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Chapter 11: Goodness-of-Fit and Contingency Tables
11.2: Contingency Tables
An introduction to logistic regression for physicians, public health students and other health workers. Logistic regression is a way to look at effect of a numeric independent variable on a binary (yes-no) dependent variable. For example, you can analyze or model the effect of birth weight on survival.
Please Subscribe to this Channel for more solutions and lectures
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Chapter 11: Goodness-of-Fit and Contingency Tables
11.2: Contingency Tables
An introduction to logistic regression for physicians, public health students and other health workers. Logistic regression is a way to look at effect of a numeric independent variable on a binary (yes-no) dependent variable. For example, you can analyze or model the effect of birth weight on survival.
Today’s overwhelming number of techniques applicable to data analysis makes it extremely difficult to define the most beneficial approach while considering all the significant variables.
The analysis of variance has been studied from several approaches, the most common of which uses a linear model that relates the response to the treatments and blocks. Note that the model is linear in parameters but may be nonlinear across factor levels. Interpretation is easy when data is balanced across factors but much deeper understanding is needed for unbalanced data.
Analysis of variance (ANOVA) is a collection of statistical models and their associated estimation procedures (such as the "variation" among and between groups) used to analyze the differences among means. ANOVA was developed by the statistician Ronald Fisher. ANOVA is based on the law of total variance, where the observed variance in a particular variable is partitioned into components attributable to different sources of variation. In its simplest form, ANOVA provides a statistical test of whether two or more population means are equal, and therefore generalizes the t-test beyond two means. In other words, the ANOVA is used to test the difference between two or more means.Analysis of variance (ANOVA) is an analysis tool used in statistics that splits an observed aggregate variability found inside a data set into two parts: systematic factors and random factors. The systematic factors have a statistical influence on the given data set, while the random factors do not. Analysts use the ANOVA test to determine the influence that independent variables have on the dependent variable in a regression study.
Sir Ronald Fisher pioneered the development of ANOVA for analyzing results of agricultural experiments.1 Today, ANOVA is included in almost every statistical package, which makes it accessible to investigators in all experimental sciences. It is easy to input a data set and run a simple ANOVA, but it is challenging to choose the appropriate ANOVA for different experimental designs, to examine whether data adhere to the modeling assumptions, and to interpret the results correctly. The purpose of this report, together with the next 2 articles in the Statistical Primer for Cardiovascular Research series, is to enhance understanding of ANVOA and to promote its successful use in experimental cardiovascular research. My colleagues and I attempt to accomplish those goals through examples and explanation, while keeping within reason the burden of notation, technical jargon, and mathematical equations.
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
Today’s overwhelming number of techniques applicable to data analysis makes it extremely difficult to define the most beneficial approach while considering all the significant variables.
The analysis of variance has been studied from several approaches, the most common of which uses a linear model that relates the response to the treatments and blocks. Note that the model is linear in parameters but may be nonlinear across factor levels. Interpretation is easy when data is balanced across factors but much deeper understanding is needed for unbalanced data.
Analysis of variance (ANOVA) is a collection of statistical models and their associated estimation procedures (such as the "variation" among and between groups) used to analyze the differences among means. ANOVA was developed by the statistician Ronald Fisher. ANOVA is based on the law of total variance, where the observed variance in a particular variable is partitioned into components attributable to different sources of variation. In its simplest form, ANOVA provides a statistical test of whether two or more population means are equal, and therefore generalizes the t-test beyond two means. In other words, the ANOVA is used to test the difference between two or more means.Analysis of variance (ANOVA) is an analysis tool used in statistics that splits an observed aggregate variability found inside a data set into two parts: systematic factors and random factors. The systematic factors have a statistical influence on the given data set, while the random factors do not. Analysts use the ANOVA test to determine the influence that independent variables have on the dependent variable in a regression study.
Sir Ronald Fisher pioneered the development of ANOVA for analyzing results of agricultural experiments.1 Today, ANOVA is included in almost every statistical package, which makes it accessible to investigators in all experimental sciences. It is easy to input a data set and run a simple ANOVA, but it is challenging to choose the appropriate ANOVA for different experimental designs, to examine whether data adhere to the modeling assumptions, and to interpret the results correctly. The purpose of this report, together with the next 2 articles in the Statistical Primer for Cardiovascular Research series, is to enhance understanding of ANVOA and to promote its successful use in experimental cardiovascular research. My colleagues and I attempt to accomplish those goals through examples and explanation, while keeping within reason the burden of notation, technical jargon, and mathematical equations.
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
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
CHI SQUARE ANALYSIS.pptx - Advanced Business Statisticsindumathi967565
The chi-square (χ2) statistic is a tool used to assess how well a model fits real-world observations. A chi-square statistic can only be computed with random, unprocessed, mutually exclusive data that is taken from a sufficiently large sample of independent variables. It helps to study the discrepancies between the observed results and expected results of the study.
A chi-squared test is a statistical hypothesis test that is valid to perform when the test statistic is chi-squared distributed under the null hypothesis, specifically Pearson's chi-squared test and variants
differences between the observed values
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Marvin neemt je in deze presentatie mee in de voordelen van non-endemic advertising op retail media netwerken. Hij brengt ook de uitdagingen in beeld die de markt op dit moment heeft op het gebied van retail media voor niet-leveranciers.
Retail media wordt gezien als het nieuwe advertising-medium en ook mediabureaus richten massaal retail media-afdelingen op. Merken die niet in de betreffende winkel liggen staan ook nog niet in de rij om op de retail media netwerken te adverteren. Marvin belicht de uitdagingen die er zijn om echt aansluiting te vinden op die markt van non-endemic advertising.
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What is Enterprise Excellence?
Enterprise Excellence is a holistic approach that's aimed at achieving world-class performance across all aspects of the organization.
What might I learn?
A way to engage all in creating Inclusive Excellence. Lessons from the US military and their parallels to the story of Harry Potter. How belt systems and CI teams can destroy inclusive practices. How leadership language invites people to the party. There are three things leaders can do to engage everyone every day: maximizing psychological safety to create environments where folks learn, contribute, and challenge the status quo.
Who might benefit? Anyone and everyone leading folks from the shop floor to top floor.
Dr. William Harvey is a seasoned Operations Leader with extensive experience in chemical processing, manufacturing, and operations management. At Michelman, he currently oversees multiple sites, leading teams in strategic planning and coaching/practicing continuous improvement. William is set to start his eighth year of teaching at the University of Cincinnati where he teaches marketing, finance, and management. William holds various certifications in change management, quality, leadership, operational excellence, team building, and DiSC, among others.
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Sustainability has become an increasingly critical topic as the world recognizes the need to protect our planet and its resources for future generations. Sustainability means meeting our current needs without compromising the ability of future generations to meet theirs. It involves long-term planning and consideration of the consequences of our actions. The goal is to create strategies that ensure the long-term viability of People, Planet, and Profit.
Leading companies such as Nike, Toyota, and Siemens are prioritizing sustainable innovation in their business models, setting an example for others to follow. In this Sustainability training presentation, you will learn key concepts, principles, and practices of sustainability applicable across industries. This training aims to create awareness and educate employees, senior executives, consultants, and other key stakeholders, including investors, policymakers, and supply chain partners, on the importance and implementation of sustainability.
LEARNING OBJECTIVES
1. Develop a comprehensive understanding of the fundamental principles and concepts that form the foundation of sustainability within corporate environments.
2. Explore the sustainability implementation model, focusing on effective measures and reporting strategies to track and communicate sustainability efforts.
3. Identify and define best practices and critical success factors essential for achieving sustainability goals within organizations.
CONTENTS
1. Introduction and Key Concepts of Sustainability
2. Principles and Practices of Sustainability
3. Measures and Reporting in Sustainability
4. Sustainability Implementation & Best Practices
To download the complete presentation, visit: https://www.oeconsulting.com.sg/training-presentations
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7. Degree of freedom
Goodness of Fit
Independent Variables
&
Homogeneity of
proportion
Number of outcomes – 1
( No of rows – 1)( No of Columns -1)
( r - 1 )( c - 1 )
9. Goodness of fit
Test of the consistency between a hypothetical
and a sample distribution.
Example : Coin is tossed 50 times
Null hypothesis is that it’s
25 times heads and 25 times tails
( expected observation E )
10. Event Frequency
Head 28
Tail 22
Total 50
Observed Values is,
Event O E O - E ( O – E ) ² ( O – E ) ²
E
Head 28 25 3 9 0.36
Tail 22 25 -3 9 0.36
Total 0.72
Solution :
= 0.72 Degree of freedom is = (outcomes – 1) = 2 – 1 = 1
Critical value is 3.841 for df 1 at 0.05
Since 0.72 < 3.841 , our null hypothesis is acceptable which means our coin is fair
11. Test of Independence
To ascertain whether there is any dependency
relationship between the two attributes.
Example: A company introduced new drug B to
cure malaria. It is being compared with
existing drug A. Data is shown in next slide.
We need to find whether the new drug B is
more effective in curing malaria.
12. Helped
(C1)
Harmed
(C2)
No effect
(C3)
Total
Drug A
(R1)
44 10 26 80
Drug B
(R2)
52 10 18 80
Total 96 20 44 160
Solution :
O E O - E ( O-E ) ² ( O – E ) ²
E
R1C1 44 48 -4 16 0.333
R1C2 10 10 0 0 0
R1C3 26 22 4 16 0.727
R2C1 52 48 4 16 0.333
R2C2 10 10 0 0 0
R2C3 18 22 -4 16 0.727
Total = 2.12
13. We setup two hypothesis,
H0 :There is no difference in the effectiveness of
the two drugs
H1 : There is difference in the effectiveness of
the two drugs
Degree of freedom = (r-1)(c-1) = (2-1)(3-1) = 2
Critical value at 0.05 for df 2 is 5.991,
and 2.12 < 5.991
So, there is no difference in the effectiveness of
the two drugs
14. Alternative method:
Helped Harmed No effect Total
Drug A 44
(a)
10
(b)
26
(c)
80
(a+b+c)
Drug B 52
(d)
10
(e)
18
(f)
80
(d+e+f)
Total 96
(a+d)
20
(b+e)
44
(c+f)
160
(N)
Its 2x3 table so for calculating chi-square we use formula:
= N a² + b² + c² + N d² + e² + f² - N
a+b+c a+d b+e c+f d+e+f a+d b+e c+f
= 160 44² + 10² + 26² + 160 52² + 10² + 18² - 160
80 96 20 44 80 96 20 44
= 2.12
Both methods give same value for which is 2.12
15. Test of homogeneity
Test indicates whether the proportions of
elements belonging to different groups in two
or more populations are similar or not.
Example : A company has two factories in Delhi
and Mumbai. It is interested to know whether
its workers are satisfied with their jobs or not
at both places.
16. Delhi Mumbai Total
Fully satisfied 50 70 120
Moderately satisfied 90 110 200
Moderately dissatisfied 160 130 290
Fully dissatisfied 200 190 390
Total 500 500 1000
We setup two hypothesis,
H0 :The proportions of workers who belong to the four job satisfaction categories are
the same in both Delhi and Mumbai
H1 : The proportions of workers who belong to the four job satisfaction categories are
not the same in both Delhi and Mumbai
Degrees of freedom = (r-1)(c-1) = (4-1)(2-1) = 3
Critical value for 3 df at 0.05 is 7.815
17. Delhi Mumbai
O E O E
Fully satisfied 50 60 70 60
Moderately satisfied 90 100 110 100
Moderately dissatisfied 160 145 130 145
Fully dissatisfied 200 195 190 195
= (50-60) ² + (90-100) ² + (160-145) ² + (200-195) ² + (70-60) ² + (110-100) ² + (130-145) ² + (190-195) ²
60 100 145 195 60 100 145 195
= 1.667 + 1.000 + 1.552 + 0.128 + 1.667 + 1.000 + 1.522 + 0.128
= 8.694
Since the value 8.694 > 7.815
we therefore, reject the null hypothesis and conclude that the distribution of job
satisfaction for workers in Delhi and Mumbai is not homogeneous
18. IMPORTANT CHARACTERISTICS OF A CHI SQUARE TEST
This test (as a non-parametric test) is based on frequencies
and not on the parameters like mean and standard
deviation.
The test is used for testing the hypothesis and is not useful
for estimation.
This test can also be applied to a complex contingency
table with several classes and as such is a very useful test in
research work.
This test is an important non-parametric test as no rigid
assumptions are necessary in regard to the type of
population, no need of parameter values and relatively
less mathematical details are involved.