This document discusses sampling distributions and their properties. It defines key terms like population parameter, sample statistic, and sampling distribution. The central limit theorem states that as sample size increases, the sampling distribution of the mean will approach a normal distribution, regardless of the shape of the original population. This allows us to use properties of the normal distribution, like calculating confidence intervals, when making inferences about a population based on a sample. Several examples show how to apply the central limit theorem to find probabilities and determine necessary sample sizes. Practice questions at the end test understanding of these concepts.
This PPT deals with the problems and solutions for sampling of large variables and relate, compare the observations with the exception of the population sample ie testing the difference between means of two samples, standard error of the difference between two standard deviations.
This PPT deals with the problems and solutions for sampling of large variables and relate, compare the observations with the exception of the population sample ie testing the difference between means of two samples, standard error of the difference between two standard deviations.
Standard error is used in the place of deviation. it shows the variations among sample is correlate to sampling error. list of formula used for standard error for different statistics and applications of tests of significance in biological sciences
Mathematics in Epidemiology and Biostatistics (Medical Booklet Series by Dr. ...Dr. Aryan (Anish Dhakal)
Basic mathematics needed for epidemiology and bio statistics. Slides include formulas and conceptual understanding of sensitivity, specificity, predictive values, likelihood ratios, odds, probability and many more.
Standard error is used in the place of deviation. it shows the variations among sample is correlate to sampling error. list of formula used for standard error for different statistics and applications of tests of significance in biological sciences
Mathematics in Epidemiology and Biostatistics (Medical Booklet Series by Dr. ...Dr. Aryan (Anish Dhakal)
Basic mathematics needed for epidemiology and bio statistics. Slides include formulas and conceptual understanding of sensitivity, specificity, predictive values, likelihood ratios, odds, probability and many more.
What is statistical analysis? It's the science of collecting, exploring and presenting large amounts of data to discover underlying patterns and trends. Statistics are applied every day – in research, industry and government – to become more scientific about decisions that need to be made.
Running Head SCENARIO NCLEX MEMORIAL HOSPITAL .docxtoltonkendal
Running Head: SCENARIO NCLEX MEMORIAL HOSPITAL 1
SCENARIO NCLEX MEMORIAL HOSPITAL 11
Course Project - Phase 4
Name: Rodney Wheeler
Institution: Rasmussen College
Course: STA3215 Section 01 Inferential Statistics and Analytics
Date: 03/14/17
Introduction
The scenario I will be working with is that I am working at NCLEX Memorial Hospital in the infectious disease unit. As a healthcare professional, I need to work to improve the health of individuals, families and communities in various settings. The current situation that has posed as a problem at the hospital and raised eyebrows is that in the past few days, there has been an increase in patients admitted with a particular infectious disease. The basic statistical analysis shows that the disease does not affect minors hence the ages of the infected patients does play a critical role in the method that shall be required to treat the patients in order to impact positively on the health and well-being of the clients being served whether infected with the disease or associated with those infected. After speaking to the manager, we decided that we shall work together in utilising the available statistical analysis to look closer into the ages of the infected patients. To do that, I had to put together a spreadsheet with the data containing the information we shall need to carry out the analysis.
Data Analysis
From the data collected and input on an Excel sheet, there are sixty patients with the infectious disease. Of the patient’s whose data has already been collected an input on the excel sheet, the ages range from thirty-five years of age to seventy-six. There is only one patient in their thirties with the age of thirty-five. There are five patients in their forties, One forty-five, one forty-six, two at forty-eight and two at forty-nine. There are fifteen patients in their fifties, two at fifty, one fifty-two, one fifty-three, one fifty-four, four at fifty-five, one fifty-six, one at fifty-eight and four at fifty-nine. There are twenty-three patients in their sixties, five at sixty, one at sixty-two, one at sixty-three, two at sixty-four, one at sixty-five, three at sixty-eight and seven at sixty-nine. Finally, we have fifteen infected patients in their seventies, six at seventy, three at seventy-one, three at seventy-two, one at seventy-three, one at seventy-four and one at seventy-six. From the graph in Figure 1 below, the horizontal axis depicts the age group of patients infected with the disease and the vertical axis depicts the number of patients in the age group infected with the disease.
