This document provides an overview of statistical estimation and inference. It discusses point estimation, which provides a single value to estimate an unknown population parameter, and interval estimation, which gives a range of plausible values for the parameter. The key aspects of interval estimation are confidence intervals, which provide a probability statement about where the true population parameter lies. The document also covers important concepts like sampling distributions, the central limit theorem, and factors that influence the width of a confidence interval like sample size. Examples are provided to demonstrate calculating point estimates, confidence intervals, and dealing with independent samples.
In statistics, regression analysis is a statistical process for estimating the relationships among variables. It includes many techniques for modeling and analyzing several variables, when the focus is on the relationship between a dependent variable and one or more independent variables. More specifically, regression analysis helps one understand how the typical value of the dependent variable (or 'Criterion Variable') changes when any one of the independent variables is varied, while the other independent variables are held fixed. Most commonly, regression analysis estimates the conditional expectation of the dependent variable given the independent variables – that is, the average value of the dependent variable when the independent variables are fixed. Less commonly, the focus is on a quantile, or other location parameter of the conditional distribution of the dependent variable given the independent variables. In all cases, the estimation target is a function of the independent variables called the regression function. In regression analysis, it is also of interest to characterize the variation of the dependent variable around the regression function which can be described by a probability distribution.
Hypothesis is usually considered as the principal instrument in research and quality control. Its main function is to suggest new experiments and observations. In fact, many experiments are carried out with the deliberate object of testing hypothesis. Decision makers often face situations wherein they are interested in testing hypothesis on the basis of available information and then take decisions on the basis of such testing. In Six –Sigma methodology, hypothesis testing is a tool of substance and used in analysis phase of the six sigma project so that improvement can be done in right direction
inferential statistics, statistical inference, language technology, interval estimation, confidence interval, standard error, confidence level, z critical value, confidence interval for proportion, confidence interval for the mean, multiplier,
In statistics, regression analysis is a statistical process for estimating the relationships among variables. It includes many techniques for modeling and analyzing several variables, when the focus is on the relationship between a dependent variable and one or more independent variables. More specifically, regression analysis helps one understand how the typical value of the dependent variable (or 'Criterion Variable') changes when any one of the independent variables is varied, while the other independent variables are held fixed. Most commonly, regression analysis estimates the conditional expectation of the dependent variable given the independent variables – that is, the average value of the dependent variable when the independent variables are fixed. Less commonly, the focus is on a quantile, or other location parameter of the conditional distribution of the dependent variable given the independent variables. In all cases, the estimation target is a function of the independent variables called the regression function. In regression analysis, it is also of interest to characterize the variation of the dependent variable around the regression function which can be described by a probability distribution.
Hypothesis is usually considered as the principal instrument in research and quality control. Its main function is to suggest new experiments and observations. In fact, many experiments are carried out with the deliberate object of testing hypothesis. Decision makers often face situations wherein they are interested in testing hypothesis on the basis of available information and then take decisions on the basis of such testing. In Six –Sigma methodology, hypothesis testing is a tool of substance and used in analysis phase of the six sigma project so that improvement can be done in right direction
inferential statistics, statistical inference, language technology, interval estimation, confidence interval, standard error, confidence level, z critical value, confidence interval for proportion, confidence interval for the mean, multiplier,
Assumptions of parametric and non-parametric tests
Testing the assumption of normality
Commonly used non-parametric tests
Applying tests in SPSS
Advantages of non-parametric tests
Limitations
Standard Error & Confidence Intervals.pptxhanyiasimple
Certainly! Let's delve into the concept of **standard error**.
## What Is Standard Error?
The **standard error (SE)** is a statistical measure that quantifies the **variability** between a sample statistic (such as the mean) and the corresponding population parameter. Specifically, it estimates how much the sample mean would **vary** if we were to repeat the study using **new samples** from the same population. Here are the key points:
1. **Purpose**: Standard error helps us understand how well our **sample data** represents the entire population. Even with **probability sampling**, where elements are randomly selected, some **sampling error** remains. Calculating the standard error allows us to estimate the representativeness of our sample and draw valid conclusions.
