22-23 March 2011

Dick Schwanke

Welcome to Data Analysis and Interpretation

What will we be doing?

Examining different mathematical /statistical analysis techniques

Applying those techniques to our data.

Definition of Statistics: the science of collecting, organizing, summarizing, and analyzing information to draw conclusions or answer questions

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What is data?Fact or Proposition used to draw a

conclusion or make a decisionCan be numerical

Can be non-numerical

Who is Data?

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DefinitionsPopulation: The group to be studied

Parameter is numerical summary of population

It is all Greek to me

Sample: The subset of the populationStatistic is a numerical summary of a sample

When in Rome, do as the Romans do

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DefinitionsQualitative variable – classification of

individuals based on some attribute or characteristic

Quantitative variable – provide numerical measures of individualsDiscrete Variable – has either countable or

finite number of possible valuesContinuous variable – has an infinite number

of possible values5

Some Administrative DetailsLet us gather some data

Introductions

Name / Job Function / Excel Experience / 1 fact

Discuss these items with adjacent team member

Class roster completed

Schedule of these two days

Mix of lecture with problems

Computer lab with Microsoft Excel 20076

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Organizing and Summarizing Quantitative DataStep 1: Organize raw data into classesStep 2: Create tables for the data:

frequency distributionrelative frequency distributioncumulative frequency distributionrelative cumulative frequency distribution

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Organizing and Summarizing Quantitative DataStep 3: Create graphs

bar chartspie chartshistogramsfrequency polygonsogivesstem-and-leaf plotsdot plots

Step 4: Be cautious of misleading graphs

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Organizing and Summarizing Quantitative Data

Steps:Organize raw data into classesCreate table with frequency distribution, relative

frequency distribution, cumulative frequency distribution, and relative cumulative frequency distribution

Create graphical displays with histogram, frequency polygon, ogive, stem & leaf plot

• Put into classes• Start with lowest value

Organize Data • Frequency distribution

• Relative frequency distribution,

• Cumulative frequency distribution

• Relative cum. frequency distrib.

Create Table

• Histogram• Frequency polygon• Ogive• Stem & leaf plot

Draw Graphic Displays

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Ways of Displaying Data - HistogramA graph using rectangles for each class of

data, where the height of each rectangle is the frequency or relative frequency of the class

Note 1 : width of each rectangle is the same and rectangles touch each other

Note 2: methods for discrete and for continuous data

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More Ways of Displaying Data – Cumulative Distributions

Cumulative frequency distribution: displays aggregate frequency of category i.e. total number of observations less than or equal to that category

Cumulative relative frequency distribution: displays the percentage (or proportion) of observations less than or equal to that category

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More Ways of Displaying Data – Cumulative Distributions

Additional notes:Works as a table or as a graphFor continuous data display the total

number of observations less than or equal to the upper class limit of a class

Class midpoint – determined by adding consecutive lower class limits then divide the result by 2

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More Ways of Displaying Data – Frequency Polygons

Construct with:class on horizontal axisfrequency on vertical axis

Plot a point above each class midpointDraw straight lines between consecutive

points

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More Ways of Displaying Data – Ogives

Like a frequency polygon except represents cumulative frequency or cumulative relative frequency for the class

Construct with: upper class limits on horizontal axiscumulative frequency (or cumulative

relative frequency) on vertical axis

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More Ways of Displaying Data – Stem and Leaf Plot

Step 1: Select stem – the digit(s) to the left Leaf will be the rightmost digit

Step 2: Write the stems in a vertical column in increasing order. Draw vertical line to right of stems

Step 3: Write each leaf to right of its stemStep 4: (re)Write leaves in ascending

order

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More Ways of Displaying Data – Stem and Leaf Plot

Other notes about stem and leaf plots:Best used when data set is smallCan use “split stem” method if data

seems too bunched

These sections give us many “tools” for our “toolbox”, so that we may use the best one (the best graphical display) for our audience’s understanding of our point

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Shapes of DistributionsUniformSymmetric (bell shaped)Skewed right (long tail to right)Slewed left (long tail to left)

Graphic SuggestionsTitle both axis, label includes unit of measureInclude data source when appropriate.Minimize white space in the graph, using

available space to let the data stand outAvoid clutter: pictures, excessive gridlinesAvoid distortion. Never lie about the dataAvoid three dimensional charts and graphsLet the data speak for themselves.

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