Figure 1
Data Classification
The qualitative variables in our data analysis would be the names of the patients infected with the disease while the quantitative data would be their ages, nu ...
Inferential statistics are often used to compare the differences between the treatment groups. Inferential statistics use measurements from the sample of subjects in the experiment to compare the treatment groups and make generalizations about the larger population of subjects.
Study of the distribution and determinants of
health-related states or events in specified populations and the application of this study to control health problems.
John M. Last, Dictionary of Epidemiology
Course Project Phase Two
Pavel Garbuz
April 12th, 2017
Rasmussen College
1. Confidence interval
1) Confidence interval is a range which is used to provide an estimate of population mean. It is believed that the population mean would be from that range.
2) Point estimate is the value which we derive from a sample to give an estimate about the population.
3) The best point estimate is an estimate about the population mean. We derive this by finding the mean of the sample as a sample represents a population and there for its mean gives the best point estimator of population mean.
4) Normally samples represent a population. In theory it should be the same as a population but in reality the sample may have higher values and may not contain lower values and vice versa thus we don’t get the best point estimators of the population. To cater to this problem we use confidence interval by which we calculate a range in which the population mean is assumed to be present.
2. Best Point estimate of population Mean
BPE = sum of all ages / number or patients
BPE = 3709 / 60
BPE = 62 (61.82 round up)
3. Confidence interval
Confidence interval = 61.82 (+-) Z0.05/2 (S/ ((n)^(1/2))
= 61.82 (+-) 1.96 ( 8.92/ (601/2 )
= 61.82 - 2.257 , 61.82 + 2.257
= 59.56 > X > 64.077
4. Interpretation of confidence interval
In the research we were looking at the significance that old people tend to have particular infectious disease. We constructed a confidence interval to have an idea were the population mean lies. By constructing a confidence interval we have a point estimate of population mean. 95% of the samples would have a mean within the above range which is between 59.56 > age > 64.077.
5. Calculating confidence interval at 99%
61.82 (+-) 2.5758 (8.92/ (601/2)
= 58.85 > age > 64.79
A) Yes I did notice change in the interval as the range has increased as we can see in the calculation above.
B) Now the range for the point estimate has increase and as it at 99% confidence level we can say that its more accurate as 99 sample means would be within this sample. Whereas in 95% confidence we had 95 sample mean in that interval.
G310 Advanced Statistics and Analytics – Option 2
An Application of Statistical Methods
Pavel Garbuz
April 6th, 2017
Rasmussen College
1. Introduction
As a health care professional, this study works to improve and maintain families, and communities in various settings. To understand current problem and its solution this study uses statistical tools to analyze results. The objective of this project is the application of basic statistical tools to a fictional scenario in order to impact the health and wellbeing of the clients being served.
2. Scenario/Problem
You are currently working at NCLEX Memorial Hospital in the Infectious Diseases Unit. Over the past few days, you have noticed an increase in patients admitted with a particular infectious disease. It is believed t.
Salas, V. (2024) "John of St. Thomas (Poinsot) on the Science of Sacred Theol...Studia Poinsotiana
I Introduction
II Subalternation and Theology
III Theology and Dogmatic Declarations
IV The Mixed Principles of Theology
V Virtual Revelation: The Unity of Theology
VI Theology as a Natural Science
VII Theology’s Certitude
VIII Conclusion
Notes
Bibliography
All the contents are fully attributable to the author, Doctor Victor Salas. Should you wish to get this text republished, get in touch with the author or the editorial committee of the Studia Poinsotiana. Insofar as possible, we will be happy to broker your contact.
The ability to recreate computational results with minimal effort and actionable metrics provides a solid foundation for scientific research and software development. When people can replicate an analysis at the touch of a button using open-source software, open data, and methods to assess and compare proposals, it significantly eases verification of results, engagement with a diverse range of contributors, and progress. However, we have yet to fully achieve this; there are still many sociotechnical frictions.
