Following points are presented in this presentation.
1. Hypothesis testing is a decision-making process for evaluating claims about a population.
2. NULL HYPOTHESIS & ALTERNATIVE HYPOTHESIS.
3. Types of errors.
Following points are presented in this presentation.
1. Hypothesis testing is a decision-making process for evaluating claims about a population.
2. NULL HYPOTHESIS & ALTERNATIVE HYPOTHESIS.
3. Types of errors.
This slideshow is related to testing of hypothesis and goodness of fit of statistics. This may be useful for students, teachers, managers concerned with bio statistics, bioinformatics, data science, etc.
Hypothesis testing and estimation are used to reach conclusions about a population by examining a sample of that population.
Hypothesis testing is widely used in medicine, dentistry, health care, biology and other fields as a means to draw conclusions about the nature of populations
A non technical overview of sample size calculation and why it is necessary with some brief examples of how to approach the problem and why it is useful to actually think of these calculations.
The error (or disturbance) of an observed value is the deviation of the observed value from the (unobservable) true value of a quantity of interest (for example, a population mean), and the residual of an observed value is the difference between the observed value and the estimated value of the quantity of interest (for example, a sample mean).
Suppose there is a series of observations from a univariate distribution and we want to estimate the mean of that distribution (the so-called location model). In this case, the errors are the deviations of the observations from the population mean, while the residuals are the deviations of the observations from the sample mean.
A statistical error (or disturbance) is the amount by which an observation differs from its expected value, the latter being based on the whole population from which the statistical unit was chosen randomly. For example, if the mean height in a population of 21-year-old men is 1.75 meters, and one randomly chosen man is 1.80 meters tall, then the "error" is 0.05 meters; if the randomly chosen man is 1.70 meters tall, then the "error" is −0.05 meters. The expected value, being the mean of the entire population, is typically not observable, and hence the statistical error cannot be observed either.
Application of statistical tests in Biomedical Research .pptxHalim AS
Here I have tried to show how to select a statistical test for a research project based on the type of data.
initially I have given an idea about the types of data, null hypothesis, p value and the types of error
Hypothesis Testing Definitions A statistical hypothesi.docxwilcockiris
Hypothesis Testing
Definitions:
A statistical hypothesis is a guess about a population parameter. The guess may or not be
true.
The null hypothesis, written H0, is a statistical hypothesis that states that there is no
difference between a parameter and a specific value, or that there is no difference between
two parameters.
The alternative hypothesis, written H1 or HA, is a statistical hypothesis that specifies a
specific difference between a parameter and a specific value, or that there is a difference
between two parameters.
Example 1:
A medical researcher is interested in finding out whether a new medication will have
undesirable side effects. She is particularly concerned with the pulse rate of patients who
take the medication. The research question is, will the pulse rate increase, decrease, or
remain the same after a patient takes the medication?
Since the researcher knows that the mean pulse rate for the population under study is 82
beats per minute, the hypotheses for this study are:
H0: µ = 82
HA: µ ≠ 82
The null hypothesis specifies that the mean will remain unchanged and the alternative
hypothesis states that it will be different. This test is called a two-tailed test since the
possible side effects could be to raise or lower the pulse rate. Notice that this is a non
directional hypothesis. The rejection region lies in both tails. We divide the alpha in two
and place half in each tail.
Example 2:
An entrepreneur invents an additive to increase the life of an automobile battery. If the
mean lifetime of the automobile battery is 36 months, then his hypotheses are:
H0: µ ≤ 36
HA: µ > 36
Here, the entrepreneur is only interested in increasing the lifetime of the batteries, so his
alternative hypothesis is that the mean is greater than 36 months. The null hypothesis is
that the mean is less than or equal to 36 months. This test is one-tailed since the interest
is only in an increased lifetime. Notice that the direction of the inequality in the alternate
hypothesis points to the right, same as the area of the curve that forms the rejection
region.
