Inferant Statistics

In this activity, you will do a factorial analysis (Two-Way ANOVA) of data collected in a study to determine if there is a difference in the amount of pressure it takes to break two different types of laminated composites under two different conditions.

Materials Science researchers create many different types of materials made from plastics, fiberglass, carbon, glass and other inexpensive materials which can be used in car engine parts, as the outer layer of airplanes, or in construction materials! Some of the materials are laminates, which means they consist of layers of materials arranged in a specific order and are held together by a special glue. In this study, the material in the layers was graphite fibers and the glue was a graphite epoxy. Two groups of laminated "sticks" were constructed. The layers in each group were arranged differently in relation to the tension that was placed on them to try to pull them apart (Figure 1).

One group was layered with the first layer in the 0 degree direction (the direction of the tension), the next layer at 90 degrees, the next at +45 degrees, the next at -45 degrees, and so forth until the required number of layers was reached (0,90,+45,-45). The second group was layered with the first layer in the 0 degree direction (the direction of the tension), the next layer at +45 degrees, the next at -45 degrees, the next at 90 degrees, and so forth until the required number of layers was reached (0,+45.-45,90). So the first factor in the Two-Way ANOVA was the type of laminate.

The two groups were then exposed to different environmental conditions. Half of each group was placed in an oven to evaporate all of the moisture out of the material. The other half of each group was placed in a chamber with 95% humidity until the material absorbed the maximum amount of moisture it could. So the second factor in the Two-Way ANOVA was the environmental condition, wet or dry.

The sticks were then put in a device that pulled on the ends and recorded the pressure when the stick broke. It is interesting to look at the various ways that the sticks broke (0,90,+45,-45), (0, +45,-45,90) and the researcher did conduct that type of analysis. In this activity, however, you will just determine if there is a difference in the breaking strength of the two types of laminates under the two environmental conditions.

Factorial Analysis (2X2)
Comparison of fracture strength
of two laminates under wet and dry conditions.

	Wet	Dry
(0,90,+45,-45)	36 pressure data points	36 pressure data points
(0,+45,-45,90)	36 pressure data points	36 pressure data points

Using the data set in Excel, perform a Factorial Analysis (Two-Way ANOVA) to determine if there is a significant difference between the two types of laminates, between the wet and dry groups, and if there is a significant interaction term.

1. Is there a significant difference in the mean fracture strengths of the two types of laminates?
2. How do you know?
3. Is there a significant difference between the fracture strength means of the wet and the dry groups?
4. How do you know?
5. Is there a significant interaction effect?
6. How do you know?

At another time, in Excel, we will construct a graph of the interaction by plotting the fracture strength means for the two types of laminates at the two conditions. (Hint: make the y axis pressure in MPa units and the x axis simply two groups; wet and dry.) Is the graph what you would expect for the type of interaction? Explain why?

The original idea and data for this activity came from Dr. Ron Kriz, a professor in the Materials Science Department at Virginia Tech.