What is the significance of p value while reporting statistical analysis. Is there an alternate approach for Fisher, if so what is that approach. These are some of the issues addressed here.
Stephen Senn slides:"‘Repligate’: reproducibility in statistical studies. What does it mean and in what sense does it matter?" presented May 23 at the session on "The Philosophy of Statistics: Bayesianism, Frequentism and the Nature of Inference"," at the 2015 APS Annual Convention in NYC
"The Statistical Replication Crisis: Paradoxes and Scapegoats”jemille6
D. G. Mayo LSE Popper talk, May 10, 2016.
Abstract: Mounting failures of replication in the social and biological sciences give a practical spin to statistical foundations in the form of the question: How can we attain reliability when Big Data methods make illicit cherry-picking and significance seeking so easy? Researchers, professional societies, and journals are increasingly getting serious about methodological reforms to restore scientific integrity – some are quite welcome (e.g., preregistration), while others are quite radical. Recently, the American Statistical Association convened members from differing tribes of frequentists, Bayesians, and likelihoodists to codify misuses of P-values. Largely overlooked are the philosophical presuppositions of both criticisms and proposed reforms. Paradoxically, alternative replacement methods may enable rather than reveal illicit inferences due to cherry-picking, multiple testing, and other biasing selection effects. Popular appeals to “diagnostic testing” that aim to improve replication rates may (unintentionally) permit the howlers and cookbook statistics we are at pains to root out. Without a better understanding of the philosophical issues, we can expect the latest reforms to fail.
Stephen Senn slides:"‘Repligate’: reproducibility in statistical studies. What does it mean and in what sense does it matter?" presented May 23 at the session on "The Philosophy of Statistics: Bayesianism, Frequentism and the Nature of Inference"," at the 2015 APS Annual Convention in NYC
"The Statistical Replication Crisis: Paradoxes and Scapegoats”jemille6
D. G. Mayo LSE Popper talk, May 10, 2016.
Abstract: Mounting failures of replication in the social and biological sciences give a practical spin to statistical foundations in the form of the question: How can we attain reliability when Big Data methods make illicit cherry-picking and significance seeking so easy? Researchers, professional societies, and journals are increasingly getting serious about methodological reforms to restore scientific integrity – some are quite welcome (e.g., preregistration), while others are quite radical. Recently, the American Statistical Association convened members from differing tribes of frequentists, Bayesians, and likelihoodists to codify misuses of P-values. Largely overlooked are the philosophical presuppositions of both criticisms and proposed reforms. Paradoxically, alternative replacement methods may enable rather than reveal illicit inferences due to cherry-picking, multiple testing, and other biasing selection effects. Popular appeals to “diagnostic testing” that aim to improve replication rates may (unintentionally) permit the howlers and cookbook statistics we are at pains to root out. Without a better understanding of the philosophical issues, we can expect the latest reforms to fail.
The number that divides the normal distribution into region where we will reject the null hypothesis and the region where we fail to reject the null hypothesis. For normal distribution Z at 5% level of significance (z= plus-minus 1.96) is often referred to as the critical value (or critical region).
These slides were presented on November 22 2016 during the Annual Julius Symposium, organised by the Julius Center for Health Sciences and Primary Care, University Medical Hospital Utrecht.
Only a few months ago, the American Statistical Association authoritatively issued an official statement on significance and p-values (American Statistician, 2016, 70:2, 129-133), claiming that the p-value is: “commonly misused and misinterpreted.”
In this presentation I focus on the principles of the ASA statement.
Deborah G. Mayo: Is the Philosophy of Probabilism an Obstacle to Statistical Fraud Busting?
Presentation slides for: Revisiting the Foundations of Statistics in the Era of Big Data: Scaling Up to Meet the Challenge[*] at the Boston Colloquium for Philosophy of Science (Feb 21, 2014).
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.
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.
The number that divides the normal distribution into region where we will reject the null hypothesis and the region where we fail to reject the null hypothesis. For normal distribution Z at 5% level of significance (z= plus-minus 1.96) is often referred to as the critical value (or critical region).
These slides were presented on November 22 2016 during the Annual Julius Symposium, organised by the Julius Center for Health Sciences and Primary Care, University Medical Hospital Utrecht.