Example 3:
A landlord who wants to lower heating bills in a large apartment complex is considering
using a new type of insulation. If the current average of the monthly heating bills is $78,
his hypotheses about heating costs with the new insulation are:
H0: µ ≥ 78
HA: µ < 78
This test is also a one-tailed test since the landlord is interested only in lowering heating
costs. Notice that the direction of the inequality in the alternate hypothesis points to the
left, same as the area of the curve that forms the rejection region.
Study Design:
After stating the hypotheses, the researcher’s next step is to design the study. In designing
the study, the researcher selects an appropriate statistical test, chooses a level of
significance, and formulates a plan for conducting the study..
Testing of hypothesis - large sample testParag Shah
Different type of test which are used for large sample has been included in this presentation. Steps for each test and a case study is included for concept clarity and practice.
This slideshow is related to testing of hypothesis and goodness of fit of statistics. This may be useful for students, teachers, managers concerned with bio statistics, bioinformatics, data science, etc.
Hypothesis testing and estimation are used to reach conclusions about a population by examining a sample of that population.
Hypothesis testing is widely used in medicine, dentistry, health care, biology and other fields as a means to draw conclusions about the nature of populations
A non technical overview of sample size calculation and why it is necessary with some brief examples of how to approach the problem and why it is useful to actually think of these calculations.
The error (or disturbance) of an observed value is the deviation of the observed value from the (unobservable) true value of a quantity of interest (for example, a population mean), and the residual of an observed value is the difference between the observed value and the estimated value of the quantity of interest (for example, a sample mean).
Suppose there is a series of observations from a univariate distribution and we want to estimate the mean of that distribution (the so-called location model). In this case, the errors are the deviations of the observations from the population mean, while the residuals are the deviations of the observations from the sample mean.
A statistical error (or disturbance) is the amount by which an observation differs from its expected value, the latter being based on the whole population from which the statistical unit was chosen randomly. For example, if the mean height in a population of 21-year-old men is 1.75 meters, and one randomly chosen man is 1.80 meters tall, then the "error" is 0.05 meters; if the randomly chosen man is 1.70 meters tall, then the "error" is −0.05 meters. The expected value, being the mean of the entire population, is typically not observable, and hence the statistical error cannot be observed either.
Application of statistical tests in Biomedical Research .pptxHalim AS
Here I have tried to show how to select a statistical test for a research project based on the type of data.
initially I have given an idea about the types of data, null hypothesis, p value and the types of error
Hypothesis Testing Definitions A statistical hypothesi.docxwilcockiris
Hypothesis Testing
Definitions:
A statistical hypothesis is a guess about a population parameter. The guess may or not be
true.
The null hypothesis, written H0, is a statistical hypothesis that states that there is no
difference between a parameter and a specific value, or that there is no difference between
two parameters.
The alternative hypothesis, written H1 or HA, is a statistical hypothesis that specifies a
specific difference between a parameter and a specific value, or that there is a difference
between two parameters.
Example 1:
A medical researcher is interested in finding out whether a new medication will have
undesirable side effects. She is particularly concerned with the pulse rate of patients who
take the medication. The research question is, will the pulse rate increase, decrease, or
remain the same after a patient takes the medication?
Since the researcher knows that the mean pulse rate for the population under study is 82
beats per minute, the hypotheses for this study are:
H0: µ = 82
HA: µ ≠ 82
The null hypothesis specifies that the mean will remain unchanged and the alternative
hypothesis states that it will be different. This test is called a two-tailed test since the
possible side effects could be to raise or lower the pulse rate. Notice that this is a non
directional hypothesis. The rejection region lies in both tails. We divide the alpha in two
and place half in each tail.
Example 2:
An entrepreneur invents an additive to increase the life of an automobile battery. If the
mean lifetime of the automobile battery is 36 months, then his hypotheses are:
H0: µ ≤ 36
HA: µ > 36
Here, the entrepreneur is only interested in increasing the lifetime of the batteries, so his
alternative hypothesis is that the mean is greater than 36 months. The null hypothesis is
that the mean is less than or equal to 36 months. This test is one-tailed since the interest
is only in an increased lifetime. Notice that the direction of the inequality in the alternate
hypothesis points to the right, same as the area of the curve that forms the rejection
region.
