When factors such as treatment group, sex, or race are in interaction with a continuous variable, testing for homogeneity of slopes is straightforward. However, when there is a significant 3-way interaction between two continuous variables and a categorical variable for analysis of a continuous dependent variable, the interpretations become complex. The next step should be to look at the parameter estimates to look for trends for interpretation purposes but this is a daunting task since the interaction involves multiple continuous values. This paper will present an approach that will dichotomize one of the continuous variables at the median, obtain the parameter estimates of the slopes for the all combinations of categorical variables, and then graphically represent the separate trends across the levels of the continuous variable. The technique is then repeated for the other continuous variable. The method requires assessing two different graphs where the dependent variable is regressed over a different continuous variable in each graph. This has proven to be an easier approach for interpretation and graphically reporting of the outcomes.
INTRODUCTIONAdolescence is a period of rapid growth and development during which youth undergo changes in not only adiposity but also bone mineral density (BMD). This early development has life-long consequences for health. It has been shown that osteoporosis ordinarily occurs late in life due to age-related reductions in bone mineral density as shown in Figure 1 [1]. Thus, it is important to understand the influences on the development of body composition early in life. Our goal in this analysis is examine the relationship between BMD with predisposing factors such as RACE, SEX, and AGE and percent body fat (PERFAT).
There is a Reaper, whose name is Death, And, with his sickle keen, He reaps the bearded grain at a breath, And the flowers that grow between. – Henry Wadsworth Longfellow, The Reaper and the Flowers
Japanese beetle (Popillia japonica Newman) is an emerging silk-feeding insect found in fields in the lower Corn Belt and Midsouthern United States. Studies were conducted in 2010 and 2011 to evaluate how silk clipping in corn affects pollination and yield parameters. Manually clipping silks once daily had modest effects on yield parameters. Sustained clipping by either manually clipping silks three times per day or by caging Japanese beetles onto ears affected total kernel weight if it occurred during early silking (R1 growth stage). Manually clipping silks three times per day for the first 5 d of silking affected the number of kernels per ear, total kernel weight, and the weight of individual kernels. Caged beetles fed on silks and, depending on the number of beetles caged per ear, reduced the number of kernels per ear. Caging eight beetles per ear significantly reduced total kernel weight compared with noninfested ears. Drought stress before anthesis appeared to magnify the impact of silk clipping by Japanese beetles. There was evidence of some compensation for reduced pollination by increasing the size of pollinated kernels within the ear. Our results showed that it requires sustained silk clipping during the first week of silking to have substantial impacts on pollination and yield parameters, at least under good growing conditions. Some states recommend treating for Japanese beetle when three Japanese beetles per ear are found, silks are clipped to < 13 mm, and pollination is < 50% complete, and that recommendation appears to be adequate.
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