Only a few months ago, the American Statistical Association authoritatively issued an official statement on significance and p-values (American Statistician, 2016, 70:2, 129-133), claiming that the p-value is: “commonly misused and misinterpreted.”
In this presentation I focus on the principles of the ASA statement.
Deborah G. Mayo: Is the Philosophy of Probabilism an Obstacle to Statistical Fraud Busting?
Presentation slides for: Revisiting the Foundations of Statistics in the Era of Big Data: Scaling Up to Meet the Challenge[*] at the Boston Colloquium for Philosophy of Science (Feb 21, 2014).
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.
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.
P-values the gold measure of statistical validity are not as reliable as many...David Pratap
This is an article that appeared in the NATURE as News Feature dated 12-February-2014. This article was presented in the journal club at Oman Medical College , Bowshar Campus on December, 17, 2015. This article was presented by Pratap David , Biostatistics Lecturer.
A comment in Nature, signed by over 800 researchers, called for a rise up against statistical significance. This was followed by a special issue of The American Statistician aimed at halting the use of the term "statistically significant", and new guidelines for statistical reporting in the New England Journal of Medicine. These slides discuss the broader context of the "p-value crisis" and alternatives for communicating the conclusions after statistical analyses.
Target audience: Medical researchers; Scientists involved in conducting or interpreting analyses and communicating the results of scientific research, as well as readers of scientific publications.
Learning objectives:
To understand the context of the reproducibility crisis in medical research.
To learn about problems with p-values and alternatives to report findings.
To understand how (not) to interpret significant and insignificant findings.
To learn how to communicate research findings in a modest, thoughtful, and transparent way.
This presentation discusses the following topics:
Hypothesis Test
Potential Outcomes in Hypothesis Testing
Significance level
P-value
Sampling Errors
Type I Error
What causes Type I errors?
What causes Type II errors?
4 possible outcomes
Check out this brief paper if you want to know more about P value calculations. There is a misconception that a very small p value means the difference between groups is highly relevant. Looking at the p value alone deviates our attention from the effect size. Consider an experiment in which 10 subjects receive a placebo, and another 10 receive an experimental diuretic. After 8 h, the average urine output in the placebo group is 769 mL, versus 814 mL in the diuretic group—a difference of 45 mL. How do we know if that difference means the drug works and is not just a result of chance? Read on and let me know if you have any questions...
Common Statistical Concerns in Clinical TrialsClin Plus
Statistics are a major part of clinical trials. This article breaks down how they are used, and things that people think about when recording statistical data.
Page 266LEARNING OBJECTIVES· Explain how researchers use inf.docxkarlhennesey
Page 266
LEARNING OBJECTIVES
· Explain how researchers use inferential statistics to evaluate sample data.
· Distinguish between the null hypothesis and the research hypothesis.
· Discuss probability in statistical inference, including the meaning of statistical significance.
· Describe the t test and explain the difference between one-tailed and two-tailed tests.
· Describe the F test, including systematic variance and error variance.
· Describe what a confidence interval tells you about your data.
· Distinguish between Type I and Type II errors.
· Discuss the factors that influence the probability of a Type II error.
· Discuss the reasons a researcher may obtain nonsignificant results.
· Define power of a statistical test.
· Describe the criteria for selecting an appropriate statistical test.
Page 267IN THE PREVIOUS CHAPTER, WE EXAMINED WAYS OF DESCRIBING THE RESULTS OF A STUDY USING DESCRIPTIVE STATISTICS AND A VARIETY OF GRAPHING TECHNIQUES. In addition to descriptive statistics, researchers use inferential statistics to draw more general conclusions about their data. In short, inferential statistics allow researchers to (a) assess just how confident they are that their results reflect what is true in the larger population and (b) assess the likelihood that their findings would still occur if their study was repeated over and over. In this chapter, we examine methods for doing so.
SAMPLES AND POPULATIONS
Inferential statistics are necessary because the results of a given study are based only on data obtained from a single sample of research participants. Researchers rarely, if ever, study entire populations; their findings are based on sample data. In addition to describing the sample data, we want to make statements about populations. Would the results hold up if the experiment were conducted repeatedly, each time with a new sample?
