Welcome to Data Analysis and Interpretation 22-23 March 2011 Dick Schwanke

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

Who is Data? What is data? Fact or Proposition used to draw a conclusion or make a decision Can be numerical Can be non-numerical

Definitions Population: The group to be studied Parameter is numerical summary of population It is all Greek to me Sample: The subset of the population Statistic is a numerical summary of a sample When in Rome, do as the Romans do

Definitions Qualitative variable – classification of individuals based on some attribute or characteristic Quantitative variable – provide numerical measures of individuals Discrete Variable – has either countable or finite number of possible values Continuous variable – has an infinite number of possible values

Some Administrative Details Let 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 2007

Organizing and Summarizing Quantitative Data Step 1: Organize raw data into classes Step 2: Create tables for the data: frequency distribution relative frequency distribution cumulative frequency distribution relative cumulative frequency distribution

Organizing and Summarizing Quantitative Data Step 3: Create graphs bar charts pie charts histograms frequency polygons ogives stem-and-leaf plots dot plots Step 4: Be cautious of misleading graphs

Organizing and Summarizing Quantitative Data Organize Data Put into classes Start with lowest value Create Table Frequency distribution Relative frequency distribution, Cumulative frequency distribution Relative cum. frequency distrib. Draw Graphic Displays Histogram Frequency polygon Ogive Stem & leaf plot Steps: Organize raw data into classes Create 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 Page &p of 6

Ways of Displaying Data - Histogram A 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

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

More Ways of Displaying Data – Cumulative Distributions Additional notes: Works as a table or as a graph For 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

More Ways of Displaying Data – Frequency Polygons Construct with: class on horizontal axis frequency on vertical axis Plot a point above each class midpoint Draw straight lines between consecutive points Page &p of 6

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 axis cumulative frequency (or cumulative relative frequency) on vertical axis

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 stem Step 4: (re)Write leaves in ascending order

More Ways of Displaying Data – Stem and Leaf Plot Other notes about stem and leaf plots: Best used when data set is small Can 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

Shapes of Distributions Uniform Symmetric (bell shaped) Skewed right (long tail to right) Slewed left (long tail to left)

Graphic Suggestions Title both axis, label includes unit of measure Include data source when appropriate. Minimize white space in the graph, using available space to let the data stand out Avoid clutter: pictures, excessive gridlines Avoid distortion. Never lie about the data Avoid three dimensional charts and graphs Let the data speak for themselves.