Slide 1Slide 2Wind Speeds in Hopkins Forest RevisitedSlide 4What Are Similarities/Differences?Using Histograms to Make ComparisonsSlide 7Slide 8Histograms vs. BoxplotsComparing GroupsSlide 11How to Handle OutliersOutliers and Data ErrorsWhat to Do With OutliersSlide 15Timeplots: Order, Please!Smoothing TimeplotsSmoothing Timeplots (Cont.)Other Statistical Topics Related to Time Ordered DataOther Statistical Topics Related to Time Ordered Data (Cont.)Beware of Misleading TimeplotsHistograms vs. Timeplots1Chapter04 Presentation 0615Copyright © 2014, 2012, 2009 Pearson Education, Inc.Chapter 4Understanding and Comparing Distributions2Chapter04 Presentation 0615Copyright © 2014, 2012, 2009 Pearson Education, Inc.4.1Comparing Groups with HistogramsChapter04 Presentation 06153Copyright © 2014, 2012, 2009 Pearson Education, Inc.Wind Speeds in Hopkins Forest RevisitedIn Chapter 3 we looked at daily average wind speeds in Hopkins Memorial Forest in 1989.How do these data compare to similar data from 2011?One way to make a comparison between these two years is to look at two histograms: one for 1989 and one for 2011.Chapter04 Presentation 06154Copyright © 2014, 2012, 2009 Pearson Education, Inc.19892011Chapter04 Presentation 06155Copyright © 2014, 2012, 2009 Pearson Education, Inc.What Are Similarities/Differences?ShapeCenterSpreadChapter04 Presentation 06156Copyright © 2014, 2012, 2009 Pearson Education, Inc.Using Histograms to Make ComparisonsWhen making comparisons with histograms, make sure the horizontal scales are the same!The data used for the example on the next page represents the number of cigarettes (hundreds) made per day by 2 different machines over a 30 day period.Which set of histograms makes the differences between these two machines clear?Chapter04 Presentation 06157Copyright © 2014, 2012, 2009 Pearson Education, Inc.Default JMP Output Common Horizontal Scales8Chapter04 Presentation 0615Copyright © 2014, 2012, 2009 Pearson Education, Inc.4.2Comparing Groups with BoxplotsChapter04 Presentation 06159Copyright © 2014, 2012, 2009 Pearson Education, Inc.Histograms vs. BoxplotsHistograms are fine for comparing two groups, but are not so good when comparing more than 2 groups.Side by side boxplots are ideal for comparing multiple groups:They graphically display the median and the upper and lower quartiles.They are naturally displayed on the same horizontal scale.Chapter04 Presentation 061510Copyright © 2014, 2012, 2009 Pearson Education, Inc.Comparing GroupsAre some months windier than others? Here are the 2011 data displayed by month.What do these boxplots tell you?11Chapter04 Presentation 0615Copyright © 2014, 2012, 2009 Pearson Education, Inc.4.3OutliersChapter04 Presentation 061512Copyright © 2014, 2012, 2009 Pearson Education, Inc.How to Handle OutliersOutliers deserve special attention. A little research may help you understand the cause of the outlier.Or…. there may be no specific cause, it may just be the maximum value in a highly skewed right distribution!Chapter04 Presentation 061513Copyright © 2014, 2012, 2009 Pearson Education, Inc.Outliers and Data ErrorsSometimes outliers are the result of incorrect data. Common data errors include:Transposing the digits or other data entry errorsA respondent not understanding the survey questionConfusion about units of measureCheating or lyingChapter04 Presentation 061514Copyright © 2014, 2012, 2009 Pearson Education, Inc.What to Do With OutliersIf they are fixable errors, fix them!Never ignore them. Outliers might be the most interesting data values in your data set.If you can justify removing them from your analysis, be sure to tell your audience that you have done so, and explain your reasoning.If you can’t justify removing outliers, you could do your analysis both with and without the outliers, and present both results.15Chapter04 Presentation 0615Copyright © 2014, 2012, 2009 Pearson Education, Inc.4.4Timeplots: Order, Please!Chapter04 Presentation 061516Copyright © 2014, 2012, 2009 Pearson Education, Inc.Timeplots: Order, Please!For some data sets, we are interested in how the data behave over time. In these cases, we construct timeplots of the data.Chapter04 Presentation 061517Copyright © 2014, 2012, 2009 Pearson Education, Inc.Smoothing TimeplotsTimeplots with lots of point-to-point variation are difficult to see the overall trends in the data.A smooth trace of the data can be added to help see the overall trends that exist.Chapter04 Presentation 061518Copyright © 2014, 2012, 2009 Pearson Education, Inc.Smoothing Timeplots (Cont.)A moving average of the original data is one way to smooth the data.Original Data(1989)5-Item Moving Average15-Item Moving AverageChapter04 Presentation 061519Copyright © 2014, 2012, 2009 Pearson Education, Inc.Other Statistical Topics Related toTime Ordered DataTime Series Analysis - looking for patterns in time ordered data. Issues such as the existences of seasonality, long-term trends and the impact of the economy are addressed to allow for making reasonable forecasts of the future. At UT, BAS475 is devoted to this topic.Statistical Process Control (SPC) - using time ordered data to help businesses improve the quality of their services and/or products. At UT, BAS340 contains material on this topic.Chapter04 Presentation 061520Copyright © 2014, 2012, 2009 Pearson Education, Inc.Other Statistical Topics Related toTime Ordered Data (Cont.)The primary tool of SPC is the “Control Chart”.A control chart is a timeplot with the average and “Control Limits” reported.The control limits define the amount of variation in the data that can be attributed to “chance” variation.Points outside the control limits probably have some sort of explanation for their behavior.Chapter04 Presentation 061521Copyright © 2014, 2012, 2009 Pearson Education, Inc.Beware of Misleading TimeplotsTime is on the x-axis in this image.What is on the y-axis?Chapter04 Presentation 061522Copyright © 2014, 2012, 2009 Pearson Education, Inc.Histograms vs. TimeplotsWinning Times in the Kentucky Derby (in Seconds) from 1896 to 2008. What does the timeplot (run chart) reveal that the histogram does
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