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Hypothesis Testing Cornell Course

Course overview.

Basic statistical tools provide a starting point, but when it comes to tackling complex business scenarios, you often need more. Making informed decisions frequently requires the ability to devise and test hypotheses.

In this course, you will practice creating and testing hypotheses. You will examine how to construct a hypothesis that is rigorous and testable and test your hypotheses using different types of statistical data. Combining this skillset with your foundations in statistics and probability, you will enhance your understanding of potential outcomes. By the end of this course, you will be equipped with the skills necessary to back up business decisions with solid mathematical justification and foster improved communication about your decisions and with your stakeholders.

You are required to have completed the following courses or have equivalent experience before taking this course:

• Data Analysis and Probability
• Decision Analysis
• Continuous Distributions

Key Course Takeaways

• Examine how to construct a hypothesis that is rigorous and testable
• Test hypotheses using different types of statistical data

How It Works

Course author.

• Certificates Authored

Dr. David C. Juran, who teaches courses in statistics for management and managing operations, is a winner of six teaching awards at Columbia Business School and at the Cornell Johnson Graduate School of Management, including the EMBA Globe Award for Teaching Excellence. Juran’s research has appeared in Management Science, Journal of Operations Management, and other journals. Juran’s academic interests are informed by extensive industrial and corporate experience at Pepperidge Farm, Spaulding Company, and Juran Institute, as well as his experience as an independent management consultant for organizations such as [x+1], Gordian Group, Johnson & Johnson, MarketBridge, MTV Networks, Opera Solutions, Veeco, and Carl Zeiss. Dr. Juran earned his Ph.D. at Cornell University’s Johnson Graduate School of Management, concentrating in the fields of operations management, operations research, and organizational behavior.

• Applied Statistics

Who Should Enroll

• Professionals looking to uncover insights from data
• Students who are pre-MBA or considering earning an MBA
• Analysts and researchers
• Individuals interested in moving into an analyst role
• Anyone seeking to leverage statistical or analytic skills

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Statistical Inference and Hypothesis Testing in Data Science Applications

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• Welcome to the course! This module contains logistical information to get you started!
• Fundamental Concepts of Hypothesis Testing
• In this module, we will define a hypothesis test and develop the intuition behind designing a test. We will learn the language of hypothesis testing, which includes definitions of a null hypothesis, an alternative hypothesis, and the level of significance of a test. We will walk through a very simple test.
• Composite Tests, Power Functions, and P-Values
• In this module, we will expand the lessons of Module 1 to composite hypotheses for both one and two-tailed tests. We will define the “power function” for a test and discuss its interpretation and how it can lead to the idea of a “uniformly most powerful” test. We will discuss and interpret “p-values” as an alternate approach to hypothesis testing.
• t-Tests and Two-Sample Tests
• In this module, we will learn about the chi-squared and t distributions and their relationships to sampling distributions. We will learn to identify when hypothesis tests based on these distributions are appropriate. We will review the concept of sample variance and derive the “t-test”. Additionally, we will derive our first two-sample test and apply it to make some decisions about real data.
• Beyond Normality
• In this module, we will consider some problems where the assumption of an underlying normal distribution is not appropriate and will expand our ability to construct hypothesis tests for this case. We will define the concept of a “uniformly most powerful” (UMP) test, whether or not such a test exists for specific problems, and we will revisit some of our earlier tests from Modules 1 and 2 through the UMP lens. We will also introduce the F-distribution and its role in testing whether or not two population variances are equal.
• Likelihood Ratio Tests and Chi-Squared Tests
• In this module, we develop a formal approach to hypothesis testing, based on a “likelihood ratio” that can be more generally applied than any of the tests we have discussed so far. We will pay special attention to the large sample properties of the likelihood ratio, especially Wilks’ Theorem, that will allow us to come up with approximate (but easy) tests when we have a large sample size. We will close the course with two chi-squared tests that can be used to test whether the distributional assumptions we have been making throughout this course are valid.

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Hypothesis Testing in Python

In this course, you’ll learn advanced statistical concepts like significance testing and multi-category chi-square testing, which will help you perform more powerful and robust data analysis.

Part of the Data Analyst (Python) , and Data Scientist (Python) paths.

• Intermediate friendly

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Stacey Ustian

Course overview.

In this course, you’ll learn about single and multi-category chi-square tests, degrees of freedom, hypothesis testing, and different statistical distributions.

To learn about hypothesis testing and statistical significance, you’ll work hands-on with multiple datasets on weight loss data — are patients losing weight due to pure luck, or is it a diet pill? You’ll run the numbers and find out!

