1. Data Collection

2. Study vs. Experiment Observational Study Experiment
Based on data in which no manipulation of factors has been employed
Experiment
Manipulates factors to create treatments
Randomly assigns subjects to the treatments
Compare the responses of the subjects across treatment levels

3. Study or Experiment? Observational study
Researchers have linked an increase in the incidence of breast cancer in Italy to dioxin released by an industrial accident in The study identified 981 women who lived near the site of the accident and were under age 40 at the time. Fifteen of the women had developed breast cancer at an unusually young average age of 45. Medical records showed that they had heightened concentrations of dioxin in their blood and that each tenfold increase in dioxin level was associated with a doubling of the risk of breast cancer.
Observational study

4. Study or Experiment? Experiment
Is diet or exercise effective in combating insomnia? Some believe that cutting out desserts can help alleviate the problem, while others recommend exercise. Forty volunteers suffering from insomnia agreed to participate in a month-long test. Half were randomly assigned to a special no-desserts diet; the others continued desserts as usual. Half of the people in each of these groups were randomly assigned to an exercise program, while the others did not exercise. Those who ate no desserts and engaged in exercise showed the most improvement.
Experiment

5. The Cycle of Statistics
Population
Sample
Parameter
Statistic

6. Principles of Experimental Design
aspects of the experiment that we know may have an effect on the response, but that are not the factors being studied.
Control
Randomize
to even out effects that we cannot control
Replicate
over as many subjects as possible.

7. Types of Sampling Random Sample Simple Random Sample
Stratified Random Sample
Probability Random Sample

8. Random Sampling Simple Random Sample (SRS)
Every member of the population has an equal chance of being chosen for the sample
Method
Assign a random number to each individual in the sampling frame
Select only those whose random numbers satisfy some rule

9. Simple Random Sample Example
There are 80 students enrolled in an introductory Statistics course; you are to select a sample of 5
Sampling frame
The roster of all students enrolled in the course
Label each student
Use a random number generator and choose the first 5 students from the list that match the random numbers. Ignore numbers not on the list and repeats.

10. Stratified Random Sample
Population is divided into similar groups of individuals
These are called strata
Then a SRS is completed in each strata
These are combined for the overall sample

11. Probability Random Sample
A sample is chosen by chance
Each sample has a probability of being chosen
We have to know this

12. What is the population. What is the sample
What is the population? What is the sample? Which random sample was used?
 A company packaging snack foods maintains quality control by randomly selecting 10 cases from each day’s production and weighting the bags. Then they open on a bag from each case and inspect the contents.
Population:
All snack foods produced at the company Sample:
10 cases from each day’s production
Random Sample:
SRS

13. What is the population. What is the sample
What is the population? What is the sample? Which random sample was used?
Dairy inspectors visit farms unannounced and take samples of the milk to test for contamination. If the milk is found to contain dirt, antibiotics, or other foreign matter, the milk will be destroyed and the farm re-inspected until purity is restored.
Population:
All milk at the dairy (in the tank) Sample:
sample from the milk tank
Random Sample:
SRS

14. Terminology Factor: What is being manipulated Response:
What is being measured
Experimental Units:
individuals on which the experiment is done
Subjects:
Human experimental units
Treatment:
specific experimental condition applied
Control group:
Group that receives no treatment or a placebo
Placebo:
A treatment known to have no effect

15. Analyzing Experiments
Aspirin Study
Factor:
Aspirin
Response:
Number of heart attacks
Subjects/Units:
1000 male volunteers
Treatment :
Aspirn
Levels:
Low dose and none (Placebo)
Blinding:
Patients not know which pill they are taking
Control:
A group will take a placebo pill
The men will be randomly assigned to either the treatment group or placebo group.
Randomization:
Replication:
Each treatment will be replicated 500 times

16. Displaying Data

17. Types of Variables
Categorical: places an individual into one of several groups or categories.
Ex: Eye color, favorite food
Quantitative: takes a range of numeric values
Ex: Height, weight, income
Discrete: finite possible values
EX: number of goals in soccer
Continuous: infinite possible values
EX: Height of males at Enloe

18. What kind of variable? Does it make sense to average the values?
Gender
Telephone area code
Amount of electricity used
Zip code
Ticket sales at Mylie Cyrus concert
Number of chicken eggs hatched on Nov. 17, 2006 at 3:00 am
Categorical
Quantitative (C)
Quantitative (D)
Does it make sense to average the values?

