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Design and Analysis of Experiments (2013)
Section outline
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Welcome to Design and Analysis of Experiments
Description:
After a short survey of basic statistical concepts such as estimation, significance tests and confidence intervals, an introduction will be given to the analysis of designed experiments, including analysis of variance and factorial designs. The course will also cover multiple and polynomial regression. The course will be accompanied by an introduction to a dedicated statistical software package.
Prerequisites:
The course assumes basic knowledge about mathematics and probability theory as obtained through the engineering courses at Aalborg University. Some knowledge about basic statistics, such as one sample estimation and test of hypotheses, will be desirable.
Organizer:
Jakob Gulddahl Rasmussen, Associate Professor, email: jgr@math.aau.dk
Lecturers:
Jakob Gulddahl Rasmussen, Associate Professor, Aalborg University
ECTS:
4.0
Time:
September 18, 20, 25 and 27 and October 2, 4, 9, 11, 16 and 18, 2013
All days from 12.30 to 16.00.
Place:
Aalborg University
Zip code:
9220
City:
Aalborg East
Number of seats:
40
Deadline:
September 11, 2013
Important information concerning PhD courses
We have over some time experienced problems with no-show for both project and general courses. It has now reached a point where we are forced to take action. Therefore, the Doctoral School has decided to introduce a no-show fee of DKK 5,000 for each course where the student does not show up. Cancellations are accepted no later than 2 weeks before start of the course. Registered illness is of course an acceptable reason for not showing up on those days. Furthermore, all courses open for registration approximately three months before start. This can hopefully also provide new students a chance to register for courses during the year. We look forward to your registrations.
Read the following introduction before the start of the course:
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Topics:
- What is an experiment?
- A bit of probability theory.
- Basics of the statistical package `R'.
Read: Montgomery: Chap. 1, and Sec. 2.1, 2.2, 2.3. We won't finish Sec. 2.3 in the first lecture, but we will continue the next time.
Location: Fredrik Bajers Vej 7B, room B2-107 - please notice that the location changes during the course.
Remarks:
- I assume that you have attended a basic course in probability and statistics, such that the material in Chapter Two of Montgomery can be considered a revision.
- We shall later include some geometrical considerations to a minor extent. Hopefully, you have not forgotten all the linear algebra from your freshman year!
- After each lecture, another file with solutions for the exercises will appear.
- Please remember to read the introduction to the course, which can be found above, and bring a laptop with R and RStudio installed.
Files:
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Topics:
- Experiments with one or two populations.
Read: Montgomery, Sec. 2.3, 2.4, 2.6.
Location: Fredrik Bajers Vej 7B, room B2-107
Files:
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Topics:
- A few left-overs on the theory of tests.
- Paired t-test.
- One-way ANOVA.
- Kruskal-Wallis test, a non-parametric alternative to ANOVA.
Location: Fredrik Bajers Vej 7B, room B2-109
Files:
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Topics:
- Model checking using residuals.
- Comparison of levels of a factor.
Location: Fredrik Bajers Vej 7C, room C2-209
Handin 1: The first handin is now available. Details (including date) on handing it in can be found in the slides.
Files:
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Topics:
- One-way ANOVA with a random factor.
- Randomised complete blocks design.
- Latin square design.
Location: Fredrik Bajers Vej 7B, room B2-109
Files:
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Topics:
- Graeco-Latin square designs.
- Balanded incomplete block design.
- Models and matrix algebra in linear regression.
Location: Fredrik Bajers Vej 7B, room B2-107
Remarks:
- For BIBD, the crossing factors Treatment and Block are not orthogonal. Fortunately, R can do the calculations of Sum of Squares, such that the cumbersome formulae in the book are not needed. You can skip the calculations from Formula (4.28) and until the end of the section.
- In this course, we assume that the response variable is quantitative (continuous). In analysis of variance (ANOVA), the explanatory variables are qualitative (factors), in regression analysis the explanatory variables are quantitative (continous), and in analysis of covariance (ANCOVA) there are both qualitative and quantitative explanatory variables.
Files:
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Topics:
- Models and matrix algebra in linear regression.
- Testing, confidence intervals and prediction intervals in regression.
- Regression diagnostics.
Location: Niels Jernes Vej 14, room 3-119
Remarks:
- Residuals can be plotted against the fitted values (this is the first choice), against explanatory variables (to check if a linear term is enough), against variables you don't consider important (just to be sure), in the order they occur (this is the index plot). But NEVER EVER plot residuals against the response variable!
Files:
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Topics:
- Test for "lack of fit".
- Two-way analysis of variance.
- ANOVA in the unbalanced case.
- Analysis of Covariance.
Location: Niels Jernes Vej 14, room 3-119
Remarks:
- Concerning explanatory variables, notice that a quantitative (continuous) variable gives one degree of freedom, whereas for a qualitative variable (factor) the number of degrees of freedom is one less than the number of levels.
- In testing "lack of fit", analysis of variance and regression analysis are combined. In the former, the explanatory variable is considered qualitative (a factor) with degrees of freedom one less than the number of levels. In the latter, the explanatory variable is considered quantitative (continuous) with only one degree of freedom.
- Remember to test interaction before main effects. Montgomery seems to suggest the other (illogical) order.
Handin 2: Handin 2 is now available.
Files:
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Topics:
- Analysis of variance with two random factors.
- The two-way mixed model.
- Three-way analysis of variance.
- Response curves and surfaces.
Location: Niels Jernes Vej 14, room 3-119
Remarks:
- For the mixed model, Sec. 13.3, the unrestricted model seems more natural than the restricted one. To me the restricted model is an artifice to avoid negative variance components.
- If a negative variance component occurs in an unrestricted mixed model, there is no problem if it is non-significant. Just remove it from the model. If significant, modelling requiring the multidimensional normal distribution is required.
Files:
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Topics:
- 2k factorial designs.
- Factorial designs with a single replicate.
- Fractional designs.
- Nested designs.
- Evaluation of the course.
Location: Niels Jernes Vej 14, room 3-119
Files: