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.
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
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.
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
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.
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.
10 test of hypothesis
,
univariate statistics
,
hypothessignificance levelis
,
null hypothesis
,
region of rejection
,
type i and type ii errors
,
t-distribution
,
choosing the appropriate statistical technique
,
degrees of freedom
,
univariate hypothesis test utilizing the t-distrib
This is a lecture that I gave to a Principles of Epidemiology MPH class. It takes a critical look at the use of p-values to judge the strength of evidence, and offers more holistic, informative approaches to interpreting statistical findings such as measures of effect size and confidence intervals.
A chi-squared test (χ2) is basically a data analysis on the basis of observations of a random set of variables. Usually, it is a comparison of two statistical data sets. This test was introduced by Karl Pearson in 1900 for categorical data analysis and distribution. So, it was mentioned as Pearson’s chi-squared test.
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.
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.
10 test of hypothesis
,
univariate statistics
,
hypothessignificance levelis
,
null hypothesis
,
region of rejection
,
type i and type ii errors
,
t-distribution
,
choosing the appropriate statistical technique
,
degrees of freedom
,
univariate hypothesis test utilizing the t-distrib
This is a lecture that I gave to a Principles of Epidemiology MPH class. It takes a critical look at the use of p-values to judge the strength of evidence, and offers more holistic, informative approaches to interpreting statistical findings such as measures of effect size and confidence intervals.
A chi-squared test (χ2) is basically a data analysis on the basis of observations of a random set of variables. Usually, it is a comparison of two statistical data sets. This test was introduced by Karl Pearson in 1900 for categorical data analysis and distribution. So, it was mentioned as Pearson’s chi-squared test.
tests of significance in periodontics aspect, tests of significance with common examples, tests in brief, null hypothesis, parametric vs non parametric tests, seminar by sai lakshmi
Objectives:
Understand the elements of hypothesis testing for testing a population mean (for large sample):
Identify appropriate null and alternative hypotheses
Select a level of significance
Compute the value of test statistic
Locate a critical or rejection region
Interpret the appropriate conclusion
Inferential Statistics:
It consists of methods for measuring and drawing conclusion about a population based on information obtained from a sample
Estimation (Point & Interval Estimation)
Significance/ Hypothesis Testing
Hypothesis Testing :
Tentative assumption related to certain phenomenon which a researcher want to verify
Allows us to use sample data to test a claim about a population, such as testing whether a population mean equals same number.
Allows us to use sample data to test a claim about a population, such as testing whether a population mean equals same number.
Hypothesis:
Hypothesis: An informed guess or a conjecture about a population parameter, which may or may not be true. It tests whether a population parameter is less than, greater than, or equal to a specified value (hypothetical).
A statement of belief used in the evaluation of a population parameter such as the mean of a population.
Example:
Frequent users of narcotics have a mean anger expression score higher than for non-users.
Types of hypotheses:
There are two types of hypotheses.
Null hypothesis (H0):
A claim that there is no difference between the population parameter and the hypothesized value. For example, the mean of a population equals the hypothesized value .
Alternative or Researcher hypothesis (Ha or H1):
A claim that disagrees with the null hypothesis. For example, the mean of a population is not equal to the hypothesized value.
One tailed hypotheses are directional.
Two-tailed hypothesis is otherwise non-directional.
Underlying assumptions for testing of hypothesis for population mean.
The sample has been randomly selected from the population or process.
The underlying population is normally distributed (or if not normally distributed, then n is large say greater than or equal to 30).
Population variance (2) either known or sample variance (s2) assumed to be approximately equal to population variance, when n is large.
Basic Elements of Testing Hypothesis:
Null Hypothesis
Alternative Hypothesis (Researcher Hypothesis)
Choice of appropriate level of significance
Assumptions
Test Statistic (Formula): Application of sample results in the formula to calculate the value of test statistic use for decision purpose.
Rejection Region (Critical Region): Based on alternative hypothesis and level of significance.
Conclusion: If the calculated value of the test statistic falls in the rejection region, reject H0 in favor of Ha, otherwise fail to reject H0.
Steps of Hypothesis Testing:
Step 1: State the hypothesis and identify the claim.
Step 2: State the Level of Significance.
Step 3: Compute the test value (Test Statistics).
D. G. Mayo (Virginia Tech) "Error Statistical Control: Forfeit at your Peril" presented May 23 at the session on "The Philosophy of Statistics: Bayesianism, Frequentism and the Nature of Inference," 2015 APS Annual Convention in NYC.
This document contain all topics of research methodology of module-3 according to the syllabus of BPUT odisha. The document is done for the PG and PHD students who are doing research.