Inspired by David Donoho's vision, this talk aims to revisit the three crucial pillars of frictionless reproducibility (data sharing, code sharing, and competitive challenges) with the perspective of deep software variability.
Our observation is that multiple layers — hardware, operating systems, third-party libraries, software versions, input data, compile-time options, and parameters — are subject to variability that exacerbates frictions but is also essential for achieving robust, generalizable results and fostering innovation. I will first review the literature, providing evidence of how the complex variability interactions across these layers affect qualitative and quantitative software properties, thereby complicating the reproduction and replication of scientific studies in various fields.
I will then present some software engineering and AI techniques that can support the strategic exploration of variability spaces. These include the use of abstractions and models (e.g., feature models), sampling strategies (e.g., uniform, random), cost-effective measurements (e.g., incremental build of software configurations), and dimensionality reduction methods (e.g., transfer learning, feature selection, software debloating).
I will finally argue that deep variability is both the problem and solution of frictionless reproducibility, calling the software science community to develop new methods and tools to manage variability and foster reproducibility in software systems.
Exposé invité Journées Nationales du GDR GPL 2024
Toxic effects of heavy metals : Lead and Arsenicsanjana502982
Heavy metals are naturally occuring metallic chemical elements that have relatively high density, and are toxic at even low concentrations. All toxic metals are termed as heavy metals irrespective of their atomic mass and density, eg. arsenic, lead, mercury, cadmium, thallium, chromium, etc.
Nutraceutical market, scope and growth: Herbal drug technologyLokesh Patil
As consumer awareness of health and wellness rises, the nutraceutical market—which includes goods like functional meals, drinks, and dietary supplements that provide health advantages beyond basic nutrition—is growing significantly. As healthcare expenses rise, the population ages, and people want natural and preventative health solutions more and more, this industry is increasing quickly. Further driving market expansion are product formulation innovations and the use of cutting-edge technology for customized nutrition. With its worldwide reach, the nutraceutical industry is expected to keep growing and provide significant chances for research and investment in a number of categories, including vitamins, minerals, probiotics, and herbal supplements.
Comparing Evolved Extractive Text Summary Scores of Bidirectional Encoder Rep...University of Maribor
Slides from:
11th International Conference on Electrical, Electronics and Computer Engineering (IcETRAN), Niš, 3-6 June 2024
Track: Artificial Intelligence
https://www.etran.rs/2024/en/home-english/
DERIVATION OF MODIFIED BERNOULLI EQUATION WITH VISCOUS EFFECTS AND TERMINAL V...Wasswaderrick3
In this book, we use conservation of energy techniques on a fluid element to derive the Modified Bernoulli equation of flow with viscous or friction effects. We derive the general equation of flow/ velocity and then from this we derive the Pouiselle flow equation, the transition flow equation and the turbulent flow equation. In the situations where there are no viscous effects , the equation reduces to the Bernoulli equation. From experimental results, we are able to include other terms in the Bernoulli equation. We also look at cases where pressure gradients exist. We use the Modified Bernoulli equation to derive equations of flow rate for pipes of different cross sectional areas connected together. We also extend our techniques of energy conservation to a sphere falling in a viscous medium under the effect of gravity. We demonstrate Stokes equation of terminal velocity and turbulent flow equation. We look at a way of calculating the time taken for a body to fall in a viscous medium. We also look at the general equation of terminal velocity.