2. **High vs. Low Standard Error**:
- **High Standard Error**: Indicates that sample means are **widely spread** around the population mean. In other words, the sample may not closely represent the population.
- **Low Standard Error**: Suggests that sample means are **closely distributed** around the population mean, indicating that the sample is representative of the population.
3. **Decreasing Standard Error**:
- To decrease the standard error, **increase the sample size**. Using a large, random sample minimizes **sampling bias** and provides a more accurate estimate of the population parameter.
## Standard Error vs. Standard Deviation
- **Standard Deviation (SD)**: Describes variability **within a single sample**. It can be calculated directly from sample data.
- **Standard Error (SE)**: Estimates variability across **multiple samples** from the same population. It is an **inferential statistic** that can only be estimated (unless the true population parameter is known).
### Example:
Suppose we have a random sample of 200 students, and we calculate the mean math SAT score to be 550. In this case:
- **Sample**: The 200 students
- **Population**: All test takers in the region
The standard error helps us understand how well this sample represents the entire population's math SAT scores.
Remember, the standard error is crucial for making valid statistical inferences. By understanding it, researchers can confidently draw conclusions based on sample data. 📊🔍
If you need further clarification or have additional questions, feel free to ask! 😊
---
I've provided a concise explanation of standard error, emphasizing its importance in statistical analysis. If you'd like more details or specific examples, feel free to ask! ¹²³⁴
Source: Conversation with Copilot, 5/31/2024
(1) What Is Standard Error? | How to Calculate (Guide with Examples) - Scribbr. https://www.scribbr.com/statistics/standard-error/.
(2) Standard Error (SE) Definition: Standard Deviation in ... - Investopedia. https://www.investopedia.com/terms/s/standard-error.asp.
(3) Standard error Definition & Meaning - Merriam-Webster. https://www.merriam-webster.com/dictionary/standard%20error.
(4) Standard err
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.
Census
Everyone in population
Eg. All Cambodian residents
Population
is a set of persons (or objects) having a common observable characteristic.
the entire collection of units about which we would like information
Sample
is a representative subject (subgroup) of a population.
the collection of units we actually measure
Example:
If we want to know many persons in a community
have quit smoking or
have health insurance or
plan to vote for a certain candidate,
Sample
is a representative subject (subgroup) of a population.
the collection of units we actually measure
Example:
If we want to know many persons in a community
have quit smoking or
have health insurance or
plan to vote for a certain candidate,
Sample
is a representative subject (subgroup) of a population.
the collection of units we actually measure
Example:
If we want to know many persons in a community
have quit smoking or
have health insurance or
plan to vote for a certain candidate,
Sample
is a representative subject (subgroup) of a population.
the collection of units we actually measure
Example:
If we want to know many persons in a community
have quit smoking or
have health insurance or
plan to vote for a certain candidate,
Sample
is a representative subject (subgroup) of a population.
the collection of units we actually measure
Example:
If we want to know many persons in a community
have quit smoking or
have health insurance or
plan to vote for a certain candidate,
Sample
is a representative subject (subgroup) of a population.
the collection of units we actually measure
Example:
If we want to know many persons in a community
have quit smoking or
have health insurance or
plan to vote for a certain candidate,
Sample
is a representative subject (subgroup) of a population.
the collection of units we actually measure
Example:
If we want to know many persons in a community
have quit smoking or
have health insurance or
plan to vote for a certain candidate,
Sample
is a representative subject (subgroup) of a population.
the collection of units we actually measure
Example:
If we want to know many persons in a community
have quit smoking or
have health insurance or
plan to vote for a certain candidate,
Statistical inference is the process by which we draw conclusions about a population from data collected on a sample.
In medical research
Population
All patients candidate for treatment
Sample
All patients candidate for treatment who volunteer for your study
Infer results from volunteers (sample) to other candidates for the same treatment (population).
We usually obtain information on an appropriate sample of the community and generalize from it to the entire population.
The way the sample is selected, not its size, determines whether we may draw appropriate inferences about a population.
The primary reason for selecting a sample from a population is to draw inferences about that population.