Francesca Gottschalk - How can education support child empowerment.pptxEduSkills OECD
Francesca Gottschalk from the OECD’s Centre for Educational Research and Innovation presents at the Ask an Expert Webinar: How can education support child empowerment?
Model Attribute Check Company Auto PropertyCeline George
In Odoo, the multi-company feature allows you to manage multiple companies within a single Odoo database instance. Each company can have its own configurations while still sharing common resources such as products, customers, and suppliers.
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Macroeconomics- Movie Location
This will be used as part of your Personal Professional Portfolio once graded.
Objective:
Prepare a presentation or a paper using research, basic comparative analysis, data organization and application of economic information. You will make an informed assessment of an economic climate outside of the United States to accomplish an entertainment industry objective.
June 3, 2024 Anti-Semitism Letter Sent to MIT President Kornbluth and MIT Cor...Levi Shapiro
Letter from the Congress of the United States regarding Anti-Semitism sent June 3rd to MIT President Sally Kornbluth, MIT Corp Chair, Mark Gorenberg
Dear Dr. Kornbluth and Mr. Gorenberg,
The US House of Representatives is deeply concerned by ongoing and pervasive acts of antisemitic
harassment and intimidation at the Massachusetts Institute of Technology (MIT). Failing to act decisively to ensure a safe learning environment for all students would be a grave dereliction of your responsibilities as President of MIT and Chair of the MIT Corporation.
This Congress will not stand idly by and allow an environment hostile to Jewish students to persist. The House believes that your institution is in violation of Title VI of the Civil Rights Act, and the inability or
unwillingness to rectify this violation through action requires accountability.
Postsecondary education is a unique opportunity for students to learn and have their ideas and beliefs challenged. However, universities receiving hundreds of millions of federal funds annually have denied
students that opportunity and have been hijacked to become venues for the promotion of terrorism, antisemitic harassment and intimidation, unlawful encampments, and in some cases, assaults and riots.
The House of Representatives will not countenance the use of federal funds to indoctrinate students into hateful, antisemitic, anti-American supporters of terrorism. Investigations into campus antisemitism by the Committee on Education and the Workforce and the Committee on Ways and Means have been expanded into a Congress-wide probe across all relevant jurisdictions to address this national crisis. The undersigned Committees will conduct oversight into the use of federal funds at MIT and its learning environment under authorities granted to each Committee.
• The Committee on Education and the Workforce has been investigating your institution since December 7, 2023. The Committee has broad jurisdiction over postsecondary education, including its compliance with Title VI of the Civil Rights Act, campus safety concerns over disruptions to the learning environment, and the awarding of federal student aid under the Higher Education Act.
• The Committee on Oversight and Accountability is investigating the sources of funding and other support flowing to groups espousing pro-Hamas propaganda and engaged in antisemitic harassment and intimidation of students. The Committee on Oversight and Accountability is the principal oversight committee of the US House of Representatives and has broad authority to investigate “any matter” at “any time” under House Rule X.
• The Committee on Ways and Means has been investigating several universities since November 15, 2023, when the Committee held a hearing entitled From Ivory Towers to Dark Corners: Investigating the Nexus Between Antisemitism, Tax-Exempt Universities, and Terror Financing. The Committee followed the hearing with letters to those institutions on January 10, 202
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1.4 modern child centered education - mahatma gandhi-2.pptx
ch04.ppt
1.
2.
3.
4. 4-1 Statistical Inference
• The field of statistical inference consists of those
methods used to make decisions or draw
conclusions about a population.
•These methods utilize the information contained in
a sample from the population in drawing
conclusions.
9. 4-3 Hypothesis Testing
We like to think of statistical hypothesis testing as the
data analysis stage of a comparative experiment,
in which the engineer is interested, for example, in
comparing the mean of a population to a specified
value (e.g. mean pull strength).
4-3.1 Statistical Hypotheses
10. 4-3 Hypothesis Testing
For example, suppose that we are interested in the
burning rate of a solid propellant used to power aircrew
escape systems.
• Now burning rate is a random variable that can be
described by a probability distribution.
• Suppose that our interest focuses on the mean burning
rate (a parameter of this distribution).
• Specifically, we are interested in deciding whether or
not the mean burning rate is 50 centimeters per second.
4-3.1 Statistical Hypotheses
11. 4-3 Hypothesis Testing
4-3.1 Statistical Hypotheses
Two-sided Alternative Hypothesis
One-sided Alternative Hypotheses
12. 4-3 Hypothesis Testing
4-3.1 Statistical Hypotheses
Test of a Hypothesis
• A procedure leading to a decision about a particular
hypothesis
• Hypothesis-testing procedures rely on using the information
in a random sample from the population of interest.
