1. Statistical Analysis of Milk Fatty Acids in Three Breeds of Dairy Cattle during a Lactation Melissa Bainbridge Lucy Greenberg

2. Why do we study milk fatty acids? Because they are a significant contributor to our fat intake

3. Objective To compare the concentration and profile of milk fatty acids between Holstein, Jersey, and Holstein x Jersey crossbreeds at four stages of lactation.

4. Power Analysis A power analysis was preformed in SAS using an effect size of two standard deviations for each fatty acid. To find this effect size with a power of 0.90 at alpha = 0.05 we would need an n=8. The study was designed with n=8 in each breed but two cows were excluded from analysis.

5. Fatty Acid Methyl Esters (FAME) Cream Gas Chromatography Study Design & Methods 3 x 4 factorial Calving 3 days in milk 93 days in milk 183 days in milk 273 days in milk Dry off Milk sampling

6. Model: y ijk =μ+α i +β j +(αβ) ij +ε ijk α i = fixed effect of breedi={jersey, Holstein, jersey-Holstein cross} β j = fixed effect of lactation stagej={3, 93, 183, 273 days in milk} (αβ) ij = interaction effect of breed and lactation stage ε ijk ~ iid N(0,σ ε 2 ) error for cowk=1,...7 or 8 Σα i =0, Σβ j =0, Σ(αβ) i  =0, Σ(αβ)  j =0 Experimental Unit = Cow Observational Unit = Fatty acid measurement

7. Sources of Variation Natural variation between cows. Variation in fatty acids measurement: Variation in extraction procedure, variation due to daily production, milking time, and season. Anticipated Difficulties Loss of sample via collection malfunction or human error. Cow health affecting sample quality, i.e. mastitis, ketosis, or milk fever. Seasonal patterns affecting milk fatty acids (nuisance factor).

8. Statistical Analysis Check validity of ANOVA assumptions (homogenous variance and normality) and for outliers.

9. Statistical Analysis Cont. Test null hypothesis of no breed, lactation stage, or breed by lactation stage interaction effect using a general linear model in SAS. If there is interaction, look at simple effects of breed at each lactation stage and lactation stage at each breed (interaction plots).

10. Statistical Analysis Cont. Run contrasts to answer research questions and adjust for multiple comparisons.