Business Statistics. Lecture 2: Descriptive Statistical Graphs and Plots

Transcription

1 Business Statistics Lecture 2: Descriptive Statistical Graphs and Plots 1

2 Goals for this Lecture Graphical descriptive statistics Histograms (and bar charts) Boxplots Scatterplots Time series plots Mosaic plots Continue our introduction to JMP 2

3 Histogram A histogram is a graph of the observed frequencies for a statistic Use for either continuous or categorical variables Categorical histogram called a bar chart With continuous data, histograms show Shape Location or central tendency Spread or amount of variation 3

4 Reading a Histogram observations 8 between and

5 Histogram Histograms help answer: What is the overall shape of the data? Are there any unusual observations? Where is the center or average of the data located? What is the spread of the data? Is the data spread out or close to the center? 5

6 Histograms Show the Shape Histograms show overall shape of data 6

7 Histogram and the Mean Shows the central tendency or average: Where the histogram balances 7

8 Histogram and the SD Shows differences in variability

9 Histograms & Distributions The distribution of a variable describes: What values the variable can assume, and The frequency that those values occur The histogram is an empirical distribution It s the distribution we observed in the sample Often, we want to know (something about) the population distribution Could be real or an abstraction The Normal distribution occurs frequently More about normal distribution in next class 9

10 Distribution of Wharton GMAT Scores You can display the histogram horizontally or vertically in JMP 10

11 Distribution of Executive Compensation Eisner of Disney With Eisner Removed

12 An Aside: Data Transformation Sometimes transforming data is useful: It helps us see patterns in the data and/or simplifies the interpretation Logs particularly useful for financial data Log base 10 or log or log 10 easy If Y=10 X, then logy=x Examples: Y logy

13 Data Transformation, Part 2 Natural logs a little more confusing Log base e or ln or log e If Y=e X, then lny=x (where e=2.71) Examples: Y lny

14 Data Transformation, Part 3 The picture: Y log(y) ln(y) 14

15 Scale easy to interpret Executive Compensation Redux Eisner of Disney $100M 8 $10M $1M 6 0 $100K 5 15

16 Histograms vs. Bar Charts Bar chart of CEO s undergraduate degrees (Forbes94.jmp) Histogram of the year of CEO s undergraduate degrees (Forbes94.jmp) 16

17 Boxplots A boxplot shows distribution in one dimension Use with continuous variables only Most useful when comparing distributions of a continuous variable between categorical groups Will not show multiple modes 17

18 Example Boxplot outliers whiskers median outliers least half quartiles Boxplot: Center spread, skewness, outliers Requires only one dimension 18

19 Boxplot for GMAT Scores Boxplot is to a histogram what a contour map is to a mountain Imagine you are looking down on the histogram

20 Side by Side Boxplots Do CEOs in some industries make more than others? One continuous and one categorical variable Aerospacedefense Business Chemicals Capital goods Consumer Construction ComputersComm Energy Entertainment Financial WideIndustry Food Forest Insurance Retailing Travel Utility Health Metals Transport 20

21 Scatterplots A scatterplot shows the relationship between two variables Use with continuous variables only Scatterplots can help determine whether there is A positive relationship between two variables As variable #1 increases, variable #2 increases A negative relationship between two variables As variable #1 increases, variable #2 decreases A linear relationship between two variables 21

22 log10comp Scatterplot Example Do older CEO s make more than younger CEO s? Shows joint distribution of two variables More information than two marginal distributions Age

23 Time Series A time series plots one variable over time Use with continuous variables only Time series plots can help determine whether there is A trend in time E.g., stock prices are going up or down Whether the data cycles in time E.g., sales are always up during Christmas season 23

24 About Time Series Data Often one observation tells something about the next observation It s what makes time series (longitudinal) data interesting Later we ll say that the data are not independent How to tell if time series? Special knowledge (common sense?) Look for trends Look for cycles 24