• If this information is consistent with the hypothesis, then we
will conclude that the hypothesis is true; if this information is
inconsistent with the hypothesis, we will conclude that the
hypothesis is false.
15. 4-3 Hypothesis Testing
4-3.2 Testing Statistical Hypotheses
Sometimes the type I error probability is called the
significance level, or the -error, or the size of the test.
21. 4-3 Hypothesis Testing
4-3.2 Testing Statistical Hypotheses
• The power is computed as 1 - b, and power can be interpreted as
the probability of correctly rejecting a false null hypothesis. We
often compare statistical tests by comparing their power properties.
• For example, consider the propellant burning rate problem when
we are testing H 0 : m = 50 centimeters per second against H 1 : m not
equal 50 centimeters per second . Suppose that the true value of the
mean is m = 52. When n = 10, we found that b = 0.2643, so the
power of this test is 1 - b = 1 - 0.2643 = 0.7357 when m = 52.
25. 4-4 Inference on the Mean of a Population,
Variance Known
Assumptions
26. 4-4 Inference on the Mean of a Population,
Variance Known
4-4.1 Hypothesis Testing on the Mean
We wish to test:
The test statistic is:
27. 4-4 Inference on the Mean of a Population,
Variance Known
4-4.1 Hypothesis Testing on the Mean
Reject H0 if the observed value of the test statistic z0 is
either:
or
Fail to reject H0 if
28. 4-4 Inference on the Mean of a Population,
Variance Known
4-4.1 Hypothesis Testing on the Mean
29. 4-4 Inference on the Mean of a Population,
Variance Known
4-4.1 Hypothesis Testing on the Mean
30. 4-4 Inference on the Mean of a Population,
Variance Known
4-4.2 Type II Error and Choice of Sample Size
Finding The Probability of Type II Error b
31. 4-4 Inference on the Mean of a Population,
Variance Known
4-4.2 Type II Error and Choice of Sample Size
Sample Size Formulas
32. 4-4 Inference on the Mean of a Population,
Variance Known
4-4.2 Type II Error and Choice of Sample Size
Sample Size Formulas
33. 4-4 Inference on the Mean of a Population,
Variance Known
4-4.2 Type II Error and Choice of Sample Size
34. 4-4 Inference on the Mean of a Population,
Variance Known
4-4.2 Type II Error and Choice of Sample Size
35. 4-4 Inference on the Mean of a Population,
Variance Known
4-4.3 Large Sample Test
In general, if n 30, the sample variance s2
will be close to σ2 for most samples, and so s
can be substituted for σ in the test procedures
with little harmful effect.
36. 4-4 Inference on the Mean of a Population,
Variance Known
4-4.4 Some Practical Comments on Hypothesis
Testing
The Seven-Step Procedure
Only three steps are really required:
37. 4-4 Inference on the Mean of a Population,
Variance Known
4-4.4 Some Practical Comments on Hypothesis
Testing
Statistical versus Practical Significance
38. 4-4 Inference on the Mean of a Population,
Variance Known
4-4.4 Some Practical Comments on Hypothesis
Testing
Statistical versus Practical Significance
39. 4-4 Inference on the Mean of a Population,
Variance Known
4-4.5 Confidence Interval on the Mean
Two-sided confidence interval:
One-sided confidence intervals:
Confidence coefficient:
40. 4-4 Inference on the Mean of a Population,
Variance Known
4-4.5 Confidence Interval on the Mean
41. 4-4 Inference on the Mean of a Population,
Variance Known
4-4.6 Confidence Interval on the Mean
42. 4-4 Inference on the Mean of a Population,
Variance Known
4-4.5 Confidence Interval on the Mean
43. 4-4 Inference on the Mean of a Population,
Variance Known
4-4.5 Confidence Interval on the Mean
Relationship between Tests of Hypotheses and
Confidence Intervals
If [l,u] is a 100(1 - ) percent confidence interval for the
parameter, then the test of significance level of the
hypothesis
will lead to rejection of H0 if and only if the hypothesized
value is not in the 100(1 - ) percent confidence interval
[l, u].