Example 3:
A landlord who wants to lower heating bills in a large apartment complex is considering
using a new type of insulation. If the current average of the monthly heating bills is $78,
his hypotheses about heating costs with the new insulation are:
H0: µ ≥ 78
HA: µ < 78
This test is also a one-tailed test since the landlord is interested only in lowering heating
costs. Notice that the direction of the inequality in the alternate hypothesis points to the
left, same as the area of the curve that forms the rejection region.
Study Design:
After stating the hypotheses, the researcher’s next step is to design the study. In designing
the study, the researcher selects an appropriate statistical test, chooses a level of
significance, and formulates a plan for conducting the study..
Testing of hypothesis - large sample testParag Shah
Different type of test which are used for large sample has been included in this presentation. Steps for each test and a case study is included for concept clarity and practice.
Hybrid optimization of pumped hydro system and solar- Engr. Abdul-Azeez.pdffxintegritypublishin
Advancements in technology unveil a myriad of electrical and electronic breakthroughs geared towards efficiently harnessing limited resources to meet human energy demands. The optimization of hybrid solar PV panels and pumped hydro energy supply systems plays a pivotal role in utilizing natural resources effectively. This initiative not only benefits humanity but also fosters environmental sustainability. The study investigated the design optimization of these hybrid systems, focusing on understanding solar radiation patterns, identifying geographical influences on solar radiation, formulating a mathematical model for system optimization, and determining the optimal configuration of PV panels and pumped hydro storage. Through a comparative analysis approach and eight weeks of data collection, the study addressed key research questions related to solar radiation patterns and optimal system design. The findings highlighted regions with heightened solar radiation levels, showcasing substantial potential for power generation and emphasizing the system's efficiency. Optimizing system design significantly boosted power generation, promoted renewable energy utilization, and enhanced energy storage capacity. The study underscored the benefits of optimizing hybrid solar PV panels and pumped hydro energy supply systems for sustainable energy usage. Optimizing the design of solar PV panels and pumped hydro energy supply systems as examined across diverse climatic conditions in a developing country, not only enhances power generation but also improves the integration of renewable energy sources and boosts energy storage capacities, particularly beneficial for less economically prosperous regions. Additionally, the study provides valuable insights for advancing energy research in economically viable areas. Recommendations included conducting site-specific assessments, utilizing advanced modeling tools, implementing regular maintenance protocols, and enhancing communication among system components.
TECHNICAL TRAINING MANUAL GENERAL FAMILIARIZATION COURSEDuvanRamosGarzon1
AIRCRAFT GENERAL
The Single Aisle is the most advanced family aircraft in service today, with fly-by-wire flight controls.
The A318, A319, A320 and A321 are twin-engine subsonic medium range aircraft.
The family offers a choice of engines
Event Management System Vb Net Project Report.pdfKamal Acharya
In present era, the scopes of information technology growing with a very fast .We do not see any are untouched from this industry. The scope of information technology has become wider includes: Business and industry. Household Business, Communication, Education, Entertainment, Science, Medicine, Engineering, Distance Learning, Weather Forecasting. Carrier Searching and so on.
My project named “Event Management System” is software that store and maintained all events coordinated in college. It also helpful to print related reports. My project will help to record the events coordinated by faculties with their Name, Event subject, date & details in an efficient & effective ways.
In my system we have to make a system by which a user can record all events coordinated by a particular faculty. In our proposed system some more featured are added which differs it from the existing system such as security.
Immunizing Image Classifiers Against Localized Adversary Attacksgerogepatton
This paper addresses the vulnerability of deep learning models, particularly convolutional neural networks
(CNN)s, to adversarial attacks and presents a proactive training technique designed to counter them. We
introduce a novel volumization algorithm, which transforms 2D images into 3D volumetric representations.
When combined with 3D convolution and deep curriculum learning optimization (CLO), itsignificantly improves
the immunity of models against localized universal attacks by up to 40%. We evaluate our proposed approach
using contemporary CNN architectures and the modified Canadian Institute for Advanced Research (CIFAR-10
and CIFAR-100) and ImageNet Large Scale Visual Recognition Challenge (ILSVRC12) datasets, showcasing
accuracy improvements over previous techniques. The results indicate that the combination of the volumetric
input and curriculum learning holds significant promise for mitigating adversarial attacks without necessitating
adversary training.