Statistical inference is the process by which we infer
Couples presenting to the infertility clinic- Do they really have infertility...Sujoy Dasgupta
Dr Sujoy Dasgupta presented the study on "Couples presenting to the infertility clinic- Do they really have infertility? – The unexplored stories of non-consummation" in the 13th Congress of the Asia Pacific Initiative on Reproduction (ASPIRE 2024) at Manila on 24 May, 2024.
Tom Selleck Health: A Comprehensive Look at the Iconic Actor’s Wellness Journeygreendigital
Tom Selleck, an enduring figure in Hollywood. has captivated audiences for decades with his rugged charm, iconic moustache. and memorable roles in television and film. From his breakout role as Thomas Magnum in Magnum P.I. to his current portrayal of Frank Reagan in Blue Bloods. Selleck's career has spanned over 50 years. But beyond his professional achievements. fans have often been curious about Tom Selleck Health. especially as he has aged in the public eye.
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Introduction
Many have been interested in Tom Selleck health. not only because of his enduring presence on screen but also because of the challenges. and lifestyle choices he has faced and made over the years. This article delves into the various aspects of Tom Selleck health. exploring his fitness regimen, diet, mental health. and the challenges he has encountered as he ages. We'll look at how he maintains his well-being. the health issues he has faced, and his approach to ageing .
Early Life and Career
Childhood and Athletic Beginnings
Tom Selleck was born on January 29, 1945, in Detroit, Michigan, and grew up in Sherman Oaks, California. From an early age, he was involved in sports, particularly basketball. which played a significant role in his physical development. His athletic pursuits continued into college. where he attended the University of Southern California (USC) on a basketball scholarship. This early involvement in sports laid a strong foundation for his physical health and disciplined lifestyle.
Transition to Acting
Selleck's transition from an athlete to an actor came with its physical demands. His first significant role in "Magnum P.I." required him to perform various stunts and maintain a fit appearance. This role, which he played from 1980 to 1988. necessitated a rigorous fitness routine to meet the show's demands. setting the stage for his long-term commitment to health and wellness.
Fitness Regimen
Workout Routine
Tom Selleck health and fitness regimen has evolved. adapting to his changing roles and age. During his "Magnum, P.I." days. Selleck's workouts were intense and focused on building and maintaining muscle mass. His routine included weightlifting, cardiovascular exercises. and specific training for the stunts he performed on the show.
Selleck adjusted his fitness routine as he aged to suit his body's needs. Today, his workouts focus on maintaining flexibility, strength, and cardiovascular health. He incorporates low-impact exercises such as swimming, walking, and light weightlifting. This balanced approach helps him stay fit without putting undue strain on his joints and muscles.
Importance of Flexibility and Mobility
In recent years, Selleck has emphasized the importance of flexibility and mobility in his fitness regimen. Understanding the natural decline in muscle mass and joint flexibility with age. he includes stretching and yoga in his routine. These practices help prevent injuries, improve posture, and maintain mobilit
Lung Cancer: Artificial Intelligence, Synergetics, Complex System Analysis, S...Oleg Kshivets
RESULTS: Overall life span (LS) was 2252.1±1742.5 days and cumulative 5-year survival (5YS) reached 73.2%, 10 years – 64.8%, 20 years – 42.5%. 513 LCP lived more than 5 years (LS=3124.6±1525.6 days), 148 LCP – more than 10 years (LS=5054.4±1504.1 days).199 LCP died because of LC (LS=562.7±374.5 days). 5YS of LCP after bi/lobectomies was significantly superior in comparison with LCP after pneumonectomies (78.1% vs.63.7%, P=0.00001 by log-rank test). AT significantly improved 5YS (66.3% vs. 34.8%) (P=0.00000 by log-rank test) only for LCP with N1-2. Cox modeling displayed that 5YS of LCP significantly depended on: phase transition (PT) early-invasive LC in terms of synergetics, PT N0—N12, cell ratio factors (ratio between cancer cells- CC and blood cells subpopulations), G1-3, histology, glucose, AT, blood cell circuit, prothrombin index, heparin tolerance, recalcification time (P=0.000-0.038). Neural networks, genetic algorithm selection and bootstrap simulation revealed relationships between 5YS and PT early-invasive LC (rank=1), PT N0—N12 (rank=2), thrombocytes/CC (3), erythrocytes/CC (4), eosinophils/CC (5), healthy cells/CC (6), lymphocytes/CC (7), segmented neutrophils/CC (8), stick neutrophils/CC (9), monocytes/CC (10); leucocytes/CC (11). Correct prediction of 5YS was 100% by neural networks computing (area under ROC curve=1.0; error=0.0).