In the hypothetical experiment described in Chapter 12 (see Table 12.1), mean aggression scores were obtained in model and no-model conditions. These means are different: Children who observe an aggressive model subsequently behave more aggressively than children who do not see the model. Inferential statistics are used to determine whether the results match what would happen if we were to conduct the experiment again and again with multiple samples. In essence, we are asking whether we can infer that the difference in the sample means shown in Table 12.1 reflects a true difference in the population means.
Recall our discussion of this issue in Chapter 7 on the topic of survey data. A sample of people in your state might tell you that 57% prefer the Democratic candidate for an office and that 43% favor the Republican candidate. The report then says that these results are accurate to within 3 percentage points, with a 95% confidence level. This means that the researchers are very (95%) confident that, if they were able to study the entire population rather than a sample, the actual percentage who preferred th ...
Similar to Reporting Results of Statistical Analysis (20)
These slides are for teachers and researchers to know how to address student-centered learning
Inclusive learning
Critical thinking , these three dimensions are addressed in the slides. Please do share your thoughts.
This presentation is provide introduction to research design with focus on distinction between different strategies' of Research. Especially qualitative, quantitative and mixed methods. .
One question that always works in the mind of the research scholar is what are the likely questions by examiners for evaluation as well a viva. Here are some guidelines.
This presentation will address the issue of sample size determination for social sciences. A simple example is provided for every to understand and explain the sample size determination.
Here different concepts you come across in the research methodology are discussed. It is applicable to social sciences to a large extent. The definitions are explained in a way that will be understood by social scientists.
This lecture will help Research scholars at the starting of their research issues regarding definitions of variables, what is theory and creating a sapling map..
As Europe's leading economic powerhouse and the fourth-largest hashtag#economy globally, Germany stands at the forefront of innovation and industrial might. Renowned for its precision engineering and high-tech sectors, Germany's economic structure is heavily supported by a robust service industry, accounting for approximately 68% of its GDP. This economic clout and strategic geopolitical stance position Germany as a focal point in the global cyber threat landscape.
In the face of escalating global tensions, particularly those emanating from geopolitical disputes with nations like hashtag#Russia and hashtag#China, hashtag#Germany has witnessed a significant uptick in targeted cyber operations. Our analysis indicates a marked increase in hashtag#cyberattack sophistication aimed at critical infrastructure and key industrial sectors. These attacks range from ransomware campaigns to hashtag#AdvancedPersistentThreats (hashtag#APTs), threatening national security and business integrity.
🔑 Key findings include:
🔍 Increased frequency and complexity of cyber threats.
🔍 Escalation of state-sponsored and criminally motivated cyber operations.
🔍 Active dark web exchanges of malicious tools and tactics.
Our comprehensive report delves into these challenges, using a blend of open-source and proprietary data collection techniques. By monitoring activity on critical networks and analyzing attack patterns, our team provides a detailed overview of the threats facing German entities.
This report aims to equip stakeholders across public and private sectors with the knowledge to enhance their defensive strategies, reduce exposure to cyber risks, and reinforce Germany's resilience against cyber threats.
Techniques to optimize the pagerank algorithm usually fall in two categories. One is to try reducing the work per iteration, and the other is to try reducing the number of iterations. These goals are often at odds with one another. Skipping computation on vertices which have already converged has the potential to save iteration time. Skipping in-identical vertices, with the same in-links, helps reduce duplicate computations and thus could help reduce iteration time. Road networks often have chains which can be short-circuited before pagerank computation to improve performance. Final ranks of chain nodes can be easily calculated. This could reduce both the iteration time, and the number of iterations. If a graph has no dangling nodes, pagerank of each strongly connected component can be computed in topological order. This could help reduce the iteration time, no. of iterations, and also enable multi-iteration concurrency in pagerank computation. The combination of all of the above methods is the STICD algorithm. [sticd] For dynamic graphs, unchanged components whose ranks are unaffected can be skipped altogether.