Forklift Classes Overview by Intella PartsIntella Parts
Discover the different forklift classes and their specific applications. Learn how to choose the right forklift for your needs to ensure safety, efficiency, and compliance in your operations.
For more technical information, visit our website https://intellaparts.com
Overview of the fundamental roles in Hydropower generation and the components involved in wider Electrical Engineering.
This paper presents the design and construction of hydroelectric dams from the hydrologist’s survey of the valley before construction, all aspects and involved disciplines, fluid dynamics, structural engineering, generation and mains frequency regulation to the very transmission of power through the network in the United Kingdom.
Author: Robbie Edward Sayers
Collaborators and co editors: Charlie Sims and Connor Healey.
(C) 2024 Robbie E. Sayers
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This presentation is about the working procedure of Shahjalal Fertilizer Company Limited (SFCL). A Govt. owned Company of Bangladesh Chemical Industries Corporation under Ministry of Industries.
CFD Simulation of By-pass Flow in a HRSG module by R&R Consult.pptxR&R Consult
CFD analysis is incredibly effective at solving mysteries and improving the performance of complex systems!
Here's a great example: At a large natural gas-fired power plant, where they use waste heat to generate steam and energy, they were puzzled that their boiler wasn't producing as much steam as expected.
R&R and Tetra Engineering Group Inc. were asked to solve the issue with reduced steam production.
An inspection had shown that a significant amount of hot flue gas was bypassing the boiler tubes, where the heat was supposed to be transferred.
R&R Consult conducted a CFD analysis, which revealed that 6.3% of the flue gas was bypassing the boiler tubes without transferring heat. The analysis also showed that the flue gas was instead being directed along the sides of the boiler and between the modules that were supposed to capture the heat. This was the cause of the reduced performance.
Based on our results, Tetra Engineering installed covering plates to reduce the bypass flow. This improved the boiler's performance and increased electricity production.
It is always satisfying when we can help solve complex challenges like this. Do your systems also need a check-up or optimization? Give us a call!
Work done in cooperation with James Malloy and David Moelling from Tetra Engineering.
More examples of our work https://www.r-r-consult.dk/en/cases-en/
2. 2
Hypothesis Testing
• The general goal of a hypothesis test is to
rule out chance (sampling error) as a
plausible explanation for the results from a
research study.
• Hypothesis testing is a technique to help
determine whether a specific treatment
has an effect on the individuals in a
population.
3. 3
Hypothesis Testing
The hypothesis test is used to evaluate the
results from a research study in which
1. A sample is selected from the
population.
2. The treatment is administered to the
sample.
3. After treatment, the individuals in the
sample are measured.
4.
5. 5
Hypothesis Testing (cont.)
• If the individuals in the sample are
noticeably different from the individuals in
the original population, we have evidence
that the treatment has an effect.
• However, it is also possible that the
difference between the sample and the
population is simply sampling error
6.
7. 7
Hypothesis Testing (cont.)
• The purpose of the hypothesis test is to decide
between two explanations:
1. The difference between the sample and
the population can be explained by sampling
error (there does not appear to be a
treatment effect)
2. The difference between the sample and
the population is too large to be
explained by sampling error (there does
appear to be a treatment effect).
8.
9. 9
The Null Hypothesis, the Alpha Level, the
Critical Region, and the Test Statistic
• The following four steps outline the
process of hypothesis testing and
introduce some of the new terminology:
10. 10
Step 1
State the hypotheses and select an α
level. The null hypothesis, H0, always
states that the treatment has no effect (no
change, no difference). According to the
null hypothesis, the population mean after
treatment is the same is it was before
treatment. The α level establishes a
criterion, or "cut-off", for making a decision
about the null hypothesis. The alpha level
also determines the risk of a Type I error.
11.
