George A. Milliken

Population Marginal Means in the Linear Model: An Alternative to Least Squares Means

Abstract The parameter concept in the term least squares mean is defined and given the more meaningful name population marginal mean; and its estimation is discussed.

Extensions of the General Linear Hypothesis Model

Abstract In the conventional general linear model it is often possible to examine a more complete model that includes nonlinear terms. This is an extension of a test for non-additivity by Tukey and a generalization of that test by Scheffe. This article shows explicitly how the theory of the well-known general linear model can be used for these problems and illustrates some extensions and computing procedures.

Healthy Youth Places: A Randomized Controlled Trial to Determine the Effectiveness of Facilitating Adult and Youth Leaders to Promote Physical Activity and Fruit and Vegetable Consumption in Middle Schools

The Healthy Youth Places (HYP) intervention targeted increased fruit and vegetable consumption (FV) and physical activity (PA) through building the environmental change skills and efficacy of adults and youth. HYP included group training for adult school site leaders, environmental change skill curriculum, and youth-led FV and PA environment change teams. Sixteen schools were randomized to either implement the HYP program or not. Participants (N =1,582) were assessed on FV and PA and hypothesized HYP program mediators (e.g., proxy efficacy) at the end of sixth grade (baseline), seventh grade (Postintervention Year 1), and eighth grade (Postintervention Year 2). After intervention, HYP schools did not change in FV but did significantly change in PA compared to control schools. Proxy efficacy to influence school PA environments mediated the program effects. Building the skills and efficacy of adults and youth to lead school environmental change may be an effective method to promote youth PA.

A Nonrandomized Unconditional Test for Comparing Two Proportions in 2×2 Contingency Tables

It is shown that the “usual” nonrandomized, conditional test for comparing proportions using independent binomial samples, is very conservative in the sense that the actual significance level attributable to an outcome is often one-fourth to one-half of the anticipated value. A nonrandomized unconditional test is proposed, and for sample sizes up to 15, tables are given in an appendix which specify one-sided critical regions of size less than or equal to the nominal values 0.05, and 0.01 (two-sided critical regions are also given). Numerical examples illustrating the use of the tables and a brief description of the algorithm used to generate the tables are included.

Effects of total iron, myoglobin, hemoglobin, and lipid oxidation of uncooked muscles on livery flavor development and volatiles of cooked beef steaks

Infraspinatus (IN), gluteus medius (GM), and psoas major (PM) steaks were obtained from A- and B-maturity carcasses with either high (⩾6.0) or normal (⩽5.7) pH, and either Slight or Small marbling. Steaks were vacuum aged either 7, 14, 21, or 35d postmortem, and were broiled and served to a highly trained, flavor-profile sensory panel. Steaks with livery flavor were analyzed by gas chromatography/mass spectrometry for flavor compounds. Steaks aged 7 or 35d postmortem were analyzed for myoglobin (Mb) and hemoglobin (Hb) concentrations and for total iron (Fe) (35 d steaks only). The IN had greater Fe (P<0.05) than did the GM or PM. Livery flavor increased (P<0.05) and beef flavor identification decreased (P<0.05) in the GM as Fe increased. The PM had the lowest (P<0.05) Mb/Fe ratios and highest (P<0.05) Hb/Fe ratios. Several statistically significant, but relatively low correlations between 16-, 17-, and 18-carbon chain fatty acids and livery flavor resulted. Thirteen volatile compounds had higher concentrations in steaks with livery flavor than in those without livery flavor. Livery flavor development is a complex trait that can be affected by concentrations of total Fe, Mb, and fatty acids, but the relationships are relatively low.

Effects of packaging atmospheres on beef instrumental tenderness, fresh color stability, and internal cooked color.