CONCLUSIONS: 5YS of LCP after radical procedures significantly depended on: 1) PT early-invasive cancer; 2) PT N0--N12; 3) cell ratio factors; 4) blood cell circuit; 5) biochemical factors; 6) hemostasis system; 7) AT; 8) LC characteristics; 9) LC cell dynamics; 10) surgery type: lobectomy/pneumonectomy; 11) anthropometric data. Optimal diagnosis and treatment strategies for LC are: 1) screening and early detection of LC; 2) availability of experienced thoracic surgeons because of complexity of radical procedures; 3) aggressive en block surgery and adequate lymph node dissection for completeness; 4) precise prediction; 5) adjuvant chemoimmunoradiotherapy for LCP with unfavorable prognosis.
Report Back from SGO 2024: What’s the Latest in Cervical Cancer?bkling
Are you curious about what’s new in cervical cancer research or unsure what the findings mean? Join Dr. Emily Ko, a gynecologic oncologist at Penn Medicine, to learn about the latest updates from the Society of Gynecologic Oncology (SGO) 2024 Annual Meeting on Women’s Cancer. Dr. Ko will discuss what the research presented at the conference means for you and answer your questions about the new developments.
Title: Sense of Smell
Presenter: Dr. Faiza, Assistant Professor of Physiology
Qualifications:
MBBS (Best Graduate, AIMC Lahore)
FCPS Physiology
ICMT, CHPE, DHPE (STMU)
MPH (GC University, Faisalabad)
MBA (Virtual University of Pakistan)
Learning Objectives:
Describe the primary categories of smells and the concept of odor blindness.
Explain the structure and location of the olfactory membrane and mucosa, including the types and roles of cells involved in olfaction.
Describe the pathway and mechanisms of olfactory signal transmission from the olfactory receptors to the brain.
Illustrate the biochemical cascade triggered by odorant binding to olfactory receptors, including the role of G-proteins and second messengers in generating an action potential.
Identify different types of olfactory disorders such as anosmia, hyposmia, hyperosmia, and dysosmia, including their potential causes.
Key Topics:
Olfactory Genes:
3% of the human genome accounts for olfactory genes.
400 genes for odorant receptors.
Olfactory Membrane:
Located in the superior part of the nasal cavity.
Medially: Folds downward along the superior septum.
Laterally: Folds over the superior turbinate and upper surface of the middle turbinate.
Total surface area: 5-10 square centimeters.
Olfactory Mucosa:
Olfactory Cells: Bipolar nerve cells derived from the CNS (100 million), with 4-25 olfactory cilia per cell.
Sustentacular Cells: Produce mucus and maintain ionic and molecular environment.
Basal Cells: Replace worn-out olfactory cells with an average lifespan of 1-2 months.
Bowman’s Gland: Secretes mucus.
Stimulation of Olfactory Cells:
Odorant dissolves in mucus and attaches to receptors on olfactory cilia.
Involves a cascade effect through G-proteins and second messengers, leading to depolarization and action potential generation in the olfactory nerve.
Quality of a Good Odorant:
Small (3-20 Carbon atoms), volatile, water-soluble, and lipid-soluble.
Facilitated by odorant-binding proteins in mucus.
Membrane Potential and Action Potential:
Resting membrane potential: -55mV.
Action potential frequency in the olfactory nerve increases with odorant strength.
Adaptation Towards the Sense of Smell:
Rapid adaptation within the first second, with further slow adaptation.
Psychological adaptation greater than receptor adaptation, involving feedback inhibition from the central nervous system.
