1. ITEC6310 Research Methods in Information Technology Instructor: Prof. Z. Yang Course Website: http://people.math.yorku.ca/~zyang/ite c6310.htm Office: Tel 3049

2. 2 Organizing Data Graph –Helps to make sense of your data by representing them visually –A basis graph represents the data in two- dimensional space. –Represent levels of your independent variable along the x-axis and value of the dependent variable along the y-axis. –The importance of graphing data Showing relationships clearly Choosing appropriate statistics Table

3. 3 Graphing Your Data Bar Graph –Presents data as bars extending from the axis representing the independent variable –Length of each bar determined by value of the dependent variable –Width of each bar has no meaning –Can be used to represent data from single-factor and two-factor designs –Best if independent variable is categorical

4. 4 Example Bar Graph

5. 5 Data represented by a series of points connected by a line Most appropriate for quantitative independent variables Used to display functional relationships Line graphs can show different shapes –Positively accelerated: Curve starts flat and becomes progressively steeper as it moves along x-axis –Negatively accelerated: Curve is steep at first and then “levels off” as it moves along x-axis Once the curve levels off it is said to be asymptotic A line graph can vary in complexity A monotonic function represents a uniformly increasing or decreasing function A nonmonotonic function has reversals in direction Line Graph

6. 6 Example Line Graph

7. 7 Used to represent data from two dependent variables The value of one dependent variable is represented on the x-axis and the value of the other on the y-axis Scatterplot

8. 8 Example Scatterplot

9. 9 Pie Graph Used to represent proportions or percentages Two types –Standard pie graph Exploded pie graph

10. 10 Example A researcher observes driving behaviour on a roadway, noting the gender of the drivers, the types of vehicle driven, and the speed at which they are traveling. The researcher wants to organize the data in graphs. Which type of graph should be used to describe each variable?

11. 11 The Frequency Distribution Represents a set of mutually exclusive categories into which actual values are classified Can take the form of a table or a graph Graphically, a frequency distribution is shown on a histogram –A bar graph on which the bars touch –The y-axis represents a frequency count of the number of observations falling into a category –Categories represented on the x-axis

12. 12 Example of a Histogram

13. 13 Example The following data represent a distribution of speed at which individuals were traveling on a highway. 64, 80,64,70,76,79,67,72, 65,73,68,65,67,65,70,62,67,68,65,54 Organize the above data into a frequency distribution table and draw the histogram for these data.

14. 14 Shapes of Histograms You should examine your frequency distribution to determine its shape. –Normal distribution: Most scores centered around the mean –Positive skew: Most scores at the lower end of the measurement scale –Negative skew: Most scores at the higher end of the measurement scale –Bimodal distribution: Two modes

15. 15 Histogram Showing a Positive Skew

16. 16 Histogram Showing a Negative Skew

17. 17 A Bimodal Distribution

18. 18 Descriptive Statistics Measures of Center –Gives you a single score that represents the general magnitude of scores in a distribution. –Three measures Mode, median and mean Measures of Spread –Measure of variability

19. 19 Measures of Center Mode –Most frequent score in a distribution –Simplest measure of center –Scores other than the most frequent not considered –Limited application and value Median –Central score in an ordered distribution –More information taken into account than with the mode –Relatively insensitive to outliers –Used primarily when the mean cannot be used

20. 20 Mean –Average of all scores in a distribution –Value dependent on each score in a distribution –Most widely used and informative measure of center Measures of Center

21. 21 Choosing a Measure of Center Mode –Used if data are measured along a nominal scale Median –Used if data are measured along an ordinal scale –Used if interval data do not meet requirements for using the mean Mean –Used if data are measured along an interval or ratio scale –Most sensitive measure of center –Used if scores are normally distributed

22. 22 Example In the example on Slide 10, a researcher collected data on driver’s gender, type of vehicle, and speed of travel. What is an appropriate measure of central tendency to calculate for each type of data? In the example on Slide 13, if one driver was traveling at 100mph (25 mph faster than anyone else), which measure of central tendency would you recommend against using?

23. 23 Example Calculate the mean, median, and mode for the data set on Slide 13. Is the distribution normal or skewed? If it is skewed, what type of skew is it? Which measure of central tendency is most appropriate for this distribution and why?

24. 24 Measures of Spread Range –Subtract the lowest from the highest score in a distribution of scores –Simplest and least informative measure of spread –Scores between extremes are not taken into account –Very sensitive to extreme scores Interquartile Range –Less sensitive than the range to extreme scores –Used when you want a simple, rough estimate of spread

25. 25 Variance –Average squared deviation of scores from the mean –Not expressed in same units as original numbers Standard Deviation –Square root of the variance –Expressed in the same units as original numbers –Most widely used measure of spread Measures of Spread

26. 26 Measures of Spread: Applications The range and standard deviation are sensitive to extreme scores –In such cases, the Interquartile range is best When your distribution of scores is skewed, the standard deviation does not provide a good index of spread With a skewed distribution, use the Interquartile range

27. 27 Example For a distribution of scores, what information does a measure of variation add that a measure of central tendency does not convey? Today’s weather report included information on the normal rainfall for this time of year. The amount of rain that fell today was 1.5 inches above normal. To decide whether this is an abnormally high amount of rain, you need to know that the standard deviation for rainfall is 0.75 of an inch. What would you conclude about how normal the amount of rainfall was today? What your conclusion be different if the standard deviation were 2 inches?

28. 28 Example Calculate the range, variance, and standard deviation for the following three distributions: 1, 2, 3, 4, 5, 6, 7, 8,9 -4,-3,-2,-1,0,1,2,3,4 10,20,30,40,50,60,70,80,90

29. 29 The Five Number Summary Five Number Summary –Convenient way to represent a distribution with a few numbers –Statistics included Minimum score The first quartile The median (second quartile) Third quartile Maximum score

30. 30 Graphic representation of the five number summary First and third quartile define the ends of the box A line in the box represents the median Vertical “whiskers” extending above and below the box represent the maximum and minimum scores (respectively) Data from multiple treatments are represented by side-by-side boxplots Box Plots

31. 31 Example of a Boxplot (left) and a Side-By-Side Boxplot (right)

32. 32 Using SPSS at home Go to the website below: http://www.yorku.ca/computing/students /labs/webfas/ Click “Login” button to login to WebFAS with your Passport York login Choose “SPSS 21” from the software list