At the end of the course, you’ll complete a guided project in which you’ll work with data from the American TV show Jeopardy. You’ll analyze text and search for winning strategies. It’s a chance for you to combine the skills you learned in this course, and to showcase a fascinating project in your portfolio. Best of all, you’ll learn by doing — you’ll practice and get feedback directly in the browser.

• Defining regular and multi-category chi-squared tests
• Performing significance testing to understand an outcome's importance

Course outline

Hypothesis testing in python [4 lessons], significance testing 1h.

• Explain how hypothesis testing works
• Define the relation between statistical significance and hypothesis testing

Chi-Squared Tests 1h

• Determine the statistical significance of a set of categorical values
• Generate the chi-squared distribution
• Define degrees of freedom

Multi-Category Chi-Squared Tests 1h

• Extend chi-squared tests to multiple categories
• Calculate the statistical significance of multi-category chi-squared tests

Guided Project: Winning Jeopardy 1h

• Answer questions using text data
• Apply chi-squared tests to real problems

Projects in this course

Guided project: winning jeopardy.

For this project, you’ll take on the role of a Jeopardy contestant looking for any edge to win. You’ll work with a dataset of 20,000 Jeopardy questions using Python and pandas to analyze question and answer text and uncover helpful patterns.

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Hypothesis Testing

Get familiar with the significant concept of Hypothesis Testing through this free online course. Learn types of errors, Z-test, T-test, sample, and population. Enroll and learn Hypothesis Testing in detail with the hands-on demo.

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What you learn in Hypothesis Testing ?

About this Free Certificate Course

This free Hypothesis Testing course will help you comprehend the major concepts that help to carry it out successfully. You will learn about Type 1 & 2 errors and understand the Z-test in detail. You will learn about the Student’s T-test where you will go through types of T-tests, and their uses, and solve real-world examples to understand them better. You will further understand random sample and population size and their role in Hypothesis Testing. Lastly, you will learn independent T-test two sample and T-test outcome and paired T-test for student’s score. You will solve real-world examples along with a hands-on demo through which you will also gain the required practical knowledge. Complete the modules and a quiz to earn a free certificate of Hypothesis Testing course completion certificate.

Check out Great Learning’s Best Data Science Courses to gain in-depth knowledge in this field and earn the certificate that helps you grab better job opportunities.

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• Course Outline

This module discusses the important concept of hypothesis testing: type 1 and type 2 errors. You will go through them in detail and understand the various assumptions concerned along with solving a Z test result-related problem. 

In this module, you will learn about the T-test from scratch. You will understand its uses, types, and solve an example to gain practical knowledge.  

This module introduces you to the important terms in hypothesis testing called sample and population. You will understand how random sample and population size plays role in hypothesis testing.

This module in detail explains to you about independent T-test two sample and T-test outcome. You will go through a hands-on demo to understand how code works in each case.  

In this module, you will go through an example where you will apply paired T-test for student scores and understand the implementation of the test and carry out the hypothesis testing.  

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Frequently Asked Questions

What are the prerequisites required to learn this free Hypothesis Testing course?

This Hypothesis Testing course is suitable for beginners, so there are no prerequisites for enrollment.

How long does it take to complete this free Hypothesis Testing course?

There are two hours of self-paced video content in this course that learners can learn at their own pace and comfort.

Will I have lifetime access to the free course?

Yes, you can access any of the Great Learning Academy’s free courses at your preferred period and resume learning.

What are my next learning options after this Hypothesis Testing course?

You can go through Great Learning’s PG Data Science and Machine Learning Course by MIT. 

Is it worth learning about Hypothesis Testing?

Yes, hypothesis testing is a useful tool for determining whether a claim is supported by evidence. It can help you to decide whether to accept or reject a claim and can also be used to compare different claims.

What is Hypothesis Testing used for?

Hypothesis testing is used to determine whether there is sufficient evidence to support a claim.

Why is Hypothesis Testing so popular?

Hypothesis testing is a powerful concept that allows researchers to test ideas and make inferences about a population based on a sample. Hypothesis testing is popular because it is relatively simple to understand and use, and it can be applied to a wide range of research questions.

What jobs demand that you learn Hypothesis Testing?

Many jobs demand that you learn Hypothesis Testing, such as:

• Statistician

Data Analyst

• Research Analyst
• Market Research Analyst
• Business Analyst
• Financial Analyst

Will I get a certificate after completing this Hypothesis Testing course?

Yes. You can proudly display your newly acquired skills through the free Hypothesis Testing certificate after completing all the modules and a quiz at the end of the course.

What knowledge and skills will I gain upon completing this Insurance in Analytics course?

