MATH 225 Chamberlain Confidence Intervals and The Use of These Intervals in The Health Sciences Paper

Week 7 Assignment: LabRequired Resources
Read/review the following resources for this activity:
•
OpenStax Textbook: Chapter 8
•
Lesson
•
Chamberlain University Library
Scenario/Summary
The highlight of this week’s lab is confidence intervals and the use of these intervals in the health
sciences. There is a short reading that specifically relates confidence intervals to health sciences
and then you are asked to demonstrate your knowledge of confidence intervals by applying them
in a practical manner.
Deliverables
The deliverable is a Word document with your answers to the questions posed below based on
the article you find.
Required Software
•
Microsoft Word
•
Internet access to read articles
Prepare
•
Download the Week 7 Lab Lecture Notes.
•
Follow along with he Week 7 Lab Video and fill out the Week 7 Lab Lecture Notes as
you watch the video.
Download Week 7 Lab Lecture Notes.
Demonstrate
Steps to Complete the Week 7 Lab
Step 1: Find these articles in the Chamberlain Library. Once you click each link, you will be
logged into the Library and then click on “PDF Full Text”.
•
•
First Article: Confidence Intervals, Part 1 (Links to an external site.)
Second Article: Confidence Intervals, Part 2 (Links to an external site.)
Step 2: Consider the use of confidence intervals in health sciences with these articles as
inspiration and insights.
Step 3: Using the data you collected for the Week 5 Lab (heights of 10 different people that you
work with plus the 10 heights provided by your instructor), discuss your method of collection for
the values that you are using in your study (systematic, convenience, cluster, stratified, simple
random). What are some faults with this type of data collection? What other types of data
collection could you have used, and how might this have affected your study?
Step 4: Now use the Week 6 Spreadsheet to help you with calculations for the following
questions/statements.
a) Give a point estimate (mean) for the average height of all people at the place where you work.
Start by putting the 20 heights you are working with into the blue Data column of the
spreadsheet. What is your point estimate, and what does this mean?
b) Find a 95% confidence interval for the true mean height of all the people at your place of
work. What
is the interval? [see screenshot below]
c) Give a practical interpretation of the interval you found in part b, and explain carefully what
the output
means. (For example, you might say, “I am 95% confident that the true mean
height of all of the
people in my company is between 64 inches and 68 inches”).
d) Post a screenshot of your work from the t value Confidence Interval for µ from the
Confidence
Interval tab on the Week 6 Excel spreadsheet
Step 5: Now, change your confidence level to 99% for the same data, and post a screenshot
of this table, as well.
Step 6: Compare the margins of error from the two screenshots. Would the margin
of error be larger or smaller for the 99% CI? Explain your reasoning.
Step 7: Save the Week 7 Lab document with your answers and include your name in the title.
References
Holmes,
A.,
Illowsky,
B.,
&
Dean,
S.
(2018). Introductory
business
OpenStax. https://openstax.org/details/books/introductory-business-statistics
statistics.
THE RESEARCH FILE
Terminology 101
Confidence intervals: Part 1
MAHER M. EL-MASRI, RN, PhD, IS AN ASSOCIATE PROFESSOR AND RESEARCH LEADERSHIP CHAIR
IN THE FACULTY OF NURSING, UNIVERSITY OF WINDSOR, IN WINDSOR, ONT.
Confidence interval: The range of values, consistent with the data, that is believed to encompass the actual or
“true” population value
Source: Lang, T.A., & Secic, M. (2006). How to Report Statistics in Medicine. (2nd ed.). Philadelphia: American College of Physicians
8
the sample. This sample mean value is probably a
more reliable estimate of the true mean value of
the population than a sample mean value with a
wider CI of, for example, 110-210 mmHg. With
such a wide CI, the population mean could be as
high as 210 mmHg, which is far from the sample
mean of 120 mmHg. In fact, a very wide CI in a
study should be a red flag: it indicates that more
data should have been collected before any
serious conclusions were drawn about the
population. Remember, the narrower the CI, the
more likely it is that the sample value represents
the population value. n
NurseONE resources
on this topic
EBSCO-MEDLINE full-text articles
• Hildebrandt, M., Vervölgyi, E., & Bender, R. (2009).
Calculation of NNTs in RCTs with time-to-event outcomes:
A literature review. BMC Medical Research Methodology,
9, 21.
• Hildebrandt, M., Bender, R., Gehrmann, U., & Blettner,
M. (2006). Calculating confidence intervals for impact
numbers. BMC Medical Research Methodology, 6, 32.
• Altman, D. G. (1998). Confidence intervals for the number
needed to treat. BMJ (Clinical Research Ed.), 317(7168),
1309-1312.
MyiLibrary
• Campbell, M. J., Machin, D., & Walters, S. J. (2010). Medical
statistics: A textbook for the health sciences (4th ed).
• Mateo, M. A., & Kirchhoff, K. T. (Eds.). (2009). Research for
advanced practice nurses: From evidence to practice.
