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What does this code mean: "assert result == repeat, (result, repeat)"? [duplicate]
From here :
What does the last assert mean? I understand result == repeat but what's the rest?
- 1 docs.python.org/3/reference/… – jonrsharpe Commented 3 hours ago
The second "argument" to assert is the message printed out if the assertion fails. The idea here is to be able to easily see the expected and actual value for debugging, especially since hypothesis here will generate a whole bunch of tests.
Not the answer you're looking for? Browse other questions tagged python assert or ask your own question .
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Hypothesis Testing ( CIE A Level Maths: Probability & Statistics 2 )
Revision note.
Language of Hypothesis Testing
What is a hypothesis test.
- A hypothesis test uses a sample of data in an experiment to test a statement made about the value of a population parameter
- A hypothesis test is used when the value of the assumed population parameter is questioned
- The hypothesis test will look at the which outcomes are unlikely to occur if assumed population parameter is true
- The probability found will be compared against a given significance level to determine whether there is evidence to believe that the assumed population parameter is not true
What are the key terms used in statistical hypothesis testing?
- Every hypothesis test must begin with a clear null hypothesis (what we believe to already be true) and alternative hypothesis (how we believe the data pattern or probability distribution might have changed)
- One example of a population parameter is the probability, p of an event occurring
- Another example is the mean of a population
- The null hypothesis is denoted H 0 and sets out the assumed population parameter given that no change has happened
- The alternative hypothesis is denoted H 1 and sets out how we think the population parameter could have changed
- When a hypothesis test is carried out, the null hypothesis is assumed to be true and this assumption will either be accepted or rejected
- A hypothesis test could be a one-tailed test or a two-tailed test
- The null hypothesis will always be H 0 : θ = ...
- The alternative hypothesis, H 1 will be H 1 : θ > ... or H 1 : θ < ...
- The alternative hypothesis, H 1 will be H 1 : θ ≠ ...
- It is important to read the wording of the question carefully to decide whether your hypothesis test should be one-tailed or two-tailed
- A sample of data is a subset of data taken from the population
- The observed value is a numerical value calculated from the of data
- Any probability smaller than the significance level would suggest that the event is unlikely to have happened by chance
- The significance level must be set before the hypothesis test is carried out
- The significance level will usually be 1%, 5% or 10%, however it may vary
Worked example
A hypothesis test is carried out at the 5% level of significance to test if a normal coin is fair or not.
Make sure you read the question carefully to determine whether the test you are carrying out is for a one-tailed or a two-tailed test.
Critical Regions
How do we decide whether to reject or accept the null hypothesis.
- The critical region is the range of values that the observed value could take which will lead to the null hypothesis being rejected
- It is the least extreme value that would lead to the rejection of the null hypothesis
- The critical value is determined by the significance level
- In a two-tailed test the significance level is halved and both the upper and the lower tails are tested
- This probability will be known as the actual significance level
- The actual significance level is the probability of incorrectly rejecting the null hypothesis
- Finding the critical region will be different for a two-tailed test than it is for a one-tailed test
Do we always need to find the critical region?
- It allows you to see how far the observed value is from the critical value and make decisions about whether further testing is necessary
- In some cases a hypothesis test can be carried out without finding the critical region
- If the test is looking for a decrease then extreme values are smaller than the observed value, so find the probability of less than or equal to the observed value
- If the test is looking for an increase then extreme values are bigger than the observed value, so find the probability of greater than or equal to the observed value
- This probability is called the " p-value "
- In a two-tailed test it is common to half the significance level and compare this with the probability found in one of the tails
For the following situations, state at the 1% and 5% significance levels whether the null hypothesis should be rejected or not.
Conclusions of Hypothesis Testing
How is a hypothesis test carried out.
- There are a number of ways that a hypothesis test can be carried out for different models, however the following steps should form the base for your test:
- Step 1. Define the test statistic and population parameter
- Step 2. Write the null and alternative hypotheses clearly
- Step 3. Calculate the critical value(s) or the necessary probability for the test
- Step 4. Compare the observed value with the critical value(s) or the probability with the significance level
- Step 5. Decide whether there is enough evidence to reject H 0 or whether it has to be accepted
- Step 6. Write a conclusion in context
How should a conclusion be written for a hypothesis test?
- Your conclusion must be written in the context of the question
- If rejecting the null hypothesis your conclusion should state that there is sufficient evidence to suggest the alternative hypothesis is true at this level of significance
- If accepting the null hypothesis your conclusion should state that there is not enough evidence to suggest the alternative hypothesis is true at this level of significance
- There is a chance that the test has led to an incorrect conclusion
- The outcome is dependent on the sample, a different sample might lead to a different outcome
- You should not state whether this change is an increase or decrease
A teacher carried out a hypothesis test at the 10% significance level to test if her students perform better in exams after using a new revision technique. Under the null hypothesis she calculates the probability that a value will be at least as extreme as the observed value to be 0.09142. Write a conclusion for her hypothesis test.
