Ivonne Santiago, Ph.D.
In partial fulfillment of the requirements for
Environmental Science & Engineering 6306
Principles of Experimental and Engineering Design
December 10, 2009Introduction
Experiments are essential to the development and improvement of engineering and scientific methods. Many experiments involve varying the values of one or more quantities to determine their effect on a response.
Using the design of experiments (DOE) capabilities we are simultaneously investigating the performance of student of different majors (Education and Biology) using multiplevariables (lab, quiz and exam). These experiments consist of a series of analysis to test the significance of various student assessments and the effects of each variable on the factorial combinations.
Design of Experiment DOE is a very important tool use to identify the process conditions and product components that influence quality and then determine the input variable (factor) settings thatmaximize results. This was also employed in this experiment.
The Null hypothesis for this experiment was, there is no significant difference between students from education and biology majors among students taking biology class. The alternative hypothesis was that the performance of Biology major students was assumed to be different than the Education major.H0: µ1 ═ µ2
H1: µ1 ≠ µ2
µ1= Education students
µ2 = Biology students.
The factorial experiment was based in two levels that are varied in this experiment; these are education and biology majors. Three factors for evaluating the performance of this experiment are the following
• Final grades.
These generate 8 possible combinations outcome for 23 factorial experiments.
Data Description and Basic Statistics:
The data used for this experiment was obtained from the University records office (table 1) 36 students were chosen randomly manner from education and biology major students that registered for Biology class from the University register systemfor Fall 2008. The registration process was done online through the university GOLDMINE thereby guarantying the randomness of the sample group.
|Major |Lab |Quiz |Final | |Major |
|Quiz |13.75 |0.63 |3.75 |14.06 |15.02 |
|Lab |21.19 |1.33 |7.95|19.88 |24.00 |
|Final |76.60 |2.38 |14.30 |72.85 |80.50 |
Table 2: Descriptive Statistics of the quizzes, lab and final grades
Figure 1 indicated the Normal, Weibull, 2-Parameter Exponential and Gamma distribution plot. The normal distribution had the best fit of the all the four distribution analysis methods ascan be observed from the significant dot plot (well spread and best fit into the blue lines) and the P-value (0.010) as stipulated by Blank and Tarquin 2005. The normal probability plot of the quiz, lab and the final also indicated a good fit with plotted points roughly follow a straight line and best fit obtained from the quiz (figure 2). Therefore normal distribution was used in the analysisof the experiment.
Figure 1: Normal, Welbull, 2-Parameter Exponential and Gamma distribution plot.
Figure 2: Normal Probability Plot of the quiz, lab and the final
The data had the following Full Factorial Design data generated from Minitab. 3 numbers of factors; 8 numbers of base design; 8 numbers of runs; 1 number of replicates; 1 block and 1...