• Webb, C., & Roe, B. (Eds.). (2007). Reviewing research
evidence for nursing practice: Systematic reviews.
canadian-nurse.com
Illustration: Vanni Loriggio
To draw conclusions about a study population,
researchers use samples that they assume truly
represent the population. The confidence
interval (CI) is among the most reliable
indicators of the soundness of their assumption.
A CI is the range of values within which the
population value being studied is believed to fall.
CIs are reported in the results section of
published research and are often calculated
either for mean or proportion data (calculation
details are beyond the scope of this article).
A 95% CI, which is the most common level used
(others are 90% and 99%), means that if
researchers were to sample numerous times
from the same population and calculate a range
of estimates for these samples, 95% of the
intervals within the lower and upper limits of
this range will include the population value.
To illustrate the 95% CI of a mean value, say
that a sample of patients with hypertension has
a mean blood pressure of 120 mmHg and that
the 95% CI for this mean was calculated to range
from 110 to 130 mmHg. This might be reported
as: mean 120 mmHg, 95% CI 110-130 mmHg.
It indicates that if other samples from the same
population of patients were generated and
intervals for the mean blood pressure of these
samples were estimated, 95% of the intervals
between the lower limit of 110 mmHg and the
upper limit of 130 mmHg would include the true
mean blood pressure of the population.
Notice that the width of the CI range is a very
important indicator of how reliably the sample
value represents the population in question.
If the CI is narrow, as it is in our example of
110-130 mmHg, then the upper and lower limits
of the CI will be very close to the mean value of
Copyright of Canadian Nurse is the property of Canadian Nurses Association and its content may not be copied
or emailed to multiple sites or posted to a listserv without the copyright holder’s express written permission.
However, users may print, download, or email articles for individual use.
J
TERMINOLOGY 101
Confidence intervals: Part 2
LU
MAHER M. EL-MASRI, RN, PhD, IS AN ASSOCIATE PROFESSOR AND RESEARCH LEADERSHIP CHAIR
IN THE FACULTY OF NURSING, UNIVERSITY OF WINDSOR, IN WINDSOR, ONT.
Confidence interval: The range of values, consistent with the data, that is believed to encompass the actual or
“true” population value
Source: Lang, T.A., & Secic, M. (2006). How to Report Statistics in Medicine. (2nd ed.). Philadelphia: American College of Physicians
Part 1, which appeared in the February 2012
issue, introduced the concept of confidence
intervals (CIs) for mean values. This article
explains how to compare the CIs of two mean
scores to draw a conclusion about whether or
not they are statistically different. Two mean
scores are said to be statistically different if their
respective CIs do not overlap. Overlap of the CIs
suggests that the scores may represent the same
“true” population value; in other words, the true
difference in the mean scores may be equivalent
NurseONE resources
ON THIS TOPIC
EBSCO-MEDLINE FULL-TEXT ARTICLES
• Hildebrandt, M., Vervölgyi, E., & Bender, R. (2009).
Calculation of NNTs in RCTs with time-to-event
outcomes: A literature review. BMC Medical
Research Methodology, 9,21.
• Hildebrandt, M., Bender, R., Gehrmann, U.,
& Blettner, M. (2006). Calculating confidence
intervals for impact numbers. ß/MCMed/co/
Research Methodology, 6, 32.
• Altman, D. G. (1998). Confidence intervals forthe
number needed to treat. BMJ (Clinical Research
Ed.), 317(7168), 1309-1312.
MYÎLIBRARY
• Campbell, M. |., Machin, D., & Walters, S. I. (2010).
Medical statistics: A textbook for the health
sciences (4th ed).
• Mateo, M. A., & Kirchhoff, K. T. (Eds.). (2009).
Research for advanced practice nurses:
From evidence to practice.
• Webb, C, & Roe, B. (Eds.). (2007). Reviewing
research evidence for nursing practice:
Systematic reviews.
10
to zero. Some researchers choose to provide the
CI for the difference of two mean scores instead
of providing a separate CI for each of the mean
scores. In that case, the difference in the mean
scores is said to be statistically significant if its
CI does not include zero (e.g., if the lower limit is
10 and the upper limit is 30). If the CI includes
zero (e.g., if the lower limit is -10 and the upper
limit is 30), we conclude that the observed
difference is not statistically significant.
To illustrate this point, let’s say that we want
to compare the mean blood pressure (BP) of
exercising and sedentary patients. The mean BP
is 120 mmHg (95% CI 110-130 mmHg) for the
exercising group and 140 mmHg (95% CI
120-160 mmHg) for the non-exercising group.
We notice that the mean BP values of the two
groups differ by 20 mmHg, and we want to
determine whether this difference is statistically
significant. Notice that the range of values
between 120 and 130 mmHg falls within the CIs
for both groups (i.e., the CIs overlap). Thus, we
conclude that the 20 mmHg difference between
the mean BP values is not statistically
significant. Now, say that the mean BP is
120 mmHg (95% CI 110-130 mmHg) for the
exercising group and 140 mmHg (95% CI
136-144 mmHg) for the sedentary group. In this
case, the two CIs do not overlap: none of the
values within the first CI fall within the range
of values of the second CI. Thus, we conclude
that the mean BP difference of 20 mmHg is
statistically significant.