44. 4-4 Inference on the Mean of a Population,
Variance Known
4-4.5 Confidence Interval on the Mean
Confidence Level and Precision of Estimation
The length of the two-sided 95% confidence interval is
whereas the length of the two-sided 99% confidence
interval is
45. 4-4 Inference on the Mean of a Population,
Variance Known
4-4.5 Confidence Interval on the Mean
Choice of Sample Size
46. 4-4 Inference on the Mean of a Population,
Variance Known
4-4.5 Confidence Interval on the Mean
Choice of Sample Size
47. 4-4 Inference on the Mean of a Population,
Variance Known
4-4.5 Confidence Interval on the Mean
Choice of Sample Size
48. 4-4 Inference on the Mean of a Population,
Variance Known
4-4.5 Confidence Interval on the Mean
One-Sided Confidence Bounds
49. 4-4 Inference on the Mean of a Population,
Variance Known
4-4.6 General Method for Deriving a Confidence
Interval
50. 4-5 Inference on the Mean of a Population,
Variance Unknown
4-5.1 Hypothesis Testing on the Mean
51. 4-5 Inference on the Mean of a Population,
Variance Unknown
4-5.1 Hypothesis Testing on the Mean
52. 4-5 Inference on the Mean of a Population,
Variance Unknown
4-5.1 Hypothesis Testing on the Mean
53. 4-5 Inference on the Mean of a Population,
Variance Unknown
4-5.1 Hypothesis Testing on the Mean
Calculating the P-value
54. 4-5 Inference on the Mean of a Population,
Variance Unknown
4-5.1 Hypothesis Testing on the Mean
55. 4-5 Inference on the Mean of a Population,
Variance Unknown
4-5.1 Hypothesis Testing on the Mean
56. 4-5 Inference on the Mean of a Population,
Variance Unknown
4-5.1 Hypothesis Testing on the Mean
57. 4-5 Inference on the Mean of a Population,
Variance Unknown
4-5.1 Hypothesis Testing on the Mean
58. 4-5 Inference on the Mean of a Population,
Variance Unknown
4-5.2 Type II Error and Choice of Sample Size
Fortunately, this unpleasant task has already been done,
and the results are summarized in a series of graphs in
Appendix A Charts Va, Vb, Vc, and Vd that plot for the
t-test against a parameter d for various sample sizes n.
59. 4-5 Inference on the Mean of a Population,
Variance Unknown
4-5.2 Type II Error and Choice of Sample Size
These graphics are called operating characteristic
(or OC) curves. Curves are provided for two-sided
alternatives on Charts Va and Vb. The abscissa scale
factor d on these charts is defined as
60. 4-5 Inference on the Mean of a Population,
Variance Unknown
4-5.3 Confidence Interval on the Mean
61. 4-5 Inference on the Mean of a Population,
Variance Unknown
4-5.3 Confidence Interval on the Mean
62. 4-5 Inference on the Mean of a Population,
Variance Unknown
4-5.4 Confidence Interval on the Mean
63. 4-6 Inference on the Variance of a
Normal Population
4-6.1 Hypothesis Testing on the Variance of a
Normal Population
64. 4-6 Inference on the Variance of a
Normal Population
4-6.1 Hypothesis Testing on the Variance of a
Normal Population
65. 4-6 Inference on the Variance of a
Normal Population
4-6.1 Hypothesis Testing on the Variance of a
Normal Population
66. 4-6 Inference on the Variance of a
Normal Population
4-6.1 Hypothesis Testing on the Variance of a
Normal Population
67. 4-6 Inference on the Variance of a
Normal Population
4-6.1 Hypothesis Testing on the Variance of a
Normal Population
68. 4-6 Inference on the Variance of a
Normal Population
4-6.1 Hypothesis Testing on the Variance of a
Normal Population
69. 4-6 Inference on the Variance of a
Normal Population
4-6.2 Confidence Interval on the Variance of a
Normal Population
70. 4-7 Inference on Population Proportion
4-7.1 Hypothesis Testing on a Binomial Proportion
We will consider testing:
71. 4-7 Inference on Population Proportion
4-7.1 Hypothesis Testing on a Binomial Proportion
72. 4-7 Inference on Population Proportion
4-7.1 Hypothesis Testing on a Binomial Proportion
73. 4-7 Inference on Population Proportion
4-7.1 Hypothesis Testing on a Binomial Proportion
74. 4-7 Inference on Population Proportion
4-7.2 Type II Error and Choice of Sample Size
75. 4-7 Inference on Population Proportion
4-7.2 Type II Error and Choice of Sample Size
76. 4-7 Inference on Population Proportion
4-7.3 Confidence Interval on a Binomial Proportion
77. 4-7 Inference on Population Proportion
4-7.3 Confidence Interval on a Binomial Proportion
78. 4-7 Inference on Population Proportion
4-7.3 Confidence Interval on a Binomial Proportion
Choice of Sample Size
79. 4-8 Other Interval Estimates for a
Single Sample
4-8.1 Prediction Interval
80. 4-8 Other Interval Estimates for a
Single Sample
4-8.2 Tolerance Intervals for a Normal Distribution
81. 4-10 Testing for Goodness of Fit
• So far, we have assumed the population or probability
distribution for a particular problem is known.
• There are many instances where the underlying
distribution is not known, and we wish to test a particular
distribution.
• Use a goodness-of-fit test procedure based on the chi-
square distribution.