Primary Sensations of Smell:
Camphoraceous, Musky, Floral, Pepperminty, Ethereal, Pungent, Putrid.
Odor Detection Threshold:
Examples: Hydrogen sulfide (0.0005 ppm), Methyl-mercaptan (0.002 ppm).
Some toxic substances are odorless at lethal concentrations.
Characteristics of Smell:
Odor blindness for single substances due to lack of appropriate receptor protein.
Behavioral and emotional influences of smell.
Transmission of Olfactory Signals:
From olfactory cells to glomeruli in the olfactory bulb, involving lateral inhibition.
Primitive, less old, and new olfactory systems with different path
Ozempic: Preoperative Management of Patients on GLP-1 Receptor Agonists Saeid Safari
Preoperative Management of Patients on GLP-1 Receptor Agonists like Ozempic and Semiglutide
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TEST BANK for Operations Management, 14th Edition by William J. Stevenson, Ve...kevinkariuki227
TEST BANK for Operations Management, 14th Edition by William J. Stevenson, Verified Chapters 1 - 19, Complete Newest Version.pdf
TEST BANK for Operations Management, 14th Edition by William J. Stevenson, Verified Chapters 1 - 19, Complete Newest Version.pdf
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These simplified slides by Dr. Sidra Arshad present an overview of the non-respiratory functions of the respiratory tract.
Learning objectives:
1. Enlist the non-respiratory functions of the respiratory tract
2. Briefly explain how these functions are carried out
3. Discuss the significance of dead space
4. Differentiate between minute ventilation and alveolar ventilation
5. Describe the cough and sneeze reflexes
Study Resources:
1. Chapter 39, Guyton and Hall Textbook of Medical Physiology, 14th edition
2. Chapter 34, Ganong’s Review of Medical Physiology, 26th edition
3. Chapter 17, Human Physiology by Lauralee Sherwood, 9th edition
4. Non-respiratory functions of the lungs https://academic.oup.com/bjaed/article/13/3/98/278874
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4. Inferential statistics
The part of statistics that allows researchers
to generalize their findings to a larger
population beyond data from the sample
collected.
5. Two ways to make inference
–Estimation of parameters
* Point Estimation
* Intervals Estimation
–Hypothesis Testing
6. Basic terminology
• Parameter –the numbers that describe the
charactreistics of the population(mean, sd,
varience etc)
• Statistic- The numbers that describe
characteristics of scores in the sample (mean,
variance, s.d., correlation coefficient,etc .)
8. Basic Logic
• Information from
samples is used to
estimate information
about the population.
• Statistics are used to
estimate parameters.
POPULATION
SAMPLE
PARAMETER
STATISTIC
9. Estimation
The process by which one makes inferences
about a population, based on information
obtained from a sample.
Point estimate
Interval estimate
10. Point estimate
• Point estimates are single points that estimates
parameter directly which serve as a "best guess" or "best
estimate" of an unknown population parameter
• sample proportion pˆ (“p hat”) is the point estimate of p
• sample mean x (“x bar”) is the point estimate of μ
• sample standard deviation s is the point estimate of σ
11. Problem
• iIn a health survey of 55 school boys,it was
found that the mean hemoglobin level was
10.2 g per 100 ml with a standard deviation of
2.1.Estimate the mean hemoglobin level of
the population of such school boys.
Point estimate of the population mean is 10.2
12. Disadvantages of point estimates
Point estimate do not provide
information about sample to sample
variability
How precise is x as an estimate of μ
How much can we expect x vary from
μ
14. Sampling Distribution
• Sampling Distribution: A theoretical distribution
that shows the frequency of occurrence of values
of some statistic computed for all possible
samples of size N drawn from some population.
• Sampling Distribution of the Mean: A theoretical
distribution of the frequency of occurrence of
values of the mean computed for all possible
samples of size N from a population
16. Central Limit Theorem
States that the sampling distribution of means, for
samples of 30 or more:
– Is normally distributed (regardless of the shape of the
population from which the samples were drawn)
– Has a mean equal to the population mean, “mu” regardless
of the shape population or of the size of the sample
– Has a standard deviation--the standard error of the mean--
equal to the population standard deviation divided by the
square root of the sample size
Square
root law
17.
