1. DESIGN OF EXPERIMENT (DOE)
Eng. Ibrahim Kuhail
DOE Lecture 2
May 13, 2019

2. Introduction
There are two types of experiments in experimental design:
Simple comparative experiments.
Comparing more that two factor levels…the analysis of variance (ANOVA).
DOE Lecture 2
May 13, 2019

3. Simple Comparative Experiments
SCE is an experiment that compares two conditions or treatments.
SCE deals with:
The hypothesis testing framework
The two-sample t-test
Checking assumptions, validity
DOE Lecture 2
May 13, 2019

4. Graphical View of the Data
Data can be presented graphically using many ways:
Dot Diagram.
Box Plot.
Histogram.
Pareto Chart.
These tools are useful for summarizing the information in a sample of data.
Box plots, histograms, and Dot Diagram are valuable aids for identifying possible outliers in a single variable.
DOE Lecture 2
May 13, 2019

5. Dot Diagram It is a diagram used to plot data points on an axis.
It is useful for displaying a small body of data.
It enable experimenters to see the general locations or central tendency of the observations and their spread.
For large data; histogram is more preferable.
DOE Lecture 2
May 13, 2019

6. Dot Diagram (Cont.)
DOE Lecture 2
May 13, 2019

7. Box Plots Used to display data.
It displays the minimum, the maximum, the lower quartile (25% percentile), the upper quartile (75% percentile), and the median (50% percentile) on a rectangular box aligned either horizontally or vertically.
DOE Lecture 2
May 13, 2019

8. Box Plots (Cont.)
DOE Lecture 2
May 13, 2019

9. Histogram
Shows the central tendency, spread, and general shape of the distribution.
It is constructed by dividing the horizontal axis into intervals and drawing a rectangle over the jth interval with the area of the rectangle is proportional to nj (# of observations fall in that interval)
Distribution Shapes:
Uniform Distribution.
Bell-Shaped Distribution.
Skewed Distribution (Left or Right).
DOE Lecture 2
May 13, 2019

10. Histogram (Cont.)
DOE Lecture 2
May 13, 2019

11. Pareto Chart
Is a bar graph in which the bars are drawn in descending order of frequency or relative frequency.
DOE Lecture 2
May 13, 2019

12. Outlier
In statistics; an outlier is an observation that is numerically distant from the rest of the data.
An outlier is an observation that lies an abnormal distance from other values in a random sample from a population.
In a sense, this definition leaves it up to the analyst (or a consensus process) to decide what will be considered abnormal. Before abnormal observations can be singled out, it is necessary to characterize normal observations.
DOE Lecture 2
May 13, 2019

13. Statistics
Statistics is a branch of mathematics that deals with the collection, analysis, interpretation, and presentation of numerical data to make decisions to solve problems and to design products and processes.
DOE Lecture 2
May 13, 2019

14. Sample Vs. Population
The sample summaries and represents the entire population.
Randomly selected from the population.
For sample: ( , S, S2,n) and for population (µ,σ, σ2,N)
Ex. Industrial engineering students are a sample of IUG population.
DOE Lecture 2
May 13, 2019

15. Descriptive Statistics
Descriptive Statistics are statistics used to organize and summarize the data collected.
It consists of charts, tables, and numerical summaries.
DOE Lecture 2
May 13, 2019

16. Basic Statistics
Average
Standard Deviation
DOE Lecture 2
May 13, 2019

17. Type I and Type II Errors
Type I Error
Type II Error
α -error.
Good items rejected.
Ex: When the jury convicts an innocent person.
β –error.
Bad items accepted.
Ex: when a guilty defendant is acquitted.
DOE Lecture 2
May 13, 2019

18. Sample Size Calculator
According to Creative Research Systems , the sample size of the study can be determined using the following equation:
Where
Z = Z value (e.g for 95% confidence level) 
P = percentage picking a choice, expressed as decimal (0.5 used for sample size needed)
C = confidence interval, expressed as decimal (e.g., 0.05 = ±5)
DOE Lecture 2
May 13, 2019

19. Sample Size Calculator (Cont.)
The value population of SS is then changed to a value for finite using the following equation:
Where
POP = population of the study.
DOE Lecture 2
May 13, 2019

20. Statistical Inference
Inferential statistics consists of methods for drawing and measuring the reliability of conclusions about a population based on information obtained from a sample of the population.
DOE Lecture 2
May 13, 2019

21. Statistical Inference
Biostatistics Academic Preview: Session 3
08/29/06
Statistical Inference
Estimation: the process by which sample data are used to indicate the value of an unknown quantity in the population. Results can be expressed as:
Point estimate
Confidence intervals
Significance tests
P-values
DOE Lecture 2
May 13, 2019

22. Statistical Estimation
Biostatistics Academic Preview: Session 3
Statistical Estimation
08/29/06
Population parameter
Sample Statistics
Mean
Proportion p
correlation ρ r
DOE Lecture 2
May 13, 2019

23. Biostatistics Academic Preview: Session 3
08/29/06
Confidence Intervals
A confidence-interval estimate of a parameter consists of an interval of numbers obtained from a point estimate of the parameter together with a percentage that specifies how confident we are that the parameter lies in the interval. The confidence percentage is called the confidence level.
DOE Lecture 2
May 13, 2019

24. Confidence Intervals (Cont.)
A range of values in which a population parameter may lie is a confidence interval.
The probability that a particular value lies within this interval is called a level of confidence.
DOE Lecture 2
May 13, 2019

25. Hypothesis Testing Inferences about the difference in means.
One sample test: test about µ0
If σ is known (known variance) and/or the data is randomly selected and/or N >25 or 30  z-test
If σ is unknown (unknown variance) (s given or calculated) and/or the data is not randomly selected and/or N < 25 or 30  t-test
Two samples test : Compares two means (µ1 ,µ2)
If σ1, σ2 are known (known variances) and/or the data is randomly selected and/or N1 , N2 >25 or 30  z-test
If σ1, σ2 are unknown (unknown variances) (s1,s2 given or calculated) and/or the data is not randomly selected and/or N1 , N2 <25 or 30  t-test
DOE Lecture 2
May 13, 2019

26. One Sample Test on Means
z- test
t- test
σ (variance)
Known
Unknown s ( calculated)
data
Randomly
Not necessary n
>25 or 30
<25 or 30
Test Statistics
DOE Lecture 2
May 13, 2019