25 Trends in Data Data trends in one direction or another Tends to go up or down over time Could be a linear trend Example: time 25

26 Cycles in Data Data shows a repeating pattern Retail sales often show weekly and annual cycles (e.g., sales go up on the weekends) Length of a cycle is called a period Must see several periods to determine a cycle

27 Can Have Both Cycles & Trends Trend Cycle around the trend 27

28 How Does GM s Stock Change? Price Trends? Cycles? Time How predictable is it from one period to the next? 28

29 How Predictable in the Short-term? Use relative change to get some insight: Price Today Price Yesterday RelChange Price Yesterday RelChange Time 29

30 A Note on Relative Changes Natural log of price ratio: Price Today LogRelative ln Price Yesterday For small changes LogRelative RelChange See BBS page 33 for an example 30

31 Mosaic Plots Utility Travel Transport Retailing Metals Insurance Health Forest Food Financial Entertainment Energy Consumer Construction ComputersComm Chemicals Capital goods Business Aerospacedefense Count Axis Utility Transport Travel Retailing Metals Insurance Health Forest Food Financial Entertainment Energy Consumer Construction ComputersComm Capital Chemicals goods Business Aerospacedefense Bar Chart Mosaic Plot (1 dimension) 31

32 Mosaic Plots for Two Variables 32

33 Histogram: Graphical Summaries for Continuous Variables Empirical distribution of contiuous variable Center, spread, skewness, bimodality, outliers Plots in two dimensions Boxplot: Center spread, skewness, outliers Plots in one dimension Scatterplot Plot of one variable against another Gives some idea about relationships between the two Time series plot Plot of one variable against time 33

34 Graphical Summaries for Bar chart: Categorical Variables Shows frequency of each type of observation Two dimensions Mosaic chart: Stacked bar chart showing proportions Can do side by side bars 34

35 Notes on Business Stats Reading In chapter 2, don t worry about: Details for calculating histograms by hand We ll let the software do the work for us Just skim the Grouped Data section Histograms with unequal bar widths ugh! Skip stem and leaf plots Never used in the real world 35

36 JMP Practice (1) Start JMP and load the data by double clicking on Forbes94.jmp dataset Reproduce histogram of year of CEO undergraduate degrees ( UGDate ) Analyze Distribution, highlight UGDate, select Y, Columns & OK Note the quantiles and moments Mean = average = x-bar Explore display and histogram options How would you create histograms of CEO age ( Age ) and UGDate simultaneously? 36

37 JMP Practice (2) Reproduce bar chart of CEO undergraduate degrees ( UGDegree ) Analyze Distribution, highlight UGDegree, select Y, Columns & OK It s a categorical variable (how do you know?) How is the display different? What is the mean and standard deviation for this variable? 37

38 JMP Practice (3) Create a scatterplot of CEO age and salary Pull down menu: Analyze Fit Y by X Highlight Salary, select Y, Columns Highlight Age, select X, Factor What does this plot show? Are there outliers? Can you identify them? Convention is X explains Y How you could simultaneously plot multiple Xs against one Y? 38

39 JMP Practice (4) Create log transformation of CEO total compensation ( TotalComp ) Create a new variable log10comp: Columns New Column Input column name Under Column Properties choose Formula Formula dialog box: Click on TotalComp Click Transcendental Log10 Once formula appears, click Apply and OK Now reproduce scatterplot from slide 22 39

40 JMP Practice (5) Reproduce side-by-side boxplots of CEO compensation (log10comp) by industry (WideIndustry) Pull down menu: Analyze Fit Y by X Highlight log10comp, select Y, Columns Highlight WideIndustry, select X, Factor Select OK Pull down menu under red triangle, select Display Options and Quantiles 40

41 What we have learned so far Types of data and why data vary Descriptive Statistics Numerical summaries of data Graphical summaries in one and two dimensions Histograms, boxplots, and scatterplots Bar plots and mosaic plots JMP software 41