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Statistics Page 1
RSPT 1325 Sciences Unit 4: Statistics
By Elizabeth Kelley Buzbee AAS, RRT-NPS
Revised notes August 7, 2009
Raw data
raw data unless the research project contains huge numbers of test subjects, it’s a good idea to
be able to see the exact ages, sexes, races and other data for each test subject available to the
reader. We need to see both the dependent and the independent variables.
Test subjects who left the study early need to be accounted for so that bias can be limited.
For example:
Test
subject
AA
BB
CC
DD
Age
years
45
66
38
39
sex
m
m
f
f
race
w
w
w
b
Base line PEFR
[best of 3] LPM
Post bronchodilator PEFR
[best of 3] LPM
244
356
600
480
259
378
567
Died of closed head injury
from anvil dropped by angry
rabbit
FF
75
f
a
450
450
GG
18
m
b
350
Unable to complete this
study due to acute confusion
Note that the raw data includes the units measured as well as a breakdown of each test subject;
note also that test subject DD died not as a result of the study but from other causes. It is
important to include the cause of death because if a second test subject was to drop dead from an
anvil attack, we need to seriously consider the fact that something associated with this study is
causing anvil attacks.
n
n = the number of test subjects you are discussing.
Every time you speak of the entire group or ‘cohort’ include how many there were [n=12]. If you
are talking about test subjects in a category [or cohort] include how many were in that category
[n= 3]
This gets important when you think about a statement such as “75% of the smokers did not get
cancer in a 10 year period.” Suppose the total number of test subjects was only 4? This tiny
number of test subjects challenges the validity of this statement a bit, doesn’t it?
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For example:
“In the study, [n=350] the males [n=155] on the drug were found to have 25% more episodes
of cardiac arrhythmias than the women.”
mean
Calculation of the mean is simply averaging each variable, and averages for each
variable among the various categories:
Σ of all in category / n of that category
For example:
“The mean PERF of the obese subjects [n=5] was 344 lpm.”
“The mean PERF of the non-obese subjects [n=8] was 488 lpm.”
Refer to the raw data above to answer these questions:
1.
Calculate the mean ages of the males in this study.
2.
Calculate the mean baseline PEFR of this study.
3.
lpm.
Calculate the mean ages of the black [b] test subjects who had PERF of more than 325
Range
At some point, include the range of lowest to highest in a given data set.
For example:
“the mean PEFR of none obese test subjects [n=3] was 550 lpm [range 350-660 lpm]
NOTE: the range is not the difference; it is 350 “to” 660.
Refer to the above raw data, to answer these questions:
1.
Identify the range of ages of the white [w] test subjects.
2.
Identify the range of post bronchodilators PEFR of the female test subjects.
Statistics Page 3
% change
The percent change is a formula that shows how much the independent variable changed the
dependent variable. Generally percent change is not clinically significant until there is at least
15% change.
% change formula
Post value - pre value
x 100
Pre value
For example:
“The mean FEV1 of younger subjects [n=66] increased post bronchodilator by 5 %.”
Complete this table. Note that if the pre-PEFR is higher than the post PEFR, the % change is
recorded as a negative number.
Test
Age
sex race
Base line
Post bronchodilator
% change
subject
years
PEFR [best of PEFR [best of 3] LPM
3] LPM
AA
45
m
w
244
259
BB
66
m
w
356
378
CC
38
f
w
600
567
DD
39
f
b
480
FF
75
f
a
450
GG
18
m
b
350
Died of closed head
injury from anvil
dropped by angry
rabbit
450
Unable to complete
this study due to
acute confusion
Statistics Page 4
median
median is the number in the absolute middle of your data.
Start with 10, 17, 34, 20, 12. Put them in order lowest to the highest:
10 12 17 20 34.
17 is the medium. It is in the absolute middle. There are two numbers less than it and two
numbers higher than it.
If the total is an even number, the median is the number that is the average of the two middle
numbers. If this number goes into decimals follow out by at least 1 place
9 10 18 22 25 26
the median is 20
For example:
“The mean PEFR of the obese test subjects [n=20] was 340 lpm [range 200-400] while the
medium was 260 lpm.”
SD
Standard deviation measures the spread of a set of data around the mean of the data.
In a normal distribution, approximately 68 percent of scores fall within plus or minus
one standard deviation of the mean, and 95 percent fall within plus or minus two
standard deviations of the mean [ see green area]. Only a few [see blue area] in the
extremes of highs and lows fall into the SD3.
Reference to this page on internet: http://www.robertniles.com/stats/stdev.shtml
SD1 is 68% of the group closest to absolute mean.
SD = sq root of ∑ (x – mean) 2
n
The most common use of Standard Deviation in respiratory care is during the
calibration of and the quality control of various measuring devices such as the arterial
blood gas machine.
To calibrate an arterial blood gas machine, we must introduce known levels of 02, Co2
and various pH levels into the machine. These calibration liquids must be within +/.05. We perform a two-part calibration for each value: oxygenation, presence of CO2
and pH in which the machine is given both high and low known values to analyze.
Quality assurance is the act of using the calibration data to make sure the arterial
blood gas machine is accurate enough for us to trust.
Statistics Page 5
Go here for a good definition of distribution:
http://en.wikipedia.org/wiki/Normal_distribution
Calculation of SD using the computer
On the Excel program, in Microsoft we can ask the computer to give us the SD of a
series of numbers by dragging the series of numbers we want a SD for, then going to the
formula section of the toolbar to find statistics and then scroll down to standard
deviation.
To tell the Excel program that you are calculating a number you must precede the
formula with an = sign
The Levey-Jennings Charts
The Y axis [vertical] contains the
data [Pa02, PaC02 and pH] along
a time line on the X axis.
As the RCP calibrates these
parameters, each is plotted on the
Levey-Jennings graph.
[reference: Sills and White]
SD3
SD 2
SD1
normal
There is a separate graph for each
value. In the absolute center is the
number expected for each value,
and each line above and below
represent the SD1, SD2 and SD3
for each value.
SD1
SD 2
SD3
Time
As each value is plotted, it can be easily visualized when a value begins to drift away
from normal. This Levey- Jennings graph shows a value that is staying within limits
When values are out of control, they are outside the limits.
In this next graph, we see that one
value is off, notice that it appears in
as higher in the SD2.
SD 3
SD1
Because it is not repeated, it is
considered a random error because
of some error made by the RCP
during calibration.
normal
SD1
SD 2
Time
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For example, suppose the RCP injected a high 02 into the analyzer when he should have
injected a lower calibration gas or maybe injected C02 when he should have injected 02.
He might have an air bubble in the sample.
In this graph, note that there are
several consecutive errors in the
SD2, this is a systemic error. A
systemic error implies there is a
serious problem with the analyzers
and it must be checked out and
corrected.
SD 3
SD1
normal
Failure to correct systemic errors is
a violation of Federal laws [CLIA
regulations] governing effective
medical lab results.
SD1
SD 2
The specific pattern established by
the drifting values in this graph is
an example of a trend. A trend pattern could be the result of worn electrode
components, or protein contamination of the electrodes-even deterioration of the
calibration liquids.
Time
This next graph shows a shift.
When there is a shift, we see
that there are 6 or more values
that are collecting on one side
of the mean.
This shift could imply that we
have a new batch of calibration
liquids or that there is a
problem with components or
that
someone
calibrated
incorrectly. Regardless of the
error, these need to be
corrected.
SD 3
SD1
normal
SD1
SD 2
Time