Earliest Galaxies in the JADES Origins Field: Luminosity Function and Cosmic ...Sérgio Sacani
We characterize the earliest galaxy population in the JADES Origins Field (JOF), the deepest
imaging field observed with JWST. We make use of the ancillary Hubble optical images (5 filters
spanning 0.4−0.9µm) and novel JWST images with 14 filters spanning 0.8−5µm, including 7 mediumband filters, and reaching total exposure times of up to 46 hours per filter. We combine all our data
at > 2.3µm to construct an ultradeep image, reaching as deep as ≈ 31.4 AB mag in the stack and
30.3-31.0 AB mag (5σ, r = 0.1” circular aperture) in individual filters. We measure photometric
redshifts and use robust selection criteria to identify a sample of eight galaxy candidates at redshifts
z = 11.5 − 15. These objects show compact half-light radii of R1/2 ∼ 50 − 200pc, stellar masses of
M⋆ ∼ 107−108M⊙, and star-formation rates of SFR ∼ 0.1−1 M⊙ yr−1
. Our search finds no candidates
at 15 < z < 20, placing upper limits at these redshifts. We develop a forward modeling approach to
infer the properties of the evolving luminosity function without binning in redshift or luminosity that
marginalizes over the photometric redshift uncertainty of our candidate galaxies and incorporates the
impact of non-detections. We find a z = 12 luminosity function in good agreement with prior results,
and that the luminosity function normalization and UV luminosity density decline by a factor of ∼ 2.5
from z = 12 to z = 14. We discuss the possible implications of our results in the context of theoretical
models for evolution of the dark matter halo mass function.
Observation of Io’s Resurfacing via Plume Deposition Using Ground-based Adapt...Sérgio Sacani
Since volcanic activity was first discovered on Io from Voyager images in 1979, changes
on Io’s surface have been monitored from both spacecraft and ground-based telescopes.
Here, we present the highest spatial resolution images of Io ever obtained from a groundbased telescope. These images, acquired by the SHARK-VIS instrument on the Large
Binocular Telescope, show evidence of a major resurfacing event on Io’s trailing hemisphere. When compared to the most recent spacecraft images, the SHARK-VIS images
show that a plume deposit from a powerful eruption at Pillan Patera has covered part
of the long-lived Pele plume deposit. Although this type of resurfacing event may be common on Io, few have been detected due to the rarity of spacecraft visits and the previously low spatial resolution available from Earth-based telescopes. The SHARK-VIS instrument ushers in a new era of high resolution imaging of Io’s surface using adaptive
optics at visible wavelengths.
Remote Sensing and Computational, Evolutionary, Supercomputing, and Intellige...University of Maribor
Slides from talk:
Aleš Zamuda: Remote Sensing and Computational, Evolutionary, Supercomputing, and Intelligent Systems.
11th International Conference on Electrical, Electronics and Computer Engineering (IcETRAN), Niš, 3-6 June 2024
Inter-Society Networking Panel GRSS/MTT-S/CIS Panel Session: Promoting Connection and Cooperation
https://www.etran.rs/2024/en/home-english/
Seminar of U.V. Spectroscopy by SAMIR PANDASAMIR PANDA
Spectroscopy is a branch of science dealing the study of interaction of electromagnetic radiation with matter.
Ultraviolet-visible spectroscopy refers to absorption spectroscopy or reflect spectroscopy in the UV-VIS spectral region.
Ultraviolet-visible spectroscopy is an analytical method that can measure the amount of light received by the analyte.
2. Statistical inference: Making
guesses about the population from a sample
Truth (not observable)
N
x
N
i
i
2
12
)(
N
x
N
i
1
Population parameters
1
)( 2
12
n
Xx
s
n
n
i
i
n
x
X
n
i
1
Sample statistics
Sample (Observation)
2
3. Statistics vs. Parameters
› Sample statistic – any summary measure
calculated from data; e.g., could be a mean, a
difference in means or proportions, an odds ratio,
or a correlation coefficient
› Population parameter – the true value/true effect
in the entire population of interest
3
4. Examples of Sample Statistics:
› Mean
› Rate
› Risk
› Difference in means
› Relative risk (odds ratio/ risk ratio…)
› Correlation coefficient
› Regression coefficient
…
4
5. › A single number calculated from our sample data
› How can a single number (e.g., a mean ) have a
distribution?
– Answer: It’s a theoretical concept!
Statistics follow distribution!