Chatty Kathy - UNC Bootcamp Final Project Presentation - Final Version - 5.23...John Andrews
SlideShare Description for "Chatty Kathy - UNC Bootcamp Final Project Presentation"
Title: Chatty Kathy: Enhancing Physical Activity Among Older Adults
Description:
Discover how Chatty Kathy, an innovative project developed at the UNC Bootcamp, aims to tackle the challenge of low physical activity among older adults. Our AI-driven solution uses peer interaction to boost and sustain exercise levels, significantly improving health outcomes. This presentation covers our problem statement, the rationale behind Chatty Kathy, synthetic data and persona creation, model performance metrics, a visual demonstration of the project, and potential future developments. Join us for an insightful Q&A session to explore the potential of this groundbreaking project.
Project Team: Jay Requarth, Jana Avery, John Andrews, Dr. Dick Davis II, Nee Buntoum, Nam Yeongjin & Mat Nicholas
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Empowering the Data Analytics Ecosystem: A Laser Focus on Value
The data analytics ecosystem thrives when every component functions at its peak, unlocking the true potential of data. Here's a laser focus on key areas for an empowered ecosystem:
1. Democratize Access, Not Data:
Granular Access Controls: Provide users with self-service tools tailored to their specific needs, preventing data overload and misuse.
Data Catalogs: Implement robust data catalogs for easy discovery and understanding of available data sources.
2. Foster Collaboration with Clear Roles:
Data Mesh Architecture: Break down data silos by creating a distributed data ownership model with clear ownership and responsibilities.
Collaborative Workspaces: Utilize interactive platforms where data scientists, analysts, and domain experts can work seamlessly together.
3. Leverage Advanced Analytics Strategically:
AI-powered Automation: Automate repetitive tasks like data cleaning and feature engineering, freeing up data talent for higher-level analysis.
Right-Tool Selection: Strategically choose the most effective advanced analytics techniques (e.g., AI, ML) based on specific business problems.
4. Prioritize Data Quality with Automation:
Automated Data Validation: Implement automated data quality checks to identify and rectify errors at the source, minimizing downstream issues.
Data Lineage Tracking: Track the flow of data throughout the ecosystem, ensuring transparency and facilitating root cause analysis for errors.
5. Cultivate a Data-Driven Mindset:
Metrics-Driven Performance Management: Align KPIs and performance metrics with data-driven insights to ensure actionable decision making.
Data Storytelling Workshops: Equip stakeholders with the skills to translate complex data findings into compelling narratives that drive action.
Benefits of a Precise Ecosystem:
Sharpened Focus: Precise access and clear roles ensure everyone works with the most relevant data, maximizing efficiency.
Actionable Insights: Strategic analytics and automated quality checks lead to more reliable and actionable data insights.
Continuous Improvement: Data-driven performance management fosters a culture of learning and continuous improvement.
Sustainable Growth: Empowered by data, organizations can make informed decisions to drive sustainable growth and innovation.
By focusing on these precise actions, organizations can create an empowered data analytics ecosystem that delivers real value by driving data-driven decisions and maximizing the return on their data investment.
Explore our comprehensive data analysis project presentation on predicting product ad campaign performance. Learn how data-driven insights can optimize your marketing strategies and enhance campaign effectiveness. Perfect for professionals and students looking to understand the power of data analysis in advertising. for more details visit: https://bostoninstituteofanalytics.org/data-science-and-artificial-intelligence/
2. Context
While reporting results researchers generally stop with p-
value significance.
Should the researchers go beyond p-value?
What are the limitations of p-value?
What reporting is expected by American Psychology
Association?
CONTENT
3. WHAT ARE THE IMPORTANT
OUTCOMES TO BE REPORTED IN
THE HUMAN RESOURCES
RESEARCH?
IS STATISTICAL
SIGNIFICANCE IS EQUAL
TO PRACTICAL
SIGNIFICANCE?
WHY P-VALUES ARE
CRITICIZED BY THE
RESEARCHERS?
4. WILL HISTORY OF
STATISTICAL
SIGNIFICANCE OFFER
SOME CLARITY?
WHAT IS
INFLATED ERROR
RATES,
STATISTICAL
POWER, EFFECT
SIZE?
HOW TO USE G-
POWER FOR TESTING
STATISTICAL
SIGNIFICANCE?
HOW SHOULD A HUMAN
RESOURCES
PROFESSIONAL WILL
REPORT HIS OR HER
FINDINGS?