- It is best to use the exact wording from the question when writing your conclusion for the hypothesis test, do not be afraid to sound repetitive.
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- Hypothesis Testing
- Hypothesis Testing (Discrete Distribution)
- Hypothesis Testing (Normal Distribution)
- Sampling & Data Collection
- Sampling & Estimation
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- Linear Combinations of Random Variables
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Author: Amber
Amber gained a first class degree in Mathematics & Meteorology from the University of Reading before training to become a teacher. She is passionate about teaching, having spent 8 years teaching GCSE and A Level Mathematics both in the UK and internationally. Amber loves creating bright and informative resources to help students reach their potential.
Exclusive Hypothesis Testing for Cox’s Proportional Hazards Model
- Published: 30 August 2024
- Volume 37 , pages 2157–2172, ( 2024 )
Cite this article
- Qiang Wu 1 ,
- Xingwei Tong 1 &
- Xiaogang Duan 1
Exclusive hypothesis testing is a new and special class of hypothesis testing. This kind of testing can be applied in survival analysis to understand the association between genomics information and clinical information about the survival time. Besides, it is well known that Cox’s proportional hazards model is the most commonly used model for regression analysis of failure time. In this paper, the authors consider doing the exclusive hypothesis testing for Cox’s proportional hazards model with right-censored data. The authors propose the comprehensive test statistics to make decision, and show that the corresponding decision rule can control the asymptotic Type I errors and have good powers in theory. The numerical studies indicate that the proposed approach works well for practical situations and it is applied to a set of real data arising from Rotterdam Breast Cancer Data study that motivated this study.
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Qiang Wu, Xingwei Tong & Xiaogang Duan
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This research was supported by the National Natural Science Foundation of China under Grant Nos. 11971064, 12371262, and 12171374.
This paper was recommended for publication by Editor SUN Liuquan.
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Wu, Q., Tong, X. & Duan, X. Exclusive Hypothesis Testing for Cox’s Proportional Hazards Model. J Syst Sci Complex 37 , 2157–2172 (2024). https://doi.org/10.1007/s11424-024-3283-0
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Received : 24 July 2023
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Published : 30 August 2024
Issue Date : October 2024
DOI : https://doi.org/10.1007/s11424-024-3283-0
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COMMENTS
Fifteen randomly chosen teenagers were asked how many hours per week they spend on the phone. The sample mean was 4.75 hours with a sample standard deviation of 2.0. Conduct a hypothesis test. The null and alternative hypotheses are: H0: ˉx = 4.5, Ha: ˉx> 4.5 H 0: x ¯ = 4.5, H a: x ¯> 4.5.
View Solution to Question 1. Question 2. A professor wants to know if her introductory statistics class has a good grasp of basic math. Six students are chosen at random from the class and given a math proficiency test. The professor wants the class to be able to score above 70 on the test. The six students get the following scores:62, 92, 75 ...
Study with Quizlet and memorize flashcards containing terms like A method for testing a claim or hypothesis about a parameter in a population, using data measured in a sample, is called: A) the central limit theorem B) hypothesis testing C) significance testing D) both b and c, The __________ hypothesis is a statement about a population parameter, such as the population mean, that is assumed ...
Table of contents. Step 1: State your null and alternate hypothesis. Step 2: Collect data. Step 3: Perform a statistical test. Step 4: Decide whether to reject or fail to reject your null hypothesis. Step 5: Present your findings. Other interesting articles. Frequently asked questions about hypothesis testing.
χ2 calculation example | χ2 test in hypothesis testing Step 2: use χ2 table for α = 5% and get χ2 value from the table. from table we got χ2 (critical value at α = 5%) = 3.841 Step 3: compare both χ2 values. The chi-square value of 18.99 is much larger than the critical value of 3.84, so the null hypothesis can be rejected.
If the biologist set her significance level \(\alpha\) at 0.05 and used the critical value approach to conduct her hypothesis test, she would reject the null hypothesis if her test statistic t* were less than -1.6939 (determined using statistical software or a t-table):s-3-3. Since the biologist's test statistic, t* = -4.60, is less than -1.6939, the biologist rejects the null hypothesis.
Study with Quizlet and memorize flashcards containing terms like What distribution is used when testing hypotheses, What does the null hypothesis state, Why do we test the null hypothesis and more.
The researchers write their hypotheses. These statements apply to the population, so they use the mu (μ) symbol for the population mean parameter.. Null Hypothesis (H 0): The population means of the test scores for the two groups are equal (μ 1 = μ 2).; Alternative Hypothesis (H A): The population means of the test scores for the two groups are unequal (μ 1 ≠ μ 2).
