1. Vamsi Sundus Shawnalee

2. “Data collected under different conditions (i.e. treatments)  whether the conditions are different from each other and […] how the differences manifest themselves.” This data concerns soil.

3. Soils are first chisel-plowed in the spring Samples from 0-2 inches were collected. Measured N percentage (TN) Measured C percentage (CN) Calculated C/N, ratio between the two treatments. Looking at the sample setup on 674, we see that it wasn’t randomly allocated. We expect perhaps some spatial autocorrelation among the sample sites.

4. Author: calculated simple pooled t-test: p =.809. p > α Thus no relation… Doesn’t account for spatial autocorrelation among the 195 chisel-plow and 200 non-till strips. Doesn’t convey the differences in the spatial structure of the treatments.

5. They used SAS to obtain least squares + restricted maximum likelihood  common nugget effect was fit. Considerable variability of C/N ratios due to nugget effect. Using “proc mixed” we get predictions of the C/N ratio.

6. With proc mixed we assume that the C/N ratios are assumed to depend on the tillage treatments. The SAS program is included in the section. Omitted since this is a class in R. But, in the programming Semivariogram – ensure both have same nugget effect.

7. Pg 677-678 (SAS Output) Looking at the curvy wavy thingy (surface plots) We see one looks smoother and more predictable (no- tillage). This means greater spatial continuity (larger range). I.e. positive autocorrelations = stronger over same distance.

8. At this point in the analysis: There is no difference in the average C/N values in the study. [when sampling two months after installment of treatment.] [pooled t-test] There are differences in the spatial structure of the treatments [3D plot]. If we do a SSR (sum of squares reduction) we see that it’s extremely significant that a single spherical semivariogram cannot be used for bother semivariograms (Ha). Using ordinary least squares we also find significance, but less so..0001 versus.00009.-3-1 versus.-4-9.

9. Next section

10. What if only one variable was important (i.e. either C or N) but not the combination of the two (i.e. C/N or N/C ratio)? Here: Consider: predicting soil carbon as a function of soil nitrogen. From the scatterplot (TC v TN) we see an extremely strong correlation of sorts. [pg. 679]

11. If we wanted to have a more accurate model though, we’d have to include spatiality: instead of linear model: TC(s i ) = β 0 + β 1 *TN(s i ) + e(s i ) Errors are spatially correlated. We need to model it though

12. Need to model the semivariogram. Two steps Model fit by normal least squares and the “empirical semivariogram of the OLS residuals is computed to suggest a theoretical semivariogram model.” We need the theoretical model to get initial semivariogram parameters. Need mean and autocorrelation structure  restricted maximum likelihood. Here: we use proc mixed to estimate both the mean function and the autocorrelation structure (and predictions at unobserved locations).

13. (1-Residual sum of squares)/corrected total sum of squares =.92 = estimate of R 2 Doing the proc mixed procedure, we generate a lot of output: 9.17 (pg 682 – 683) From the output generated we look at the “solutions for fixed effects” for estimates of the parameters were interested in. Specifically, β 0 = intercept and β 1 = TN.

14. For every additional percent of N, we increase C by 11.11 percentage points. After playing a short game of “find the difference” on 9.50, I see that they are nearly the same patterns. Wow…estimates of the expected value of TC and Predictions of TC are almost the same. Amazing! [pg 684]