5. The Cult of Statistical Significance
Statistical significance is, we argue, a diversion from the proper
objects of scientific study.
Significance, reduced to its narrow and statistical meaning only…
“p < .05”—has little to do with a defensible notion of scientific
inference.
Its arbitrary, mechanical illogic, though currently sanctioned by
science and its bureaucracies of reproduction, is causing a loss of
jobs, justice, profit, and even life.
The Cult of Statistical Significance, Stephen T. Ziliak and Deirdre
N. McCloskey 2008.
6. Reporting Results
For the reader to appreciate the magnitude or importance of a study's findings, it is almost
always necessary to include some measure of effect size in the Results section.
Whenever possible, provide a confidence interval for each effect size reported to indicate
the precision of estimation of the effect size.
Effect sizes may be expressed in the original units and are often most easily understood
when reported in original units.
The general principle to be followed, however, is to provide the reader with enough
information to assess the magnitude of the observed effect.
Publication Manual of the American Psychological Association, p.34
8. Florence Nightingale: An English social
reformer and statistician and Data
Visualizer in modern terms
9. Ronald A. Fisher (1890-1962) introduced p values, level of
significance to evaluate evidences
Tea experiment: A woman claimed to be able
to find by tasting whether a cup of tea with
milk had the tea poured first or the milk
poured first.
An experiment was performed, and eight cups
of tea are prepared and given to her in random
order to identify. Four had the milk poured
first, and four had the tea poured first.
The lady tasted each one and gave her opinion.
If she guesses all four correctly, the probability
of happening of the event is 1/70= 0.014.
10. Tea experiment: A woman claimed to be able
to find by tasting whether a cup of tea with milk
had the tea poured first or the milk poured first.
• An experiment was performed, and eight cups of tea are
prepared and given to her in random order to identify.
Four had the milk poured first, and four had the tea poured
first.
• The lady tasted each one and gave her opinion. If she
guesses all four correctly, the probability of happening of
the event is 1/70 = 0.014.
13. Neyman and Pearson Approach
They believed
scientific
statements
should be split
into
hypotheses
that may be
tested. They
called them as
experimental
hypothesis or
(alternative
hypothesis)
and null
hypothesis.
The hypothesis
or a prediction
from the
theory will
generally have
an “effect”.
When we
designed
experimental
hypothesis or
alternative
hypothesis
why there is a
need for a null
hypothesis?
We will not be
able to prove
the alternative
hypothesis by
statistics. What
we do instead
is to try to
reject the null
hypothesis so
that we have a
support (not
causation) for
our alternative
hypothesis.
14. Neyman and Pearson
Identification of Errors
Type 1
Error:
• We conclude that there is effect when there
is no effect. Probability of this error
generally set to .05.
Type 2
Error:
• We conclude that there is no effect when
there is effect.
15. While Type 1 error is
intuitive and to a
large extent
appreciated by
researchers, Type 2
error requires more
reporting.
It is important effects
happening the real
world should not be
missed and it is
known as β-level.
Cohen
(1988)suggested the
maximum acceptable
probability for this
error to be .20.
Translated into
practical terms out of
100 samples we will
not be able to detect
20 samples even if
the effect exists.
Neyman and Pearson
Identification of Errors
16. Is failing to reject null hypothesis is equal to
accepting null hypothesis?
Failing to reject the null hypothesis is not equal to accepting the null
hypothesis.
The null hypothesis is never accepted, and failing to find an effect is not the
same thing as showing that there is no effect.
It is incorrect to claim evidence of no treatment effect or no difference if we
fail to reject the null hypothesis. We may say that there is inconclusive
results.
17. The theories
are
complements
and not
competing
with each
other.
There exists
difference
between both
the
approaches.
However, they
are
complementary.
Lehmann, E. L. (1993). The Fisher, Neyman-Pearson theories of testing hypotheses:
one theory or two?. Journal of the American statistical Association, 88(424), 1242-1249
18. Null Hypothesis Significance Testing
(NHST)
We assume null hypothesis is true (there is no effect).
We fit the data to an experimental results or model to represent
alternative hypothesis and how well it fits.
We find a p-value of getting the model if the null hypothesis is true.
If the probability is very small such as .05 or less then we gain confidence in
the alternate or experimental hypothesis.