– Sampling distribution
5
7. › The sampling distributions are defined by:
• Shape (e.g., normal distribution, T-distribution)
• Mean
• Standard error
7
8. The Central Limit Theorem
If all possible random samples, each of size n, are
taken from any population with a mean and a
standard deviation , the sampling distribution of
the Means will:
1. Have mean:
2. Have standard deviation (standard error):
3. Be approximately normally distributed
regardless of the shape of the parent
population (normality improve with larger n)
x
n
x
x
The mean of the sample meansx
The standard deviation of the sample means. Also called
“the standard error.” - 𝜎 𝑥 𝑆𝐷 𝑥 𝑆𝐸 𝑥 𝑆𝐸𝑀 𝑆𝐸 8
9. n
x
n 1 SEM is always smaller than
SD of the population
n increase variation decreases
Finally, if n is large enough, the sampling
distribution of the mean is approximately
normal!
9
11. Applications Using the Sampling
distribution of the Mean
! Apply tables of standard
normal distribution
Serum cholesterol levels for all 20 – 74-year-old males
in US have:
= 211 mg/dL
= 46 mg/dL
If we select repeated samples of size 25, what
proportion of the samples of size 25 will have mean
value of 230 mg/dL or above?
𝜇 𝑥 = 𝜇 = 211
𝜎 𝑥 =
46
25
= 9.2
𝑧 =
230 − 211
9.2
= 2.07
11
𝑧 =
𝑋 − 𝜇
𝜎
𝒛 =
𝑿 − 𝝁
𝝈/ 𝒏
12. 𝑃 𝑍 < 2.07 = 0.9808
𝑃 𝑍 ≥ 2.07 = 1 − 0.9808
= 0.192
About 1.9% of sample will
have a mean ≥ 230 mg/dL
12
13. Upper and lower limits that enclose 95% of the means
of sample size 25 draw from the population?
𝑃 −1.96 ≤ 𝑍 ≤ 1.96 = 0.95
−1.96 ≤ 𝑍 ≤ 1.96
−1.96 ≤
𝑋 − 211
9.2
≤ 1.96
193.0 ≤ 𝑋 ≤ 229
About 95% of the means of
samples size of 25 lie between
193.0 mg/dL and 229 mg/dL
13
14. How large would the samples need to be for 95% of
their means to lie within 5 mg/dL of the population
mean ?
= 211 mg/dL
= 46 mg/dL
𝑃 𝜇 − 5 ≤ 𝑋 ≤ 𝜇 + 5 = 0.95
1.96SE = 5
1.96
𝜎
𝑛
= 5
𝑛 =
1.96 × 46
5
2
= 326
Samples size of 326 would be
required for 95% of the sample
means to lie within 5 mg/dL of
the population mean
14
15. Practice
Q1. A laboratory value with a mean of 18 g/dL and a standard
deviation of 1.5 implies
a. The true value is between 16.5 and 19.5 g/dL
b. The true value is between 15.0 and 21.0 g/dL
c. The error is too large for the determination to have any value
d. In repeated determination on the same samples, 95% could be
expected to fall between 15.0 and 21.0 g/dL
e. The true value has a 5% chance of being less than 16.5 or more
than 19.5 g/dL
15
16. Q2. Data for patients at a certain hospital show the mean length of
stay is 10 days and the median is 8 days. The most frequent length of
of stay is 6 days. From these facts, we conclude
a. Approximately 50% of the patients stay less than 6 days
b. The distribution of length of stay follows the normal curve
c. The standard deviation is 2 days
d. The mean length of stay is shifted away from the center of the
distribution by stays of very long duration
e. The mean length of stay is shifted away from the center of the
distribution by stays of very short duration
17
17. Q3. A random sample of teenage prenatal patients seen at University
Hospital during 1973 had a mean hematocrit of 29 with a standard
error of 1.5. From this information, we may conclude
a. The hematocrit for any teenage prenatal patient in the sample
will not deviate from the mean by any more than 50%
b. The normal range for teenage prenatal patients seen at
University Hospital is 26 to 32
c. The range of 26 to 32 will include the mean of all teenage
prenatal patients seen at University Hospital in 1973 with 95%
probability
d. It is to be expected that 95% of all teenage prenatal patients seen
seen at University Hospital in 1973 will have hematocrits in the
the range of 26 to 32
18
18. Q4. The IQs of a class of students attending a university are
distributed according to the normal curve, with a mean of 115
115 and a standard deviation of 10. Therefore
a. 50% have IQs between 105 and 115
b. 95% have IQs between 105 than 115
c. 2.5% have IQs above 135
d. 5% have IQs above 135
e. 5% have IQs below 95
19
19. Q5. The primary use of the standard error of the mean is in
calculating the:
a. Confidence interval
b. Error rate
c. Standard deviation
d. Variance
20
20. References
1. Dawson, B., & Trapp, G. R. (2004). Basic & Clinical
Biostatistics (4th edition ed.): Lange Medical Books /
McGraw-Hill.
