhaps the row and column sums, F_i+ and F_+j, > > omitting F_0+ and F_+0? > > > > In any case, the question is about the nature of any asymmetry in F. > > I cannot see how this question turns into a contingency table unless > the data given are count data. And yet the original question indicated > that the numbers represent severity, which to me indicates continuous > or ratio scaled data. If I understand the OP correctly, they are indeed counts, of cases of different severities. Jan wrote, somewhat telegraphically, >>Left: 1: 91, 2: 31, 3: 7, 4:3; >>Right: 1:66, 2:28, 3:6, 4:3; totals: left: 132, right: 103. which I took to mean "Severity = 1, 91 cases; severity = 2, 31 cases; severity = 3, 7 cases; severity = 4, 3 cases" for the left ovaries: and similarly for the right ovaries. These would correspond to Ray's F_0+ and F_+0. > Even if the data are indeed counts of some type of pathology within an > ovary, I can't see how this fits into a contingency table. With this I agree (1st paragraph above). > Thus I would continue to advise that the proper analysis method be a > paired t-test if the data are approximately normal, and a > nonparameteric Fisher's Sign Test if the data are not approx normal. The DATA, it seems to me, are distinctly positively skewed (I see two histograms, each with four bars, heights of bars = 91, 31, 7, 3 for left ovaries and 66, 28, 6, 3 for right ovaries. I should think the question were more compound (after sorting out how much of the data are paired!): (1) Is it reasonable to construct a weighted mean, using the severity codes (or some monotonic function thereof) as data values and the numbers of cases as weights? (2) Is the sampling distribution of the sample mean so constructed believably normal (at least approximately?) Or, to take a different run at it, is there a discrete probability model that applies to these severity ratings, the parameters of which could be fitted separately to the two sets of data and then compared for possible differences? -- Don Burrill. ----------------------------------------------------------------------- Donald F. Burrill [EMAIL PROTECTED] 56 Sebbins Pond Drive, Bedford, NH 03110 (603) 626-0816 . . ================================================================= Instructions for joining and leaving this list, remarks about the problem of INAPPROPRIATE MESSAGES, and archives are available at: . http://jse.stat.ncsu.edu/ . =================================================================