19. Every graph I ever make will always
Have a title
Axes labeled
Units identified
Legend
For categorical data

20. Graphs for categorical data
Bar Chart
Bars never touch!

21. Graphs for categorical data
Pie Chart
*Used for comparing parts to a whole

22. Create a graph for the following…
A survey was conducted of 1000 individuals regarding their favorite color. The results are as follows:
Red 367
Yellow 100
Green 68
Blue 159
Purple 200
Grey 26
Pink 80

23. Data Representation of Favorite color survey

24. Graphs for Quantitative Variables
Dot Plot
Useful for small sets of data
Stem and Leaf Plot
More information than dot plot
Histograms
Box Plots
More about these tomorrow!

25. Creating a Stem and Leaf plot
Sort the data
Identify the min and max values to establish what kind of stems and leaves to use
If leaves become too long split them
Create a legend

26. Back to back stem and leaf plots
Used for comparing two similar sets of data
Stems are in the middle and the leaves expand to the left for one data set and to the right for the other data set

27. Histograms Groups nearby values and displays frequencies
National SAT scores 2007

28. How to construct Histograms
Determine the bin size
Divide the range into equal sections
Min of 5 bins
Create a frequency table
Draw the graph

29. Wake County 2008 SAT scores
Sort the data
Identify the range of the data
Identify a bin size that makes sense and will produce at least 5 bins

30. Relative Frequency Table
Score
Count
1500 – 1599
1600 – 1699
1700 – 1799
Use this table to help draw your histogram!

32. Graphs can be MISLEADING!
Number of deaths in Iraq as Published by AOL news in March of 2006

35. Describing Data

36. Describing Data Shape Outlier Center Spread
Mound, symmetrical, skewed, single peak, multiple peaks
Outlier
Any observation that appears to not belong with the others
Center
The middle of the data
Spread
Min value to max value
(including or excluding outliers)

37. Describing Graphs (Shape)
Symmetric: If the right and left sides of the histogram are approximately mirror images
Skewed right: If the right side has outliers
Skewed left: If the left side has outliers
Bi-modal: If there are 2 peaks
Uniform: There are the same number of observations for each value

38. Measures of center Median Mean Exact middle of a set of data
Arithmetic average of all of the observations in a data set

39. Ex: 1,2,3,4,5,6,7,8,9 What is the median? What is the mean?
What if 10 is added to the data set?
What is the median and mean?

40. Resistant measures
Def: A measure is resistant if it is not easily influenced by extreme observations
Is the median a resistant measure?
Yes
Is the mean a resistant measure? No

41. Measures of spread Standard deviation Quartiles Range
Find this in your calculator under 1 variable stats!
Quartiles
IQR (Inter Quartile Range)
Q3-Q1
These are found in your 5 # Summary!
Range
=Max-min

42. 5 number summary Min Q1: quartile 1, median of the lower half
Median (Q2)
Q3: quartile 3, median of the upper half
Max

43. Components of a box plot
5 number summary
Min, Q1, Median, Q3, Max
Outliers
Q1-1.5(IQR)
Q3+1.5(IQR)

44. Q3
Max
Min Q1
Med

45. Where’s the data?
25%
25%
50%

46. What about outliers? Smallest obs. That is not an outlier
Largest obs. That is not an outlier
Min Q1
Med Q3
Max

47. Standard Deviation and Normal Distributions

48. Standard deviation
Gives a measure of how far the data varies from the mean “on average”
Is only used if the mean is the chosen measure of center
Is the standard deviation a resistant measure?
No!

49. Beginning pulse in class (n=23)
Min = 50
Q1 = 66
Median = 79
Q3 = 87
Max = 110

50. End pulse in class (n=24)
Min = 54
Q1 = 64.5
Median = 70
Q3 = 77.5
Max = 109

51. Outliers Interquartile range (IQR) = Q3 – Q1
An observation is an outlier if it lies
1.5(IQR) above Q3 or 1.5(IQR) below Q1
End Class Data Q1 = Q3 = 77.5
IQR = 77.5 – 64.5 = 13
1.5(13) = 19.5
Q1 – 1.5(IQR) = 64.5 – 19.5 = 45
Q (IQR) = = 97

52. Outliers
Any observation below 45 or above 97 will be an outlier
109 is an outlier

53. What is Normal? A bell shaped curve
Standard Normal distribution is when…
Mean=0
Standard Deviation=1

54. Rule
The normal curve can give us an idea of how extreme a value is based on how far away from the mean it is.
68%
95%
99.7% -3 -2 -1
mean 1 2 3
Standard Deviations
Standard Deviations

55. Homework
P. 65 # 12, 13
Make graph (box plot for #12 and histogram for #13)
Describe the shape
Find any outliers
Find mean, and median
Find range, standard deviation and IQR