2. Fisher, L. D., & van Belle, G. (1993). Biostatistics: A
Methodology for the Health Sciences (1st edition ed.):
Wiley.
3. Pagano, M., & Gauvreau, K. (2000). Principles of
Biostatistics (2nd edition ed.): Duxbury Press.
4. Sainani, K. (2014). Statistics in Medicine. Retrieved
May, 2017, from
https://lagunita.stanford.edu/courses/Medicine/MedSt
ats/Summer2014/courseware/8016c68f703d4b888e44
4e97481b6830/71fad5f25fc64e6383bb9cc6be846a2b/
21
Editor's Notes
Statistical inference is all about making guess about a population from a sample.
There is some large population, and there is something we want to know about the population, like what is the effectiveness of the vaccine, what is the mean height of Japanese adult female (called population parameters). But we can not measure everybody, so the truth is not observable.
What we can do instead is we take a subset, a small representative subset of the larger population, that we call a sample.
We can observe the sample, calculate all the measure in the sample: The mean height, the proportion of vaccinated children in the sample. And we call those number calculated from our data Sample statistics.
Then we use those number to guess back to the home population.
On the other hand, a population parameter is the true value or the true effect in the entire population of interest if you can measure it. Of course, usually you can’t actually measure it
There are lots of examples of statistics that we calculate from our data. You can calculate a mean, you can calculate a rate…
More simply, it is the distribution of a statistic across an infinite number of sample
Suppose that in a specified population, the mean of .. Let’s say a test result is muy = 82.5 and the SD is delta. We randomly select a sample of 20 observations from the population and compute the mean of this sample; call the sample mean x1. We then obtain a second random sample of 20 observations and calculate the mean of this new sample, call x2. If we were to continue this procedure indefinitely, we would end up with a set of means.
If we treat each mean as an observation, their collective probability distribution is know as a sampling distribution of means of samples of size 20.
What are the 2 parameters (from last time) that define any normal distribution?
Remember that a normal curve is characterized by two parameters, a mean and a variability (SD)
Remember standard deviation is natural variability of the population. The standard deviation of a statistic is called a SE
Standard error can be standard error of the mean or standard error of the odds ratio or standard error of the difference of 2 means, etc. The standard error of any sample statistic.
I would like to talk about maybe one of the most fundamentally and profound concepts in statistics, and that is the Central Limit Theorem.
The mean of the means is equal to population mean
Even if the population is skewed or even bimodal, a sample size 30 is often sufficient.
A sample of 30 is commonly used as a cutoff value because sampling distributions of the mean based on sample sizes of 30 or more are considered to be normally distributed. A sample this large is not always needed, however. If the parent population is normally distributed, the means of samples of any size will be normally distributed.
Who remember the first step ? Liu –san had guided us through last week?
That’s calculate the Z score.
Z score transforms a normally distributed variable with mean muy and SD delta to the standard normal distribution with mean = 0 and SD = 1.
According to the central limit theorem: the mean of sampling distribution is still muy, but SD => SEM the Z score calculating is therefore:
So, assuming that a sample size of 25 is large enough, the central limit theorem states that the distribution of means of samples of size 25 is approximately normal with mean = 211 mg/dL and SE = 46/25
Since we’ve already known that 2.5% of the area lies above z= 1.96 and another 2.5% lies below z=-1.96
Recall that 95% of the area lies between mean 2SD (SE in this case) – actually 1.96
Distribution of proportion:
Shape: Normal distribution if np>5
Mean = true proportion of the population
SE = [p(1-p)/n]