You will learn about type 1&2 errors, Z-test, T-test, sample, population, independent T-test two sample and T-test outcome and paired T-test for student’s score in-depth.

How much does this Hypothesis Testing course cost?

This is a free Hypothesis Testing course offered by Great Learning and any learner can enroll for free and start learning.

Is there a limit on how many times I can take this Hypothesis Testing course?

No, there is no limit on the number of times you can attain this free Hypothesis Testing course.

Can I sign up for multiple courses from Great Learning Academy at the same time?

Yes, you can anytime register for multiple courses that will help you establish a successful profession.

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                                                                            hypothesis testing.

What is hypothesis-testing?

Hypothesis testing is when an assumption is made and evidence is collected in favor of the assumption. In Statistics, hypothesis-testing is performed using sample data to draw inferences regarding a given population parameter or population probability distribution. An analyst decides which hypothesis-testing methodology to be catered to on the basis of the nature of data used and the analysis reason. 

The sample data used while testing a hypothesis might come from a large population or a process of data generation. The term ‘population’ is used to refer to this sample data irrespective of its source.  

The stats library of Python allows you to perform hypothesis-testing. There is a Python package, named ht, exclusively available for carrying out hypothesis tests in Machine Learning. 

Hypothesis-Testing Terminology

There are some commonly used terms in hypothesis testing that one must know before conducting a hypothesis test. Those commonly used terms are:

Null Hypothesis: An assertion concerned with a population that you want to test. It is called the ‘null hypothesis in the sense that it assumes the contrast of our belief.  For instance, if we are testing the presence of a specific ingredient in hair oil, our null hypothesis would state the absence of that ingredient in the oil. It is denoted by H0.

Alternative Hypothesis: The opposite of a null hypothesis is the alternative hypothesis in a test. Evidence for approval of this hypothesis is to be found through a hypothesis test. For the example mentioned above of hair oil, the alternative hypothesis would state the ingredient’s presence in the oil. It is denoted by HA.

Null and alternative hypotheses are always mutually exclusive of each other. 

Test Statistic: A random variable computed from a random population sample is known as a test statistic. It is used in a hypothesis test to decide the rejection of the null hypothesis. For example, the test statistic for a t-test is t-statistic. 

P-value: The probability of getting a value of the test static at least as extreme as the computed value in the null hypothesis of the hypothesis test is known as p-value. The smaller the p-value, the stronger is the evidence in support of the alternative hypothesis. 

Significance Level: The significance level represents the probability of rejecting the null hypothesis when it is true. It is denoted by alpha (α). For example, a significance level of 0.01 marks a 1% risk of drawing an inference even though there is no actual difference.

Steps of Hypothesis-Testing

The entire process of testing a hypothesis is carried out in the following order of events:

State the Null and Alternative Hypotheses: The very first step that an analyst takes is to specify the null and alternative hypothesis for the corresponding hypothesis test.

Formulate an Analysis Plan: The second step is to map out an analysis plan depending on the nature of the data and the reason behind the analysis.

Analyze the Sample Data: In the next step, the analyst carries out the formulated plan to analyze the sample data based on the determined hypothesis.

Determine plausibility of Null Hypothesis: The last step that comes is to decide whether to reject the null hypothesis or state the plausibility of the null hypothesis for the given sample data. The decision made is determined by the p-value and significance value of the hypothesis test. 

Need of Hypothesis-Testing in Machine Learning

All the discoveries made based on hypotheses need to pass the hypothesis test. The result of a hypothesis test is used to assert the statistical significance of a finding. As mentioned in the hypothesis-testing introduction, the result of a hypothesis test tells us whether the statement of the null hypothesis or the statement of the alternative hypothesis best reflects the sample data of the population parameter. 

In Machine Learning, when we train an ML model, we must be confident about the population itself first. Thus, to analyze the nature and trend of a population, we need to conduct a hypothesis test as it tells whether a speculated hypothesis about the population is true. 

Basis of Hypothesis

The entire hypothesis revolves around the basics of normalization and standard normalization. A variable is normally distributed when its curve is a normal bell-shaped curve representing the equal mean, median, and mode. On the other hand, we say that a variable has standard normal distribution when its mean 0 and the standard deviation is 1. 

Types of Hypothesis Test

Four types of hypothesis tests can be performed. These types are:

• Z-test: This test concludes whether two population means are different for known variances and a large volume of sample data. The test static, in this case, is z-static and the formula used is:

Z= X- µₒs

Here, Z = Z-test

X = sample average

µₒ = mean

s = standard deviation

T-test (Student t-test): Another hypothesis-testing tool differentiates between the means of two groups when their variances are not given. The test static, in this case, is t-static. It is further categorized into three kinds which are as follows:

One sample t-test

Independent two-sample t-test,

Paired sample t-test

t-tests have common applications in the field of Data Science, CS Research, and ML.

