Due to the close proximity of end of classes, publishing my comments on project solutions, and the final exam date, I have decided that the exam will be an easy one. So do not panic. Some recommendations follow:
1. Study well all project problem solutions and my comments on them. Be sure you understand my arguments in those problems where I have found mistakes or other faults.
2. Study well Chapter 14, and the examples 14.1 to 14.4.
3. Understand very well and know how to determine all terms of an ANOVA table. The Anova table is a useful tool in Chapters 11 to 14.
4. Some terms, like sum of squares have lousy formulae, I will hand-in any equation needed to calculate things, you do not need to memorize formulae.
5. You do need to know by heart certain statistical terms, as an example, not knowing to differentiate between population average from sample average; or variance from standard deviation would be a great dissapointment to me after talking about this during a whole semester.
6. Scores from Exam 2 will be taken to the exam site for you to see and check. No scores of project will be available this week.
L. Saliceti
Both groups worked well solution to part (a). There would be need to have the nine point experiment to perform the hypothesis test.
In part (b) Group # 2 proposed the correct equation to calculate Beta, because the hypothesis test is a one-sided test. Group # 8 failed to recognize this fact. However, group # 2 made mistake in calculating the delta term, should have used the absolute value, which changes a little bit the value between brackets of "Phi".
Part (c) is similar to (b), but all groups failed to recognize that if the value of x_A results closer to the value of 0.30, then the probability of making a type II error (Beta) becomes larger.
Both groups worked well the solution, although Group # 7 did a better job at understanding the differences among Treatment Substance pairs. From the data provided, it should be evident that a completely randomized block design was the analysis to perform, because each individual patient would represent a "block" effect.
When in doubt as to use blocks or not, follow the instructions given by the book author on page 496, penultimate paragraph, last two sentences: "As a general rule, when in doubt as to the importance of block effects, the experimenter should block and gamble that the block effect does exist. If the experimenter is wrong, the slight loss in the degrees of freedom for error will have a negligible effect, unless the number of degrees of freedom is very small." In other words, treat the data using the randomized block design analysis and compare to the randomized fixed-effects analysis.
Both groups solutions are Ok. In part (b) a Tukey Kramer Multiple Comparison analysis could be made, but that was not part of our class and text discussions. An alternative was to perform the Fisher LSD test, covered in class. Anyway, any of these tests would result in that the run to run mean comparisons are not significantly different. The Tukey Kramer Multiple Comparison method is similar to the Fisher LSD method, both can be made using Minitab.
The solution presented by the two groups is Ok. They performed the transformation of variables, regression and ANOVA analyses, and the adequacy tests by plotting the residuals. One thing they only missed to do was to make the residual probability plot.
Solution of part (a) for both groups is Ok, however, they failed to perform the adequacy of the regression model (Section 11-8): residual analysis and plots.
In part (b) the groups calculated the estimator of the variance of error, not the variance of the estimator of the kinetic parameter "k". The variance of "k" must be determined using the standard error estimation of Beta 1 found in the blue squared section on page 384.
The solution from both groups are Ok, but some tables show different values, although they are close to each other.
Best model is the first model based on the ANOVA table results and R^2, however, better models can be sought.
One comment is that group #6 incorrectly plotted the converted variables as ln x versus ln x, so a perfect fit shows.
Now, both groups failed in that they should have done the adequacy tests of the models (Section 11-8): residual analysis and plots to find out any strange behavior among the two proposed models.
The solution from group #7 is correct in the sense that the population variances are unknown, therefore the hypothesis test should be based on the "t" statistic, not the "z" statistic.
However, there are two choices to make: are both population variances equal or not? Depending on the answer we can test using Equation set 10.14 (equal variances, what group #7 used), or Equation set 10.15 and 10-16 (unequal variances).
The answer to this is that first we must make a hypothesis test on the ratio of the two variances, section 10-5.3. Through this test it can be shown that there is no statistical difference in variances among the two biocatalysts. After that, then we can proceed to the test using Equation set 10.4 as done by group #7.
