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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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. 1.96 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

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

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

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

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

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

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

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

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