18. Confidence interval
CI is the probability that the interval
computed from the sample data includes
the population parameter of interest
19.
20. FACTORS AFFECTING CONFIDENCE INTERVAL
Distribution of Means and Standard Error of
the Means
u
mu
+2sem-2sem +1sem-1sem-3sem +3sem
Population mean
22. Confidence limits
• The α (“alpha”) level represents the “lack of
confidence”
• (1−α)100% represent the confidence level of a
confidence interval
• Confidence interval =
• z1-α/2 instead of z1-α in this formula is because the
random error (imprecision) is split between right
and left tail
23. Z values for different confidence level
Area under the curve
24. Z table 2 tailed
Areaunderthecurve
Second decimal places
1.96=1.9+0.06
25. Process for Constructing Confidence
Intervals
• Compute the sample statistic (e.g. a mean)
• Compute the standard error of the mean
• Make a decision about level of confidence that is
desired (usually 95% or 99%)
• Find tabled value for 95% or 99% confidence
interval
• Multiply standard error of the mean by the tabled
value
• Form interval by adding and subtracting
calculated value to and from the mean
26. Problems
• iIn a health survey of 55 school boys,it was found that
the mean hemoglobin level was 10.2 g per 100 ml with a
standard deviation of 2.1.Estimate the mean
hemoglobin level of the population of such school boys.
27. Problems
• iIn a health survey of 55 school boys,it was found
that the mean hemoglobin level was 10.2 g per 100
ml with a standard deviation of 2.1.Estimate the
mean hemoglobin level of the population of such
school boys.
X =10.2 s=2.1
SE= =0.283
95% CI= 10.2-1.96 x 0.283 to 10.2+ 1.96 x 0.283
=9.6 to 10.75
99% CI= 9.47 to 10.93
28. Problem
• In a survey on hearing level of schoolchildren
with normal hearing it was found that in the
frequency 500 cycles per second,62 children
tested in the sound proof room had a mean
hearing threshold of 15.5 db with a standard
deviation of 6.5.Another 76 comparable
children who were tested in the field had a
mean threshold of 20 db with a standard
deviation of 7.1.what is the 95% confidence
interval for the difference in mean.
29. Here 2 independent samples,sound proof room tested and
field tested sample given
The confidence interval of difference in means =difference in
means +/_ 1.96 SE of difference in means
sqrt [ s2
1 / n1 + s2
2 / n2 ]
= 4.5-1.96x1.17 to 4.5+1.96x1.17= 2.21 to 6.79
SE of difference in means = Pooled SD x sqrt [1/ n1 + 1 / n2 ]
30.
31. Problemm
• In an otological examination of school children
out of 146 children examined 21 were found
to have otological abnormalities,Find the 99%
confidence interval for the proportion of
children with otological abnormalities.
32. Answer
• p=21 x 100/146 = 14.4%
• q= 85.3
• 99% CI= p +/_2.57 SE of proportion
• SE of proportion = √pq/n
33. Problem
• Find the best estimate of the mean and 95%
CI of the mean using the data
Sl no Protein value
1 6
2 7
3 8
4 6
5 8
6 7
7 6
8 7
9 8
10 6
34. • Best estimate is the mean of sample= 6.9
• Interval estimate -95% CI= x +/- t0.05 SE of x
t0.05 is found from t table with df= 9
35. • In case If 2 independent sample is given with
sample size less than 30 and difference in CI
to be found
• CI=difference in means +/_ t0.05 SE of
difference in means
t0.05 found from the t table with df = n1+n2-2
SE of difference in means = use n-1 in the
equation for pooled sd
![Statistics
][ STATISTICAL
ANALYSIS
DESCRIPTIVE INFERENTIALL
NUMERICAL GRAPHICAL
UNIVERIATE ?
MULTIVARIATE
?
Estimation Hypothesis
testing
Point
estimate
Interval
estimate Univariate
Multivariate](data:image/gif;base64,R0lGODlhAQABAIAAAAAAAP///yH5BAEAAAAALAAAAAABAAEAAAIBRAA7)