Fresh meat color is a major factor influencing the purchase of meat products by consumers, whereas tenderness is the primary trait determining overall eating satisfaction of consumers. The objectives of this research were to determine the effects of packaging atmosphere on fresh beef color stability, cooked color, and tenderness. Longissimus lumborum muscles (n = 14 pairs) from USDA Select, A-maturity carcasses were assigned to either 14-d tenderness measurement or to display and then to 18-d [80% O(2), 20% CO(2) (HiO(2)) modified atmosphere packaging (MAP)] or 28-d [vacuum package (VP) and ultra low (ULO(2)) plus CO MAP blends] tenderness measurement. Loins were then fabricated on d 7 postmortem into 2.54-cm-thick steaks. Steaks 8 to 10 caudal to the first 7 steaks were bisected, assigned to a packaging treatment, and used for internal cooked color. One full steak was used for initial tenderness. Packaging treatments were as follows: vacuum-packaging (VP); 80% O(2), 20% CO(2) (HiO(2)); 0.4% CO, 35% CO(2), 64.6%N(2) (ULO(2)CO); 0.4% CO, 99.6% CO(2) (ULO(2)COCO(2)); 0.4% CO, 99.6% N(2) (ULO(2)CON(2)); or 0.4% CO, 99.6% Ar (ULO(2)COAr). Steaks packaged in HiO(2) MAP were in dark storage (2 degrees C) for 4 d, and all other steaks were in dark storage for 14 d. Steaks were displayed under fluorescent lighting (2,153 lx; 3,000 K) for 7 d, with instrumental color measured on d 0 and 7 of display. Trained color panelists (n = 10) assigned color scores. Steaks for Warner-Bratzler shear force and cooked color were cooked to 70 degrees C. Steaks packaged in the 4 ULO(2) MAP blends with CO had no change (P > 0.05) or increased (P < 0.05) a* values for fresh color. Steaks packaged in VP or the 4 ULO(2) MAP blends with CO had little or no surface discoloration. Steaks packaged in HiO(2) MAP discolored faster (P < 0.05) and 56% more (P < 0.05) than those in any other packaging treatment. There were no differences (P > 0.05) in Warner-Bratzler shear force on d 14 postmortem. Steaks packaged in HiO(2) MAP were less tender (P < 0.05) than the other treatments at the end of display but had 10 d less aging due to a shorter dark storage period. Steaks packaged in HiO(2) had the lowest (P < 0.05) a* values for internal cooked color of all packaging treatments. Steaks packaged in ULO(2)COCO(2) and VP had intermediate a* values, whereas those packaged in ULO(2)COAr, ULO(2)CO, and ULO(2)CON(2) had the greatest (P < 0.05) a* values for internal cooked color. Ultra-low oxygen packaging treatments had longer fresh color stability than steaks packaged in HiO(2) MAP and equal or better tenderness. Packaging atmospheres altered the internal cooked color, with steaks packaged in HiO(2) MAP exhibiting premature browning.

Effects of different packaging atmospheres and injection-enhancement on beef tenderness, sensory attributes, desmin degradation, and display color.

