Proficient Lab Assignment
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.
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.
Step 8: Submit the document.
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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
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
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
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 intervals: Part 1
TERMInoLogy 101
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.
8 CANADIAN-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.
J
LU
TERMINOLOGY 101
Confidence intervals: Part 2
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.
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. •
10 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.
Lavf58.29.100
Lab 7 Lecture Notes
You will need your Week 5 Lab Data!!
1. Go to Modules in the course room and click on Week 7 Lesson: Hypothesis Testing
2. Click on Week 7 Assignment: Lab
3. Download the Week 6
4. Let’s look at our data from Lab 5!
Data Set: Ten Grades on the Midterm Exam
|
50 |
68 |
74 |
77 |
80 |
|
|
86 |
78 |
90 |
Mean: ________ Our Score: _________
Standard Deviation: _________
5. Find a 95% confidence interval for the true mean Midterm Average of all the people in the class. What is the interval? [Provide a Screenshot].
6. Give a practical interpretation of the 95% confidence interval.
7. Find a 99% confidence interval for the true mean Midterm Average of all the people in the class. What is the interval? [Provide a Screenshot].
8. Give a practical interpretation of the 99% confidence interval. Would the margin of error be larger or smaller for the 99% CI? Explain your reasoning.
Lab 7 Overview
Hello, Sylvain. What I wanna do is give you a brief overview of what you have to do for your week seven Lab. So in the week seven lab, the only spreadsheet we’re going to really need is your week six spreadsheet. So if you go to Modules and under week six and got the lesson here shall weeks, Week six spreadsheet. I’ve already downloaded it, so it looks like this. So this is the spreadsheet you should have downloaded for the lab. So I will download that. Another thing that I would download is the week seven Lab. So that looks like this. Now remember these lecture notes are for you to write all over them. Make any little documentation that you would like to help you do your lab. Ok. So in the week seven lab, you’re, the only spreadsheet you need is the week six spreadsheet, but you do need your week five lab data. So go ahead and take a moment to pull that. That should be the ten heights that your instructor gave you and then the ten heights that you gathered. Ok. So to get, I talk about how to get the weeks, six spreadsheets. So you have that. Now in order to kind of give an example of what you’re going to do in your lab. I want to go back and look at our data from lab five. Now remember the scenario for lab five. I’m a principal of a high school. I walk down the senior map hallway and I picked one class in one class had ten students in it. And I pooled their midterm exam math scores. And they’re listed here. If you remember from lab from last week that our mean, I’m just going to write it here. Feel free to fill in on your sheet. Our mean was a 76.9. Our standard deviation was 11.3964. And if remember our score that we were comparing was an 85. So I’m gonna write those down. Okay? So what I wanna do is I want to find a 95% confidence interval for the true mean midterm average of all the people in the class spraying it all. And then even trying to branch out further if we could to all the people in that or see years or whatever, what would the population we’re trying to represent. So if you open up your week six spreadsheet, it’s asking for competence level. And so our first one is 95. N is how many pieces of data we have. We only have ten. Are mean was 76.9, our standard deviation was 11.396 for population standard deviation, our answer is no, we don’t know, we didn’t have a population. They’re asking if this standard deviation is a population standard deviation or not. And it was not because we’ve pulled a sample. Okay. You would only type yes, here if you’ve actually pulled an entire population. Okay? And so then it gives us some great information here in yellow. But the one thing you’re going to take a look at are these the margin of error, you’re lower and your upper limit. So I’m going to take a screenshot because that’s the first thing that’s asking for. Take a screenshot or Dina and you feel free to do the same so that you have it. And then I’ll even, and then you can print these out and look at them while you’re doing it for lab. Let me make it very small. So it, since he got up into space. Okay. So there’s my 95% confidence at all. Now, give a practical interpretation of what this means. Well, what this means is that I can write, I am 95% confident. I am 