LSSG Green Belt Training

Overview of Charts and Graphs: Mini Case

Overview – The Story

A retail company has 3 regional shipping centers, each with its own computer system.

Goal: To determine which of the 3 systems is most efficient, determine if it helps meet customer needs regarding shipping, and improve it further. Then, the system can be used companywide to facilitate integration and enhance efficiency.

Source: Meet Minitab (http://www.minitab.com/support/docs/rel14/MeetMinitab14.pdf)

Shipping Example Data

A few records from the dataset (total 319 records) are shown below:

Center Order Arrival Days Status DistanceEastern 3/3/2003 8:34 3/7/2003 15:21 4.28264 On time 255Eastern 3/3/2003 8:35 3/6/2003 17:05 3.35417 On time 196Eastern 3/3/2003 8:38 * * Back order 299Central 3/3/2003 8:58 3/6/2003 14:59 3.25069 On time 81Central 3/3/2003 9:04 3/8/2003 10:12 5.04722 On time 235Central 3/3/2003 9:06 3/9/2003 16:13 6.29653 Late 259Western 3/3/2003 9:44 3/6/2003 10:08 3.01667 On time 291Western 3/3/2003 9:46 3/6/2003 9:50 3.00278 On time 271

Source: Minitab Software V14 Example file

Categorical Data Continuous (Numerical) Data

First Look at Shipping Data – Univariate Analysis

Univariate analysis simply means looking at data one variable at a time, as a precursor to multivariate analysis.

Purpose: To understand the individual variables before exploring relationships

among variables, To check for extraordinary, incorrect, or missing data.

The basic method is to graph the data to look at the distribution, and compute measures of central tendency (Mean/Median) and variation (Range, Standard Deviation).

Individual Value PlotsDa

ys

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Individual Value Plot of Days

Center

Days

WesternEasternCentral

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Individual Value Plot of Days vs Center

The graphs below show the number of days for shipping for all data together on the left, and separated by shipping center on the right. The graph on theright also shows the mean values for each center connected by a line. At first glance, it is evident that the Western center has the lowest mean number of daysfor shipping.

Frequency Histograms – A look at the distribution

Days

Freq

uenc

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7654321

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Histogram of Days

Days

Freq

uenc

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3.984 1.280 994.452 1.252 1012.981 1.090 102

Mean StDev N

CentralEastern

Western

Center

Histogram of DaysNormal

Frequency histograms help us see how the data are distributed. At left we can see that the number of days for shipping across all centers is normally distributed with a mean of about 4, and ranging from about 1 to 8 days. At the right is the distribution of the 3 centers shown separately.

Box Plots – Comparing Distributions

Box plots are a useful way to compare distributions visually. Box plotsshow the smallest value, the first quartile, median, third quartile, and the Largest value of the variable. In the plots below, the Mean is also marked.

Center

Days

WesternEasternCentral

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Boxplot of Days vs Center

Graphing Categorical Data – Bar/Pie Charts

Central Eastern

Western

Back orderLateOn time

Category

Pie Chart of Status

Panel variable: Center

The Bar chart below shows the status of orders in the sample as A percentage. About 7-8% of the orders are on back-order, whileAbout 5% are shipped late overall. The Pie charts show the percent Of back-orders and late shipments by each center.

Status

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On timeLateBack order

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Chart of Status

Descriptive Statistics

Descriptive Statistics: Days Results for Center = Central

Variable Status N N* Mean SE Mean StDevDays Back order 0 6 * * * Late 6 0 6.431 0.157 0.385 On time 93 0 3.826 0.119 1.149

Results for Center = Eastern

Variable Status N N* Mean SE Mean StDevDays Back order 0 8 * * * Late 9 0 6.678 0.180 0.541 On time 92 0 4.234 0.112 1.077

Results for Center = Western

Variable Status N N* Mean SE Mean StDevDays Back order 0 3 * * * On time 102 0 2.981 0.108 1.090

Descriptive statistics give us numerical insight into the data. Compare this information to the graphs on the previous page.

Testing Hypotheses - ANOVA

One-way ANOVA: Days versus Center

Source DF SS MS F PCenter 2 114.63 57.32 39.19 0.000Error 299 437.28 1.46Total 301 551.92

S = 1.209 R-Sq = 20.77% R-Sq(adj) = 20.24%

Individual 95% CIs For Mean Based on Pooled StDevLevel N Mean StDev -----+---------+---------+---------+----Central 99 3.984 1.280 (----*---)Eastern 101 4.452 1.252 (----*----)Western 102 2.981 1.090 (----*---) -----+---------+---------+---------+---- 3.00 3.50 4.00 4.50

Pooled StDev = 1.209

While it looks like the centers are different in their efficiencies, a hypothesis test can confirm that. A one-way ANOVA tests whether the mean number of days for the 3 centersare in fact significantly different from each other. The low p-value (almost 0) indicates that one can conclude with great confidence (almost 100%) that there at least one of the centers is different from the others.

Examining relationships - scatterplot

Distance

Days

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Scatterplot of Days vs Distance

Is the better performance of the Western center due to smaller shipping distances than the other regions? First, a scatterplot of Number of Days for shipping against the Distance across all centers seems to show no relationship between the two.

Scatterplot separated by Center

Distance

Days

5004003002001000

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CentralEasternWestern

Center

Scatterplot of Days vs Distance

When we look at it by center, there still seems to be no relationship between distance and number of days.