A STUDY OF THE EFFECTS OF BAKING MATERIALS AND OVEN TEMPERATURE ON CAKE HEIGHT: SPLIT-PLOT CENTRAL COMPOSITE DESIGN APPROACH

Abstract

Most people love a delicious piece of cake. But what is the secret to a good cake? While many may comment on flavor, frostings or other attributes, most people agree on one thing: texture. The texture of the cake needs to be “fluffy”. While there are exceptions to the traditional textures, one of the easiest ways to get the right texture of a cake is by having the cake rise to a maximum height. By having the tallest cake with the same amount of starting material, more air is allowed into the cake, thereby creating the “fluffy” texture that people desire. In this work, a central composite design (CCD) experiment within a split-plot structure was conducted to assess the impact of some baking materials on cake height. The experimental factors (cake-baking materials) include oven temperature (factor A), amount of flour (factor B), baking powder (factor C), and amount of milk (factor D) with a fixed amount of other necessary ingredients present. The generated data were analyzed using Design Expert (version 10) statistical package. The restricted maximum likelihood (REML) estimates of the variance components were first obtained and the generalized least squares (GLS) estimator was used to obtain the factor effects estimates. The set of levels of these factors that yields optimum value of the cake height (the stationary point) was then sought using optimization facility of the statistical package. It was observed that each of the linear terms: A, B, C, D, the interaction term: BC and the quadratic terms: A2 , C2 , and D2 contributes significantly to the height of the cake. The fitted generalized least squares model accounted for 95% of the total variation in the cake height. The estimated optimum cake height was found to be 𝑦̂ = 11.047 at the stationary point: 𝑜𝑣𝑒𝑛 𝑡𝑒𝑚𝑝 = 250𝑜𝐶, 𝑎𝑚𝑜𝑢𝑛𝑡 𝑜𝑓 𝑓𝑙𝑜𝑢𝑟 = 1.5 𝑐𝑢𝑝𝑠, 𝑏𝑎𝑘𝑖𝑛𝑔 𝑝𝑜𝑤𝑑𝑒𝑟 = 1.5 𝑡𝑒𝑎𝑠𝑝𝑜𝑜𝑛𝑓𝑢𝑙𝑙, 𝑎𝑛𝑑 𝑚𝑖𝑙𝑘 = 0.75𝑐𝑢𝑝.