Remember, we can use either the CIs of two
mean scores or the CI of their difference to draw
conclusions about whether or not the observed
difference between the scores is statistically
significant. •
CANADL!\N-NURSE.COM
Copyright of Canadian Nurse is the property of Canadian Nurses Association and its content may not be copied
or emailed to multiple sites or posted to a listserv without the copyright holder’s express written permission.
However, users may print, download, or email articles for individual use.
1
Lab Week 7
Your Name (without credentials)
Chamberlain University College of Nursing
Course Number: Course Name
Name of Instructor
Assignment Due Date
2
1. Please find the two short journal articles indicated on the Week 7 lab assignment
web page in Modules. However, please only read the Part 1 article. The Part 2
article covers information not taught in our Math 225 course and it always causes
a lot of confusion for class members who read it and try to understand it. Please
pull something meaningful and relevant out of the Part 1 article and include it
here as a direct quote or as a paraphrase, with in-text citation of course. Please
make your response here no more than 3-4 sentences, but potentially, this
response here could be a single sentence. Include the Part 1 article in the
References list at the end of this document too please. Thank you !
Commentary:
3
2. Survey or measure 10 people to find their heights ( in INCHES ). Record the
heights below. Use the same numbers here that you used in the previous Week 5
lab turn in assignment.
4
3. Record the 10 heights ( in Inches ) provided by the Instructor just below here.
Use the same numbers here that you used in the previous Week 5 lab turn in
assignment.
5
4. Using the data you collected for the previous Week 5 lab ( the 20 different
numbers considered as one data set ) , discuss your method of collection ( the
method of collection that you used to gather 10 heights for the Week 5 lab turn in
assignment ) for the values that you are using in your study. Was your method of
collection for the Week 5 lab assignment a systematic, convenience, cluster,
stratified, or simple random sample ? What are some faults with this type of data
collection ( the specific data collection method that you used for the Week 5 lab )
? Give one alternative method for data collection that you could have used
instead, and how might this new alternative choice for method for data collection
have affected your study ?
Answer( s ):
6
5. Please use the Week 6 Excel spread sheet calculator from the Week 6 Lesson web
page in Modules to help you with the remainder of this Week 7 lab turn in
assignment. Using the Sample Mean and Standard Deviation tab on the Week 6
Excel spread sheet calculator, enter your 20 pieces of data into the input column
and then of course click away into some empty unused blank cell so that the outputs
can update. Give a point estimate ( mean ) for the average height of all people in
your population of interest for your study. What is your point estimate, and what
does it mean in practical, concrete terms ?
Answer( s ):
7
6. Please place a screen shot of your work using the Sample Mean and Standard
Deviation tab of the Week 6 Excel spread sheet calculator into the grey / gray box
below. It should please look like the example image / graphic for this part located
on the Week 7 Lab assignment web page in Modules.
8
7. Find a 95% confidence interval for the true mean height of all the people in your
population of interest for your study. Type this 95% confidence interval into the
grey / gray box below. Give a practical interpretation of this 95% confidence
interval that you have found here, and explain carefully what this 95% confidence
interval communicates and conveys. In other words, interpret this 95% confidence
interval. The sample interpretation on the Week 7 lab assignment web page in
Modules is NOT CORRECT, so please don’t use it as a guide or template here
!! Rather see the two slides in the Week 6 regular graded discussion posting area
that address the interpretation of a confidence interval. Thanks much !!
Answer( s ):
9
8. Please place a screen shot of the input and output areas from the Confidence
Interval tab on the Week 6 Excel spread sheet calculator into the gray / grey box
below. This is a screen shot for the 95% confidence interval calculated and found
in the question just previous. It should please look like the example image / graphic
for this part located on the Week 7 Lab assignment web page in Modules.
10
9. Find a 99% confidence interval for the true mean height of all the people in your
population of interest for your study. Type this 99% confidence interval into the
grey / gray box below.
Answer:
11
10. Please place a screen shot of the input and output areas from the Confidence
Interval tab on the Week 6 Excel spread sheet calculator into the gray / grey box
below. This is a screen shot for the 99% confidence interval calculated and found
in the question just previous. It should please look like the example image / graphic
for this part located on the Week 7 Lab assignment web page in Modules.
12
11. Compare and contrast the two margins of error from the two screen shots that you
submitted for questions 8 and 10 just above here. Is the margin of error larger or
smaller for the 99% confidence interval, compared and contrasted with the margin
of error for the 95% confidence interval ? Why ? A good answer for the “why”
question would be to compare and contrast the critical t values in the output areas (
2.093 and 2.861, respectively ) and to explain how those critical t values impact the
respective margins of error.
Answer and commentary:
13
References
Type your references here using hanging indent and double line spacing (under
“Paragraph” on the Home toolbar ribbon). See your APA Manual ( seventh edition ) and
the resources in the APA section of Resources for reference formatting.
14