ANOVA test: ANOVA stands for Analysis of Variance. This test reports a statistically significant result when one of the groups differs significantly from the overall mean of the groups. It can be one-way, two-way, or n-way. The test static here is F-static.

Chi-square test: This hypothesis test is used to test the independence of two variables. It is sensitive to the size of the test sample. A chi-square test holds a comparison between expectations and model results. The test static in this type of test is chi-squared static. 

Alpha Risk & Beta Risk

In statistical hypothesis-testing, there might be a risk of rejecting the null hypothesis when it is true. This risk is referred to as alpha risk. The other term for alpha risks is Type-I error and false positive. The amount of alpha risk is mainly governed by the size of the sample used. A large sample size corresponds to low alpha risk. 

In contrast to alpha risk, there is a beta risk, commonly known as Type-II error. It is the likelihood of approving the null hypothesis when it is actually false, i.e., it is a false negative. 

Real-World Examples of Hypothesis Tests

The real-world examples in various fields that involve hypothesis-testing are given below:

Example-1: Hypothesis tests are done in different clinical trials to check the effectiveness of a new drug for curing a certain symptom. 

Example-2: To test the presence of a specific ingredient in any cosmetic item, food item, etc. 

Example-3: A hypothesis test can be used to determine whether a new type of manure will increase soil fertility. 

Example-4: Hypothesis tests are useful to find evidence in favor of a certain marketing strategy by analyzing the business growth.

Example-5: A hypothesis test can be run to determine whether an ML model fulfills the requirement in concern.

Likewise, endless real-world examples can be cited to show the implementation of hypothesis tests.

About the Course – Hypothesis Testing

The planned curriculum of this course will highly benefit the enthusiastic learners seeking opportunities in the field of Machine Learning. The hypothesis-testing course of Great Learning will help the learners to build a strong base in hypothesis-testing. Taking up this course enables you to get an insight into of Machine Learning Analytics job. Another advantage of this online course is that it is going to cost you nothing except for your time and dedication. 

The content of this online course is well structured to give a boost to beginners. It starts with a descriptive hypothesis-testing introduction and ends with a quiz to test your skills. On qualifying for the quiz, you can claim your free course completion certificate. Hence, along with learning new skills, you get a certificate to upgrade your CV and LinkedIn profile. This course contains two hours of video content presenting lectures on the basics of hypothesis-testing, including a description of student t-test and paired tests, for example.  

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• Prof. Philippe Rigollet

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Statistics for applications, lecture 7: parametric hypothesis testing.

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Official PyTorch implementation of Learning to (Learn at Test Time): RNNs with Expressive Hidden States

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Learning to (learn at test time): rnns with expressive hidden states.

Paper | JAX Codebase | Setup | Quick Start

This is the official PyTorch model implementation of Learning to (Learn at Test Time): RNNs with Expressive Hidden States . We do not recommend training with this codebase, because it is written in pure PyTorch without any systems optimization, so training will be slow, especially when the per-device batch size is small. For training code, or to replicate results from our paper, please view our JAX codebase .

Self-attention performs well in long context but has quadratic complexity. Existing RNN layers have linear complexity, but their performance in long context is limited by the expressive power of their hidden state. We propose a new class of sequence modeling layers with linear complexity and an expressive hidden state. The key idea is to make the hidden state a machine learning model itself, and the update rule a step of self-supervised learning.

Since the hidden state is updated by training even on test sequences, our layers are called Test-Time Training (TTT) layers . We consider two instantiations: TTT-Linear and TTT-MLP, whose hidden state is a linear model and a two-layer MLP respectively.

Environment Setup

Quick start.

Our implementation is based on Huggingface Transformers. You can use the following code to load the model and generate text.

Note: This is a naive implementation of TTT layers for tutorial purposes. This model can be trained using Huggingface Accelerate, or custom training loops. We will release a faster inference kernel soon.

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Title: learning to (learn at test time): rnns with expressive hidden states.

