1. Experimental Design Experiments Observational Studies
Random assignment
Observational Studies
Random sampling
Equal chance of group assignment/ selection from population for each person/observation

2. Frequency Distributions & Graphs

3. Descriptive Statistics
The goal of descriptive statistics is to summarize a collection of data in a clear and understandable way.
What is the pattern of scores over the range of possible values?
Where, on the scale of possible scores, is a point that best represents the set of scores?
Do the scores cluster about their central point or do they spread out around it?

4. What is the pattern of scores?
Create a Frequency Distribution
Frequency distributions organize raw data or observations that have been collected.
Ungrouped Data
Listing all possible scores that occur in a distribution and then indicating how often each score occurs.
Grouped Data
Combining all possible scores into classes and then indicating how often each score occurs within each class.
Easier to see patterns in the data, but lose information about individual scores.

5. Las Vegas Hotel Rates

6. Las Vegas Hotel Rates

7. An Example: Grouped Frequency Distribution
Las Vegas Hotel Rates
An Example: Grouped Frequency Distribution
Find the lowest and highest score (order scores from lowest to highest).
891 is highest score.
52 is lowest score.
Find the range by subtracting the lowest score from the highest score.
= 839
Divide range by 10.
839/10 = 83.9
Round off to the nearest convenient width.
100
Determine the scores at which the lowest interval should begin (an interval of the class width).

8. An Example: Grouped Frequency Distribution
Record the limits of all class intervals, placing the interval containing the highest score value at the top.
Count up the number of scores in each interval.
Hotel Rates
Frequency 1 4
Las Vegas Hotel Rates 2 6 8 8 4
0-99 2

9. Frequency Table Guidelines
Intervals should not overlap, so no score can belong to more than one interval.
Make all intervals the same width.
Make the intervals continuous throughout the distribution (even if an interval is empty).
Place the interval with the highest score at the top.
For most work, use 10 class intervals.
Choose a convenient interval width.
When possible, make the lower score limit a multiple of the interval width.
Sum to N

10. An Example: Grouped Frequency Distribution
Proportion (Relative Frequency)
Divide frequency of each class by total frequency.
Hotel Rates
Frequency
Proportion
1/35=.03 1
.03 4
.11 2
.06 6
.17 8
.23 8
.23 4
.11
0-99 2
.06
N = 35
Σ = 1.0

11. An Example: Grouped Frequency Distribution
Cumulative Frequency: sum of each frequency and all below it
Cumulative Proportion (Cumulative Relative Frequency):
Divide Cumulative Frequency by Total Frequency
Percentile Rank
Cumulative Proportion * 100
35/35=
34/35=

12. What is the pattern of scores?
Graphs often make it easier to see certain characteristics and trends in a set of data.
Graphs for quantitative data.
Stem and Leaf Display
Histogram
Frequency Polygon
Graphs for qualitative data.
Bar Chart
Pie Chart
number/count
class/category

13.
Raw data
Stem
Leaf 1 2 3 4 5 6 7 9
0339
2466
467
357

14. 36 59 65 70 74 78 83 88 38 79 41 84 42 60 75 89 44 66 45 71 90 61 91 48 67 72 49 62 76 92 50 80 85 93 63 51 73 54 81 94 86 56 77 95 64 68 82 87 96 57 58 69 99

16. Range
Frequency
35-39 2
40-44 3
45-49 4
50-54 7
55-59 12
60-64 19
65-69 25
70-74 31
75-79
80-84 26
85-89 20
90-94
95-99 8

17. Histogram Consists of a number of bars placed side by side.
The width of each bar indicates the interval size.
The height of each bar indicates the frequency of the interval.
There are no gaps between adjacent bars.
Continuous nature of quantitative data.
Include a descriptive title for the graph.
Label each axis.The independent variable is on the X axis The dependent variable (or frequency) is on the Y axis. The numbers along the Y axis indicate the measurement increments.

18. Histogram

19. Shapes of Histograms

20. Frequency Polygons
Uses a single point rather than a bar

21. Bar Graph
A graphical representation of qualitative data.Unlike in a histogram, the bars do not touch. Discontinuous nature of qualitative data.

22. Pie Graph

23. Misleading Graphs

24. Homework CANDY BARS EATEN THIS MONTH:
1. Create grouped, relative, & cumulative relative frequency distributions of the data.
2. Create a stem-leaf plot and a histogram of the data.
3. Describe the shape of the distribution. Any outliers?
4. What would you consider an typical value, based on this sample? What number would you guess for the next person?
5. Create a bar graph or pie chart to compare how many ate a candy bar on more than half the days.
6. Create a misleading graph to exaggerate # candy bars eaten.
7. Create a misleading graph to minimize the # candy bars eaten.