Cornell’s famous fish patty experiment refers to an experiment carried out by John A. Cornell, a leading figure in the development of mixture designs, a branch of Design of Experiments (DOE).

The experiment has become well-known as an illustration of mixture designs in food product development.

Background of the Experiment

John A. Cornell used this fish patty experiment to demonstrate how mixture designs can be applied when optimising product formulations where the factors (ingredients) are proportions of a total mixture. The basic premise of mixture designs is that the sum of all the ingredients must equal 100% (or 1 in normalised terms), unlike factorial designs where factors can vary independently of each other.

Objective of the Experiment

The objective of Cornell’s fish patty experiment was to optimise the sensory quality of fish patties by adjusting the proportions of various ingredients in the mixture, such as fish, potato, and water. The main challenge was to find the right balance between these ingredients to maximise the overall acceptability of the patties, particularly in terms of texture and flavour.

Factors (Mixture Components)

The key factors in the experiment were the ingredients that make up the fish patty mixture. Each factor represents a proportion of the total mix, and their sum must always equal 100%. The primary ingredients Cornell studied were:

1. Fish (X1): The main protein source.
2. Potato (X2): Acting as a binder and texture modifier.
3. Water (X3): Influences moisture content and texture.

These three components represent the entire mixture in different proportions.

Responses (Output Variables)

The responses in this experiment were based on the sensory evaluation of the fish patties. Sensory tests would involve:

• Texture: How firm or soft the patties were.
• Flavour: Overall taste perception, including the balance of fishiness, seasoning, and any aftertaste.
• Moisture content: Juiciness or dryness of the patties, which is linked to both the water content and the effect of cooking.

Sensory panels, consisting of trained evaluators, typically rate these qualities on a standardised scale. These ratings become the data used for statistical modelling.

Mixture Design Approach

Unlike factorial designs, mixture designs are more suited to experiments where the factors are ingredients in a formulation. Cornell used a simplex-centroid design, a common type of mixture design, to explore the relationships between the proportions of fish, potato, and water.

In a simplex-centroid design with three components (fish, potato, water), the design points represent different combinations of the three ingredients, including:

• Pure component points: 100% of one ingredient, with the others at 0%.
• Binary blends: Equal parts of two ingredients (e.g., 50% fish, 50% potato, 0% water).
• Ternary mixtures: A combination of all three components at different proportions.

In the simplex design, the response is evaluated at each of these points, which allows for the creation of a response surface model. The goal is to understand how changes in the proportions of fish, potato, and water affect the sensory qualities of the fish patty.

Experimental Setup

1. Selecting Proportions: Various combinations of fish, potato, and water were tested. For example:
   • Fish: 30–50%
   • Potato: 20–40%
   • Water: 10–30%
   These proportions add up to 100%, but the specific amounts varied across different trials.
2. Randomisation: The order in which different combinations were tested was randomised to reduce bias and account for any external variability during cooking or sensory testing.
3. Replication: To ensure reliable results, each combination was replicated several times, with multiple batches of patties produced for each formulation.
4. Data Collection: Sensory panel members evaluated each patty for texture, flavour, and overall acceptability. The scores were averaged for each combination of fish, potato, and water.

Data Analysis and Modelling

Once the data was collected, Cornell applied response surface methodology (RSM) to model the relationships between the mixture components and the responses. The key results of this analysis were:

• Main effects: Each component (fish, potato, and water) had a significant impact on the texture, flavour, and moisture of the patties.
• Interaction effects: The proportions of fish, potato, and water interacted with each other, meaning that the effect of one component depended on the levels of the others. For example, increasing water might improve texture if potato is also high, but might degrade texture if potato is low.

The response surface models allowed Cornell to visualise how different combinations of the three ingredients affected the quality of the fish patties. Contour plots and 3D surfaces were generated, showing which regions of the mixture space led to the most desirable sensory qualities.

Conclusion and Optimisation

The key outcome of the experiment was determining the optimal mixture for producing fish patties with the best sensory qualities. The optimal proportions were those that maximised the desirable attributes (e.g., good texture, balanced flavour) while minimising undesirable ones (e.g., excessive moisture loss).

Cornell’s fish patty experiment demonstrated how mixture designs can be used effectively in food product development, where the ingredients’ proportions need to be fine-tuned to optimise product quality. It also showed how DOE can uncover complex interactions between ingredients that would be difficult to identify using simpler experimental methods.

Importance of the Experiment

The fish patty experiment is widely cited in DOE literature and textbooks because it exemplifies the power of mixture designs in product formulation. It also shows how statistical tools like RSM can be applied to develop optimal products in the food industry, ensuring that multiple factors are considered simultaneously to achieve the best possible outcome.

This experiment is a foundational case study in mixture design and has influenced various industries beyond food, including pharmaceuticals and cosmetics, where formulation plays a critical role.