The objectives were to determine the effects of packaging atmosphere and injection-enhancement on tenderness, sensory traits, desmin degradation, and display color of different beef muscles. Longissimus lumborum (LL; n = 12 pairs), semitendinosus (ST; n = 12 pairs), and triceps brachii (TB; n = 24 pairs; 12 from the same carcasses as the LL and ST and 12 additional pairs) were obtained from the same USDA Select, A-maturity carcasses. On d 7 postmortem, each muscle from one side of the carcass was injection-enhanced, and each muscle from the other side was nonenhanced. Steaks 2.54-cm thick were cut from the muscles and packaged in vacuum packaging (VP), ultra-low oxygen with CO (ULO(2)CO; 0.4% CO/35% CO(2)/69.6% N(2)) modified atmosphere packaging (MAP), or high-oxygen MAP (HiO(2); 80% O(2)/20% CO(2)) and assigned to 14-d tenderness or display followed by 18- or 28-d tenderness measurement. Steaks packaged in HiO(2) MAP were in dark storage (2 degrees C) for 4 d and all other steaks for 14 d. Steaks for Warner-Bratzler shear force, sensory panel (n = 8 trained panelists), and desmin degradation were cooked to 70 degrees C. Steaks were displayed under fluorescent lighting (2,153 lx, 3,000 K) for 7 d. Trained color panelists (n = 10) assigned display color scores. Enhanced steaks had lower (P < 0.05) Warner-Bratzler shear force values than nonenhanced steaks. Sensory panelists found that nonenhanced steaks packaged in ULO(2)CO MAP or VP were more tender (P < 0.05), had more (P < 0.05) beef flavor, and had less (P < 0.05) off-flavors than steaks packaged in HiO(2) MAP. The LL and TB were more tender (P < 0.05) according to myofibrillar tenderness than the ST. Nonenhanced steaks were less (P < 0.05) juicy than enhanced steaks. The most common off-flavors associated with steaks packaged in HiO(2) MAP were oxidative or rancid. Enhanced steaks had more (P < 0.05) off-flavors than nonenhanced steaks, with typical descriptors of salty, metallic, or chemical, in addition to an undesirable mushy texture. Desmin degradation increased (P < 0.05) from 7 to 14 d postmortem and differed among muscles but was not affected (P > 0.05) by packaging or enhancement. Enhanced steaks were darker (P < 0.05) initially than nonenhanced steaks. Steaks packaged in HiO(2) MAP discolored faster (P < 0.05) and to a greater extent (P < 0.05) than steaks packaged in VP or ULO(2)CO MAP. Nonenhanced muscles packaged in VP and ULO(2)CO MAP had more stable display color and very desirable tenderness and flavor compared with those packaged in HiO(2) MAP.

On the Calibration Problem Extended to Nonlinear Models

The traditional calibration problem is concerned with estimating the unknown value of an explanatory variable X corresponding to an observed value of a response variable Y that is assumed to be functionally related to X. The problem for which Y is related to X by a simple linear model has been discussed in the literature. This paper is concerned with obtaining a confidence interval for an unknown value of X corresponding to a specified or fixed value of Y, where Y and X are related through a known nonlinear function. Given a specified value y, of a response variable Y that is related to X through a known function, linear or nonlinear, a point estimate of xc can be found through the inverse function, if the inverse exists, or through an iterative search procedure. Two approaches are presented for determining a confidence interval for xc, given a value y . When the inverse function exists, a confidence interval about xc can be obtained from the approximate distribution of kc, which provides a symmetric confidence interval about xc. Confidence intervals based on the asymptotic distribution of f3 are not symmetric about kc, which is particularly appropriate when considering nonlinear functions that have asymptotes. The technique based on the distribution of f3 is more general because it does not depend on having a closed form of the inverse function. A simulation study for sample sizes of 20, involving an exponential decay function, indicates that both approaches attained the desired confidence coefficient. A test procedure comparing two calibration points from different populations or treatment groups is presented. A simulation study of sample sizes of 20, involving an exponential decay function, indicates that the test procedure attains the desired level of significance with good power. Additional simulation studies may be necessary to determine the appropriateness of these techniques for different model types and/or sample sizes. An example from meat sciences research is presented demonstrating the techniques discussed.

A theorem on the difference of the generalized inverses of two nonnegative matrices

A necessary and sufficient condition for to be a non-negative matrix is presented when are assumed to be nonnegative matrices. To demonstrate the applicability of the theorem, the intra-block and combined intra-inter-block estimators of the treatment effects for an incomplete block model are compared.

Approaches To The Statistical Analysis Of Family Data

Family scholars are now becoming more and more concerned about the extent to which data collected from only one family member can accurately describe what is happening in the family. Little systematic guidance, however, has been available to researchers on how to analyze data collected from more than one family member. This paper presents several alternatives for the statistical analysis of family data. In general, it appears that multivariate multiple regression, typo logical analysis, and repeated measures designs are among the more useful tech niques for studying family data.