S.3 Hypothesis Testing. In reviewing hypothesis tests, we start first with the general idea. Then, we keep returning to the basic procedures of hypothesis testing, each time adding a little more detail. The general idea of hypothesis testing involves: Making an initial assumption. Collecting evidence (data).
In hypothesis testing, the goal is to see if there is sufficient statistical evidence to reject a presumed null hypothesis in favor of a conjectured alternative hypothesis.The null hypothesis is usually denoted \(H_0\) while the alternative hypothesis is usually denoted \(H_1\). An hypothesis test is a statistical decision; the conclusion will either be to reject the null hypothesis in favor ...
Null and Alternative Hypotheses. The actual test begins by considering two hypotheses.They are called the null hypothesis and the alternative hypothesis.These hypotheses contain opposing viewpoints. \(H_0\): The null hypothesis: It is a statement of no difference between the variables—they are not related. This can often be considered the status quo and as a result if you cannot accept the ...
A teacher believes that 85% of students in the class will want to go on a field trip to the local zoo. The teacher performs a hypothesis test to determine if the percentage is the same or different from 85%. The teacher samples 50 students and 39 reply that they would want to go to the zoo. For the hypothesis test, use a 1% level of significance.
A hypothesis test consists of five steps: 1. State the hypotheses. State the null and alternative hypotheses. These two hypotheses need to be mutually exclusive, so if one is true then the other must be false. 2. Determine a significance level to use for the hypothesis. Decide on a significance level.
Stats 2 Hypothesis Testing Questions . Stats 2 Hypothesis Testing Answers . 6 In previous years, the marks obtained in a French test by students attending Topnotch College ... the hypothesis test in part (a). Give a reason for your answer. (2 marks) 3 David is the professional coach at the golf club where Becki is a member. He claims that,
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Hypothesis testing is a crucial procedure to perform when you want to make inferences about a population using a random sample. These inferences include estimating population properties such as the mean, differences between means, proportions, and the relationships between variables. This post provides an overview of statistical hypothesis testing.
Enter statistics. Hypothesis testing formalizes our intuition on this question. It quantifies: in what % of parallel worlds would the results have come out this way? This is what we call a p-value. p<.05 intuitively means "a result like this is likely to have come up in at least 95% of parallel worlds" (parallel world = sample)
A hypothesis test is carried out at the 5% level of significance to test if a normal coin is fair or not. (i) Describe what the population parameter could be for the hypothesis test. (ii) State whether the hypothesis test should be a one-tailed test or a two-tailed test, give a reason for your answer. (iii)
A statistical hypothesis test has a null hypothesis, the status quo, what we assume to be true. Notation is H 0, read as "H naught". The alternative hypothesis is what you are trying to prove (mentioned in your research question), H 1 or H A. All hypothesis tests must include a null and an alternative hypothesis.
The first step in hypothesis testing is to set a research hypothesis. In Sarah and Mike's study, the aim is to examine the effect that two different teaching methods - providing both lectures and seminar classes (Sarah), and providing lectures by themselves (Mike) - had on the performance of Sarah's 50 students and Mike's 50 students.
In a quiz, students have to choose the correct answer to each question from three possible options. There is only one correct answer for each question. Ethan got answers correct, and he claims that he merely guessed the answer to every question but his teacher believes he used some knowledge in the quiz. She uses the null hypothesis.
Exam Questions - Hypothesis tests: binomial distribution - ExamSolutions.
To put this company's claim to the test, create a null and alternate hypothesis. H0 (Null Hypothesis): Average = 95%. Alternative Hypothesis (H1): The average is less than 95%. Another straightforward example to understand this concept is determining whether or not a coin is fair and balanced.
The e-learning format gives you flexibility to work on your own schedule, and at the pace you choose. The course also includes a pre-test at the start (to help you target focus areas) and a post-test at the end (to compare with the pre-test and verify improvement). In this Certified Quality Technician (CQT) exam preparation course, you will:
The second "argument" to assert is the message printed out if the assertion fails. The idea here is to be able to easily see the expected and actual value for debugging, especially since hypothesis here will generate a whole bunch of tests. >>> a = 1 >>> b = 2 >>> assert a == b, (a, b) Traceback (most recent call last): File "<stdin>", line 1, in <module> AssertionError: (1, 2) >>>
There are a number of ways that a hypothesis test can be carried out for different models, however the following steps should form the base for your test: Step 1. Define the test statistic and population parameter. Step 2. Write the null and alternative hypotheses clearly.
In this paper, the authors consider doing the exclusive hypothesis testing for Cox's proportional hazards model with right-censored data. The authors propose the comprehensive test statistics to make decision, and show that the corresponding decision rule can control the asymptotic Type I errors and have good powers in theory.