95% confident that the true average of the mass mid-term exam is between 68.785.1 k. I am 95% confident that the true average, remember we only pull ten people. But if I were, if I wanted that to represent the entire average of the midterm exam of everybody who took it. It’s between a 68.785.1. I’m 95% sure that the average will be there. So what I mean by that is I would have to verify I would have to go and pull the midterm math exam of every single student who took it in that senior year at that school and average it out. And what I’m saying is a 95% sure that that average will fall between 60.785.1. A lot of students say, oh, I’m 95% confident that the average of my sample, now, you know the average of your sample, the average of your sample with 76.9. So don’t, when you’re making a practical interpretation, you’re not saying something about the sample. You’re seeing something about the true mean of the population. If that makes sense. So you’re basing it off of the sample that you have. Okay? Then what you’re gonna do is you’re going to do a 99% confidence interval. So all you have to do is go back to our spreadsheet and I, and when its height in, in blue, that I’m changing the confidence level from 0.952.99. So let’s change this to 0.99. Then I’m going to take a screenshot in your answers should match mine right now. We’re doing this together for the midterm math example. Okay? So here’s my screenshot. Now this is for a 99% confidence interval. So what is the practical interpretation of that? Again, let’s write this out. I am 99% confident that the true average of the midterm exam is between 65.288.6. So 60 by 0.288.6. And I’m getting that from the lower and the upper limit of my confidence interval. Now, want you to do is I want you to look at the margin of error. The margin of error for being 99% confident was 11.7, and the margin of error for being 95% confident was 8.15. What does that mean? Explain what that even means. What would the margin of error be larger or smaller? So in this case, and I want to tell you the answer for years, but for this case, it would be larger. And I want you to think about why that is. Look at the confidence intervals themselves. If you come back up here for the 95, mm, the 95 was between 68.785.1 and this is 65.288.6. It’s kind of hard. You want to see if we can look at them side-by-side even that would be great. But you should notice that the interval for the 99% confidence is wider. It’s a wider interval. Why is that? Think about that. Why is it, why is it bigger? Well, I want you to think about this. If you’re 99% confident, that means that you don’t want to be wrong, right? I mean, you never want to be wrong anytime. But 99% confidence means that you’re, you’re, you’re pretty sure, like you’re very, very sure that it’s going to fall between 65.20.6. That the more sure. How could you even me washer by opening up the interval? Does that make sense? So let me demonstrate here, maybe this will make more sense. Let’s say I was like, I am sure that the average amount of rain I’m going to get is two inches and six inches of rain, I’m sure but 95%. Well, I don’t want you to be 95%. I want you to be 99%. All of you want me to be that sure. I’m sure is between 015 Inches of rain. I don’t know where we’re living but 0.15. so what I did is I’ve widened my interval so that I could have the amount of inches of rain inside of my interval. You widen it, you include more numbers. Therefore, that makes you more confident. Okay? So that’s what happened here. So what we did just to recap, we took data from last week, okay? And we looked at the mean, the score, and the standard deviation, and we constructed a 9599% confidence interval. We talked about what they mean in context of the problem. Okay? We also looked at what happened to the interval itself as we become more confident and feel free to play around with this a little bit. What if you’re 80% confident? What if you’re 90% confident? So look what happens to your margin as you do that. Look what happens to the length of your interval when you change your level of confidence. That’s really great to bring in to your lab. So hopefully that explains what we’re gonna do in your actual lab. So let’s look at your actual lab. So what you’re going to be doing is you’re going to first, I want you to read articles about competence intervals. I would really like you to see how they apply, especially in the health sciences. And these articles will kind of inspire that thought. Okay? And then what you’re gonna do is you’re going to, and I would love the little summary. I would love a little summary starting off this lab of what you learned from these articles. Then the next step, using the data that you collected in week five. Now remember in week five, you had ten different peoples height plus the ten that you or your professor gave you. So you should have 20 numbers. I want you to discuss the Gad Yair method of