Chapter 4 Understanding and Comparing Distributions Chapter04 Presentation 0615 Copyright 2014 2012 2009 Pearson Education Inc 1 4 1 Comparing Groups with Histograms Chapter04 Presentation 0615 Copyright 2014 2012 2009 Pearson Education Inc 2 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 0615 Copyright 2014 2012 2009 Pearson Education Inc 3 1989 2011 Chapter04 Presentation 0615 Copyright 2014 2012 2009 Pearson Education Inc 4 What Are Similarities Differences Shape Center Spread Chapter04 Presentation 0615 Copyright 2014 2012 2009 Pearson Education Inc 5 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 0615 Copyright 2014 2012 2009 Pearson Education Inc 6 Default JMP Output Chapter04 Presentation 0615 Common Horizontal Scales Copyright 2014 2012 2009 Pearson Education Inc 7 4 2 Comparing Groups with Boxplots Chapter04 Presentation 0615 Copyright 2014 2012 2009 Pearson Education Inc 8 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 0615 Copyright 2014 2012 2009 Pearson Education Inc 9 Comparing Groups Are some months windier than others Here are the 2011 data displayed by month What do these boxplots tell you Chapter04 Presentation 0615 Copyright 2014 2012 2009 Pearson Education Inc 10 4 3 Outliers Chapter04 Presentation 0615 Copyright 2014 2012 2009 Pearson Education Inc 11 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 0615 Copyright 2014 2012 2009 Pearson Education Inc 12 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 lying Chapter04 Presentation 0615 Copyright 2014 2012 2009 Pearson Education Inc 13 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 Chapter04 Presentation 0615 Copyright 2014 2012 2009 Pearson Education Inc 14 4 4 Timeplots Order Please Chapter04 Presentation 0615 Copyright 2014 2012 2009 Pearson Education Inc 15 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 0615 Copyright 2014 2012 2009 Pearson Education Inc 16 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 0615 Copyright 2014 2012 2009 Pearson Education Inc 17 Smoothing Timeplots Cont A moving average of the original data is one way to smooth the data Original Data 1989 Chapter04 Presentation 0615 5 Item Moving Average Copyright 2014 2012 2009 Pearson Education Inc 15 Item Moving Average 18 Other Statistical Topics Related to Time 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 0615 Copyright 2014 2012 2009 Pearson Education Inc 19 Other Statistical Topics Related to Time 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 0615 Copyright 2014 2012 2009 Pearson Education Inc 20 Beware of Misleading Timeplots Time is on the x axis in this image What is on the y axis Chapter04 Presentation 0615 Copyright 2014 2012 2009 Pearson Education Inc 21 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 not Chapter04 Presentation 0615 Copyright 2014 2012 2009 Pearson Education Inc 22
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