1. Basic Statistics
Frequency Distributions & Graphs

2. Structure of Research (The Scientific Method)
Reviewing
Information
Identify the Problem
A Systematic Approach
Collecting
Data
Since the scientific method is circuitous, it is a never-ending process. One discovery leads to the next discovery. Both qualitative and quantitative methods are part of the scientific process. However, qualitative research is more adept at identifying research questions and explaining why relatiionships are as they are. Quantitative methods are the only process that can establish relationships, cause-and-effect or otherwise.
Drawing
Conclusions
Analyzing
Data

3. STRUCTURE OF STATISTICS
TABULAR
DESCRIPTIVE
GRAPHICAL
NUMERICAL
STATISTICS
CONFIDENCE INTERVALS
INFERENTIAL
TESTS OF HYPOTHESIS

4. Now, we will look at the tabular and graphical approaches.
STRUCTURE OF STATISTICS
Now, we will look at the tabular and graphical approaches.
TABULAR
DESCRIPTIVE
GRAPHICAL
NUMERICAL
STATISTICS
CONFIDENCE INTERVALS
INFERENTIAL
TESTS OF HYPOTHESIS

5. Step 1 QUESTIONNAIRE A Self-Concept Scale
Scale: 1=Strongly Disagree 4=Neither Agree nor Disagree 7=Strongly Agree
ITEMS:
I usually achieve what I want when I work hard for it.
Once I make a plan, I am almost certain to make it work
10. Almost anything is possible for me if I really want it.

6. Step 2
Scores of 100 college students on the self-concept questionnaire.

7. Step 3
The most basic and common method of tabularizing data is
A possible first step in organizing data for interpretation is to arrange the scores by size, usually from highest to lowest.

8. RELATIVE FREQUENCY DISTRIBUTION
The relative frequency of a class is obtained by dividing the class frequency by the total frequency.

9. Use to present the data as a graph or as table
Grouped Frequency Distribution
Use to present the data as a graph or as table

10. tradeoff Accuracy Grouping and Loss of Information
More usable/ comprehensible information
Precise Information
Ease of communication
Accuracy

11. GRAPHIC PRESENTATION OF A FREQUENCY DISTRIBUTION
Histogram vs. Bar Graph
Polygons (Line Graphs)
Frequency/Relative Freq
Cumulative Distributions
Percentiles
Stem-and-Leaf Displays

12. HISTOGRAM
The Histogram is a series of column, each having as its base one class interval as its height the number of cases, or frequency, in that class.
FOR WATER USAGE (1,000 GALLONS)

13. Percent Frequency score
25%
ordinate
20%
15%
10%
5 %
score
abscissa
Histogram is a graphing technique that is appropriate for quantitative data.
To avoid having the figure appear too flat or too steep, it is usually well to arrange the scales so that the height of the histogram is 2/3 to 3/4 of its width.

14. Percent
25%
20%
15%
10%
5 %
South
North
West
male
female
When one is comparing two distributions that are based on unequal numbers of observations, percentages are preferable.

15. FREQUENCY POLYGON
In the polygon a point is located above the midpoint of each class interval to represent the frequency in that class. These points are then joined by straight lines. 5 40
The lowest class interval midpoints have zero frequencies. Frequency polygons are closed at both ends.

16. Describing Distributions
normal
Positively skewed
Negatively skewed Y Y Y X X X
Rectangular
Bimodal
The Y-axis represents frequency, and the X-axis represents the numerical value of the observations Y Y X X

17. THE BAR GRAPH
A Bar graph is used to present the frequencies of the categories of qualitative variable. A conventional bar graph looks exactly like a histogram except for the wider spaces between the bars.
A bar chart can be used to depict any of the levels of measurement (nominal, ordinal, interval, or ratio).

18. Number with AIDS per 100,000 Population
Construct a bar chart for the number of persons with AIDS per 100,000 population for selected metropolitan areas of July 1990.
City
Number with AIDS per 100,000 Population
Atlanta, GA
922
Austin, TX
245
Dallas, TX
711
Houston, TX
1,245
New York, NY
6,565
San Francisco, CA
1,935
Washington, DC
1,059
West Palm Beach, FL
353
Source: Dept. of Health & Human Services.

19. BAR CHART FOR THE AIDS DATA
ATLANTA
AUSTIN
DALLAS
HOUSTON
NY, NY.
SAN. FRAN.
WASH., D.C.
W. P. BEACH

20. Cumulative Percentage Curve
Frequency and percentage polygons can be readily converted into cumulative percentage curve. The cumulative percentage or Ogive Curve is the most common type of cumulative distribution.
Cumulative percent
IQ score

21. Step 1: Percent ( ) = 363/2200 = 0.165
Step 2: x100 = 16.50%
Step 3: % %=90.27%

22. Cumulative percentageY
Cumulative percentage
P45=100
IQ score X
Percentile and percentile score
Percentiles are points in a distribution at or below which a given percent of the cases lie.
P45 corresponds to an IQ 100 score of approximately 100; therefore 55 % of the IQ scores exceed 100.

23. THE LINE GRAPH
A line graph is used to show a picture of the relationship between two variables.
A point on a line graph represents the value on the Y variable that goes with the corresponding value on the X variable.

24. Stem-and-Leaf Plots
When summarizing the data by a group frequency distribution, some information is lost since we would only have the classes and the frequency counts for the classes. We will not know what are the actual values in the classes.
A stem-and-leaf display offsets this loss of information.
The stem is/are the leading digit(s).
The leaf is the trailing digit (units digit).
The stem is placed to the left of a vertical line and the leaf to the right.

25. The Dean of the College of Education reports the following number of students in the 15 sections of basic statistics offered this semester. Construct a stem-and-leaf chart for the data.
27, 36, 29, 21, 24, 26, 32, 30, 36, 30, 28, 23, 17, 41, 19.
Another advantage of a stem-and-leaf display is that it is easily reproduced with a line printer.
STEM
LEAF 1 2 3 4
7 9 1

26. PIE CHART
A pie chart is especially useful in displaying a relative frequency (percentage) distribution.
A circle is divided proportionally to the relative frequency (percentage) and portions of the circle are allocated for the the different groups.

27. EXAMPLE
A sample of 200 college students were asked to indicate their favorite soft drink. The results of the survey are given on the next slide. Draw pie chart for this information.

28. PIE CHART FOR THE TASTE TEST
Coca-Cola
Others
Pepsi
Seven-Up
Dr. Pepper