Clinical Calculation
5th Edition
Computer Assignments Need to Know
Graphical Representations of Data
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Pie Chart
Distribution of Percent of Students Attended
Training by Class
Freshman
14%
Senior
36%
Junior
7%
Sophomore
43%
Class
Frequency (%)
Freshman
Sophomore
Junior
Senior
14.3
42.9
7.1
35.7
100
Graphical Representations of Data

Bar Chart
Distribution of Percent of Students Attended
Training by Class
100
90
80
Percent of students
70
60
50
40
30
20
10
0
Freshman
Sophomore
Junior
Senior
Class
Frequency (%)
Freshman
Sophomore
Junior
Senior
14.3
42.9
7.1
35.7
100
Graphical Representations of Data
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Histogram
Distribution of Students Attended
Training by Age
50
Age
< 20
20-39.9
40-59.9
60-79.9
> 80
Students
40
30
20
10
0
< 20
20-39.9
40-59.9
60-79.9
> 80
Students
10
33
45
37
13
Symmetric and Skew Distribution
If we look at the outline of histogram
Skewed to the Left
Symmetric – Single Pick
Normal distribution
Skewed to the Right
Symmetric – Two Picks
Web site to find data
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http://www.hospitalcompare.hhs.gov/Hospital/Search/Se
archCriteria.asp?version=default&browser=IE%7C6%7C
WinXP&language=English&pagelist=Home&dest=NAV|H
ome|Search|SearchCriteria&Type=State#astep1a
http://www.census.gov/prod/www/abs/income.html
Percent of Pneumonia Patients Given Initial Antibiotic(s) within 4 Hours
After Arrival The rates displayed in this graph are from data reported for
discharges January 2006 through December 2006.
Percent of Surgery Patients Who Received Preventative Antibiotic(s) One
Hour Before Incision - The rates displayed in this graph are from data
reported for discharges January 2006 through December 2006.
Assignment 3
Describing Distributions with Numbers
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Mean - Average
Median – Measuring Center – Middle data
Minimum – Smallest data
Maximum – Greatest data
Mode – Most repeated
Describing Distributions with Numbers
Example 1: 20, 40, 22, 22, 21, 31, 19, 25, 23
• Mean – Average
•
•
•
•
20  40  22  22  21  31  19  25  23
 24.78
9
Median – Measuring Center
Minimum
Maximum
Mode
Sort the data: 19 20 21 22 22 23 25 31 40
Median: 9 different data + 1 is 10, the divide by 2 is 5 so the
median is the 5th location. (22)
Minimum = 19, maximum = 40, Mode = 22
Describing Distributions with Numbers
Example 2: 20, 40, 22, 22, 21, 31, 19, 25
• Mean – Average
•
•
•
•
20  40  22  22  21  31  19  25
 25
8
Median – Measuring Center
Minimum
Maximum
Mode
Sort the data: 19 20 21 22 22 25 31 40
Median: 8 different data + 1 is 9, the divide by 2 is 4.5 so the median is
the average between data in 4th location and the 5th location. (22)
Minimum = 19, maximum = 40, Mode = 22.
Assignment 4
Relations between variables
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Independent Variables (x-axis)
Dependent Variables (y-axis)
A dependent variable measures an outcome of a study.
Where independent variable explains or influences the
changes in a dependent variable
Example:
1-The amount of time a student studies and the grade on the exam.
2-Car age and asking price for the car.
3- age and salary
4-the yield of flower and the amount of fertilizer used
Displaying Relationships
3.5
1.0
2.0
4.0
1.0
0.5
3.0
5.0
0.5
1.0
Asking Price
$10,300
$11,875
$8,990
$6,990
$9,992
$14,992
$7,999
$4,990
$13,900
$11,900
Scatter Plot
Asking Price of Car by Age of the Car
$16,000
$14,000
$12,000
Asking price
Age (years)
$10,000
$8,000
$6,000
$4,000
$2,000
$0
0.0
1.0
2.0
3.0
car age (years)
4.0
5.0
6.0
Displaying relationships
Asking Price of Car by Age of the Car
Scatter Plots
$16,000
$14,000
Asking price
$12,000
$10,000
$8,000
$6,000
$4,000
$2,000
$0
0.0
1.0
2.0
3.0
4.0
5.0
6.0
car age (years)
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Shows the relationship between two variables
Values of independent variable are plotted on the horizontal axis.
Values of dependent variable are plotted on the vertical axis.
Each individual is displayed as a point with fixed value on the plot corresponding
with its two independent and dependent variables.
y-axis
y-axis
Look for patterns in the Data
x-axis
y-axis
y-axis
x-axis
x-axis
x-axis
Measuring the Linear Associations between Variables
Correlation (r):
Measures the direction and strength of
the linear relationship between two
variables.
Facts about Correlation
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The choice between the independent and dependent variable does not influence
its calculations.
Both variable has to be numbers.
Not influences by the units of measures
Positive correlation ( r ) indicates positive correlation between independent and
dependent variable
negative correlation ( r ) indicates negative correlation between independent
and dependent variable
Correlation r is always a number between –1 and 1.
 r = +1 indicated strong positive relations.
 r =-1 indicates strong negative correlations.
 r = 0 indicates NO relationship between variables.
Describes linear relationships.
It is influenced by the value of outlier, if outlier exists in data.
y-axis
y-axis
Look for patterns in the Data
x-axis
y-axis
y-axis
x-axis
x-axis
x-axis
Use r = + or – 0.7 as guideline for establishing your conclusion.
Regression line
Describes how a dependent variable y changes as values of
independent x increases.
Regression line is a line that describes the data.
Asking Price of Car by Age of the Car
$16,000
$14,000
Asking price
$12,000
$10,000
$8,000
$6,000
$4,000
$2,000
$0
0.0
1.0
2.0
3.0
car age (years)
4.0
5.0
6.0
Regression Line
It may not necessary crosses all the points in the data set.
Unless correlation between the two variable is one (1).
Otherwise you will find error when drawing and calculation the
regression line.
This error is calculated by the difference between actual data (yvalue) and predicated values of y for a given x.
Error = observed y – predicated y
Asking Price of Car by Age of the Car
$16,000
$14,000
Asking price
$12,000
$10,000
$8,000
$6,000
$4,000
$2,000
$0
0.0
1.0
2.0
3.0
car age (years)
4.0
5.0
6.0
Least Square Regression Line
Is the line that makes the sum of the squares of the error
created as smallest possible.
Asking Price of Car by Age of the Car
$16,000
y = -1700.1x + 13848
$14,000
Asking price
$12,000
$10,000
$8,000
$6,000
$4,000
$2,000
$0
0.0
1.0
2.0
3.0
car age (years)
4.0
5.0
6.0
Facts about least-squares regression (LSR)
Correlation coefficient (r):
Variation we expect as x moves and y moves with it along the
regression line.
Positive correlations indicated positive increase in y,
where negative correlation indicated the decrease in y.
Correlation of independence (r2):
How successful the regression was in explaining the dependent
variable.
It is always positive.