collection was its systematic convenience. Cluster, cluster stratified simple random. What are some false? I know you highlighted this in week five, but now I want you to talk about what are some faults with the type of data collection, okay. What other types of data collections could you used instead? And how might that affected your survey? So this right here is the really important part. This is what I am trying to see what you have learned, okay? So it’s about telling me again what type of method you chose. Telling me what faults come with that method, some research might be involved. And then telling me another type of method that you would’ve liked to try if you could have and how that would affect your study. Okay. Then you’re going to tell me what the point estimate was, the point estimates, your mean. So in our case when we’re talking about the midterm, whereas my lecture notes here again, this right here, maybe I should write this down. The mean, the 76.9, that’s your point estimate. This is what we’re basing it off of. Okay? So the point estimate is the mean. Okay? So give a point estimate for the mean of the average height of all people at the place of your work. If that’s where you pull your sample and start by putting the 20 heights you are working with into the blue data. So we’ve done this already. You should already have your data in and you know what your mean is in your sample standard deviation. Then what you’re gonna do is you’re going to construct a 95% confidence interval for the true mean height of all the pupil, the place of your work, what is the interval? And provide a screenshot which we did today. Then you’re going to give me a practical interpretation what this means. So what you’re explaining is your 95% confident that the true mean height of all the people that you work with or the population that you have is between this and this, okay? Then you’re gonna put, of course going to post a screenshot. Then you’re going to change your confidence levels. With 99% confidence level, you’re going to take a screenshot and provide that as well. You’re going to compare the margins of error. So this is where you’re going to talk about what happened to your margin of error when we went from a 95 to 99% confidence interval, what happened to your interval when he went from 95 to 99% confidence interval? There should be a good paragraph explaining what happened, why it’s happening, and try to explain it in the context of the data and the lab. And that’s it. And then you’re just going to save your document and upload and that will submit your work. Please feel free to reach out if you have any questions or concerns.
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fidence Interval
| Put values in GREEN cells; output or answers in YELLOW cells | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
| Enter input in blue cells ; Look for answers in yellow cells | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
| t or | z | Confidence Interval for p Proportions | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
| Confidence Level | 0 | Enter decimal | 0.950 | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
| 27 | 3 | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
| Mean | 17 | Number of Successes | 141 | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
| StDev | 3.4029 | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
| pop stdev | no | Enter yes if population stdev known | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
| Enter No if population stdev is unknown | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
| SE | 0.654888 | Sample Proportion | 0.428571 | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
| 2.779 | 0.027283 | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
| Margin of | Error | 1.819935 | 1.960 | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
| Lower Limit | 15 | 0.053475 | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
| Upper Limit | 19.1 | 43 | 0.37 | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
| 0.482046 |
sample
mean
& standard deviatio
| Put values in blue cells; output or answers in YELLOW cells | |
| Enter values starting from B5 cell | |
| Data | |
| 18.4 | |
| 16.1 | Sample Standard Deviation |
| 19.5 | |
| 16.5 | |
| 12.5 | |
| 17.2 | |
| 13.8 | |
| 17.9 | |
| 9.8 | |
| 23.8 | |
| 18.7 | |
| 19.2 | |
| 11.5 | |
| 15.7 | |
| 22.5 | |
| 23.7 | |
| 19.9 | |
| 17.6 | |
| 17.8 | |
| 20.7 | |
| 14.2 | |
| 15.4 |
Minimum Sample Size
| Minimum Sample Size μ for population mean | Minimum Sample Size p for Proportion | |
| 0.920 | ||
| 10 | 0.5 | If sample proportion unknown enter 0.5 |
| 0.03 | Write percentage as decimal | |
| z-Value | 1.751 | |
| 852 |
EMPIRICAL RULE
| Empirical Rule | ||||
| ANSWER | ||||
| 68-95-99.7 | ||||
| 0.43 | Lower number | Upper number | ||
| standard deviation | 68% | 0.49 | ||
| Standard error | 0.06 | 95% | 0.31 | 0.55 |
| 99.70% | 0.25 | 0.61 |