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UT Knoxville STAT 201 - Chapter 04 Student 0615

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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 RevisitedIn 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?ShapeCenterSpreadChapter04 Presentation 06156Copyright © 2014, 2012, 2009 Pearson Education, Inc.Using Histograms to Make ComparisonsWhen 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. BoxplotsHistograms 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 GroupsAre 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 OutliersOutliers 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 ErrorsSometimes outliers are the result of incorrect data. Common data errors include:Transposing the digits or other data entry errorsA respondent not understanding the survey questionConfusion about units of measureCheating or lyingChapter04 Presentation 061514Copyright © 2014, 2012, 2009 Pearson Education, Inc.What to Do With OutliersIf 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 TimeplotsTimeplots 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 DataTime 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 TimeplotsTime 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. TimeplotsWinning 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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UT Knoxville STAT 201 - Chapter 04 Student 0615

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