Welcome to Data Analysis and Interpretation

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

2. 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 What will we be doing?

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

4. 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

5. 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 Definitions

6. 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

7. 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

8. 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 ofmisleading graphs

9. Organizing and Summarizing Quantitative Data • 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

10. 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

11. 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

12. 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

13. 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

14. 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

15. 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

16. 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

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

18. 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.