19. What is
Significance
Test?
It is a process of comparing
the p value obtained from
the sample data to a
predetermined level of
significance decided by
researcher.
The level of significance is
the probability of committing
a Type I error. This we define
as finding evidence in sample
or difference when there is
no evidence or difference.
20. What is
Significance
Test?
The conventional level of
significance used in most
studies is .05, which
corresponds to rejecting the
null hypothesis incorrectly in
approximately 1 out of every
20 experiments.
The p value does not give
information on hypothesis being
true or false. The p value gives the
probability of observing the sample
data or something more extreme,
assuming the null hypothesis is true.
What is extreme? Let us do an
experiment.
21. Coin Experiment
Here is a coin and we assume that the coin will give head or tail with
equal probability if it is a fair coin.
I am having this coin and I have no ability to find it as a fair coin or
biased coin.
Let us test the hypothesis.
H0 : The coin is fair.
Now let us toss the coin. I get head.
The P(H)= ½ ; I have no evidence to suspect the coin.
22. Coin Experiment
Then I toss the coin: This time I get again a head.
The probability of this event is = ½*1/2 = ¼
I toss the coin again. I get a head.
The probability of the event is = ¼*1/2= 1/8 = .125
I toss the coin again. I get a head.
The probability of the event is = 1/8*1/2= 1/16 = 0.0625
I started suspecting my null hypothesis.
23. Coin Experiment
I toss the coin again. I get a head.
The probability of happening of the event is = 1/16*1/2 = 0.03125
After the fourth toss, there is a little evidence to support that null
hypothesis is true.
This is considered as extreme and the null hypothesis is rejected.
25. What is the p-value of .05 and why it is
needed to interpreted carefully?
The level of significance (p<0.05) is a
subjective quantity arrived at by the
researcher and (it may differ from other
researchers) selection determines the result of
a significance test.
This suggests clearly that it is a
subjective procedure. Therefore, to
believe that a significance test is an
objective measure of scientific evidence
may not be correct.
26. What happens if the p-values are
.03 and .00005?
Let us assume that two
studies are conducted by
two researchers in similar
areas.
The results of researcher A
gives p = .03 and the result
of researcher B gives
p = .00005.
27. What happens if the p-values are
.03 and .00005?
In both the cases, the p value is less than the predetermined level
of significance .05 which is predetermined by the researchers.
Therefore both the researchers conclude that the null hypothesis
is rejected.
Both the researcher A as well as researcher B inferences are
treated the same. The p-value of .00005 is of no much significance
than p-value of .03.
28. p-value and Sample Size
The p value and
statistical significance
are influenced by
sample size.
If the sample size is very
large, the p value necessarily
will be very small. An
increasingly large sample
size yields a decreasingly
smaller p value; thus, a large
sample size leads to a
statistically significant result,
regardless of scientific
importance.
A statistically
significant effect
based on a small
sample is more
impressive than a
statistically significant
effect based on a large
sample.
29. Inflated Error Rates or
Multiple Comparisons
Let us imagine we use the .05 level of significance in a research. The
probability of no Type 1 error is .95. This is for one test only in one
research.
However in reality we conduct multiple tests. If we conduct two tests the
overall probability of no type 1 error will be .95*.95=.9025.
Then the probability of at least one type error is given by 1-.9025=.0975 or
9.75%.
30. Inflated Error Rates or
Multiple Comparisons
Thus across the tests the type 1 error increases or it
is known as experiment wise error rate. The general
formula for the same is given by 1-(.95)n
This may be controlled by using Bonferroni Correction =
P
cri
= α/k where K is the number of comparisons.
However, it reduces the statistical power.
31. Important Remarks
• Systematic variation if the
variation that can be explained
by the model.
• Unsystematic variation is one
thig that cannot be explained
by the model we have
designed. That is the variation
is not attributable to the effect
we are experimenting.
There are two
variations that
are there in any
experiment,
32. Important Remarks
In effect we are finding the
• Test statistic = variance explained by the model/variance not explained
by the model = effect/error.
The ratio of effect to error is called the test statistic and
t,F and Chi-Square or Signal to noise ratio. If the
effect/error=1 or more the effect is more than error but
need not be significant.