Abstract: Self-attention performs well in long context but has quadratic complexity. Existing RNN layers have linear complexity, but their performance in long context is limited by the expressive power of their hidden state. We propose a new class of sequence modeling layers with linear complexity and an expressive hidden state. The key idea is to make the hidden state a machine learning model itself, and the update rule a step of self-supervised learning. Since the hidden state is updated by training even on test sequences, our layers are called Test-Time Training (TTT) layers. We consider two instantiations: TTT-Linear and TTT-MLP, whose hidden state is a linear model and a two-layer MLP respectively. We evaluate our instantiations at the scale of 125M to 1.3B parameters, comparing with a strong Transformer and Mamba, a modern RNN. Both TTT-Linear and TTT-MLP match or exceed the baselines. Similar to Transformer, they can keep reducing perplexity by conditioning on more tokens, while Mamba cannot after 16k context. With preliminary systems optimization, TTT-Linear is already faster than Transformer at 8k context and matches Mamba in wall-clock time. TTT-MLP still faces challenges in memory I/O, but shows larger potential in long context, pointing to a promising direction for future research.

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An Overview of the IELTS

The International English Language Testing System (IELTS) is designed to measure English proficiency for educational, vocational and immigration purposes. The IELTS measures an individual's ability to communicate in English across four areas of language: listening , reading , writing and speaking . The IELTS is administered jointly by the British Council, IDP: IELTS Australia and Cambridge English Language Assessment at over 1,100 test centres and 140 countries. These test centres supervise the local administration of the test and recruit, train and monitor IELTS examiners.

IELTS tests are available on 48 fixed dates each year, usually Saturdays and sometimes Thursdays, and may be offered up to four times a month at any test centre, including Elektrostal' depending on local needs. Go to IELTS test locations to find a test centre in or nearby Elektrostal' and to check for upcoming test dates at your test centre.

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There are no restrictions on re-sitting the IELTS. However, you would need to allow sufficient time to complete the registration procedures again and find a suitable test date.

The Unique Burial of a Child of Early Scythian Time at the Cemetery of Saryg-Bulun (Tuva)

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Pages:  379-406

In 1988, the Tuvan Archaeological Expedition (led by M. E. Kilunovskaya and V. A. Semenov) discovered a unique burial of the early Iron Age at Saryg-Bulun in Central Tuva. There are two burial mounds of the Aldy-Bel culture dated by 7th century BC. Within the barrows, which adjoined one another, forming a figure-of-eight, there were discovered 7 burials, from which a representative collection of artifacts was recovered. Burial 5 was the most unique, it was found in a coffin made of a larch trunk, with a tightly closed lid. Due to the preservative properties of larch and lack of air access, the coffin contained a well-preserved mummy of a child with an accompanying set of grave goods. The interred individual retained the skin on his face and had a leather headdress painted with red pigment and a coat, sewn from jerboa fur. The coat was belted with a leather belt with bronze ornaments and buckles. Besides that, a leather quiver with arrows with the shafts decorated with painted ornaments, fully preserved battle pick and a bow were buried in the coffin. Unexpectedly, the full-genomic analysis, showed that the individual was female. This fact opens a new aspect in the study of the social history of the Scythian society and perhaps brings us back to the myth of the Amazons, discussed by Herodotus. Of course, this discovery is unique in its preservation for the Scythian culture of Tuva and requires careful study and conservation.

Keywords: Tuva, Early Iron Age, early Scythian period, Aldy-Bel culture, barrow, burial in the coffin, mummy, full genome sequencing, aDNA

Information about authors: Marina Kilunovskaya (Saint Petersburg, Russian Federation). Candidate of Historical Sciences. Institute for the History of Material Culture of the Russian Academy of Sciences. Dvortsovaya Emb., 18, Saint Petersburg, 191186, Russian Federation E-mail: [email protected] Vladimir Semenov (Saint Petersburg, Russian Federation). Candidate of Historical Sciences. Institute for the History of Material Culture of the Russian Academy of Sciences. Dvortsovaya Emb., 18, Saint Petersburg, 191186, Russian Federation E-mail: [email protected] Varvara Busova  (Moscow, Russian Federation).  (Saint Petersburg, Russian Federation). Institute for the History of Material Culture of the Russian Academy of Sciences.  Dvortsovaya Emb., 18, Saint Petersburg, 191186, Russian Federation E-mail:  [email protected] Kharis Mustafin  (Moscow, Russian Federation). Candidate of Technical Sciences. Moscow Institute of Physics and Technology.  Institutsky Lane, 9, Dolgoprudny, 141701, Moscow Oblast, Russian Federation E-mail:  [email protected] Irina Alborova  (Moscow, Russian Federation). Candidate of Biological Sciences. Moscow Institute of Physics and Technology.  Institutsky Lane, 9, Dolgoprudny, 141701, Moscow Oblast, Russian Federation E-mail:  [email protected] Alina Matzvai  (Moscow, Russian Federation). Moscow Institute of Physics and Technology.  Institutsky Lane, 9, Dolgoprudny, 141701, Moscow Oblast, Russian Federation E-mail:  [email protected]

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