12. 12
Step 2
Locate the critical region. The critical
region consists of outcomes that are very
unlikely to occur if the null hypothesis is
true. That is, the critical region is defined
by sample means that are almost
impossible to obtain if the treatment has
no effect. The phrase “almost impossible”
means that these samples have a
probability (p) that is less than the alpha
level.
13.
14. 14
Step 3
Compute the test statistic. The test
statistic (in this chapter a z-score) forms a
ratio comparing the obtained difference
between the sample mean and the
hypothesized population mean versus the
amount of difference we would expect
without any treatment effect (the standard
error).
15. 15
Step 4
A large value for the test statistic shows that the
obtained mean difference is more than would be
expected if there is no treatment effect. If it is
large enough to be in the critical region, we
conclude that the difference is significant or
that the treatment has a significant effect. In this
case we reject the null hypothesis. If the mean
difference is relatively small, then the test
statistic will have a low value. In this case, we
conclude that the evidence from the sample is
not sufficient, and the decision is fail to reject the
null hypothesis.
16.
17. 17
Errors in Hypothesis Tests
• Just because the sample mean (following
treatment) is different from the original
population mean does not necessarily
indicate that the treatment has caused a
change.
• You should recall that there usually is
some discrepancy between a sample
mean and the population mean simply as
a result of sampling error.
18. 18
Errors in Hypothesis Tests (cont.)
• Because the hypothesis test relies on
sample data, and because sample data
are not completely reliable, there is always
the risk that misleading data will cause the
hypothesis test to reach a wrong
conclusion.
• Two types of error are possible.
19. 19
Type I Errors
• A Type I error occurs when the sample data appear to
show a treatment effect when, in fact, there is none.
• In this case the researcher will reject the null
hypothesis and falsely conclude that the treatment has
an effect.
• Type I errors are caused by unusual, unrepresentative
samples. Just by chance the researcher selects an
extreme sample with the result that the sample falls in
the critical region even though the treatment has no
effect.
• The hypothesis test is structured so that Type I errors
are very unlikely; specifically, the probability of a Type I
error is equal to the alpha level.
20. 20
Type II Errors
• A Type II error occurs when the sample does
not appear to have been affected by the
treatment when, in fact, the treatment does have
an effect.
• In this case, the researcher will fail to reject the
null hypothesis and falsely conclude that the
treatment does not have an effect.
• Type II errors are commonly the result of a very
small treatment effect. Although the treatment
does have an effect, it is not large enough to
show up in the research study.
21.
22. 22
Directional Tests
• When a research study predicts a specific
direction for the treatment effect (increase
or decrease), it is possible to incorporate
the directional prediction into the
hypothesis test.
• The result is called a directional test or a
one-tailed test. A directional test includes
the directional prediction in the statement
of the hypotheses and in the location of
the critical region.
23. 23
Directional Tests (cont.)
• For example, if the original population has a
mean of μ = 80 and the treatment is predicted to
increase the scores, then the null hypothesis
would state that after treatment:
H0: μ < 80 (there is no increase)
• In this case, the entire critical region would be
located in the right-hand tail of the distribution
because large values for M would demonstrate
that there is an increase and would tend to reject
the null hypothesis.
24. 24
Measuring Effect Size
• A hypothesis test evaluates the statistical
significance of the results from a research study.
• That is, the test determines whether or not it is
likely that the obtained sample mean occurred
without any contribution from a treatment effect.
• The hypothesis test is influenced not only by the
size of the treatment effect but also by the size
of the sample.
• Thus, even a very small effect can be significant
if it is observed in a very large sample.
25. 25
Measuring Effect Size
• Because a significant effect does not necessarily
mean a large effect, it is recommended that the
hypothesis test be accompanied by a measure
of the effect size.
• We use Cohen=s d as a standardized measure
of effect size.
• Much like a z-score, Cohen=s d measures the
size of the mean difference in terms of the
standard deviation.
26.
27. 27
Power of a Hypothesis Test
• The power of a hypothesis test is defined
is the probability that the test will reject the
null hypothesis when the treatment does
have an effect.
• The power of a test depends on a variety
of factors including the size of the
treatment effect and the size of the
sample.