What is Hypothesis testing: Definition and 86 Discussions

A statistical hypothesis is a hypothesis that is testable on the basis of observed data modelled as the realised values taken by a collection of random variables. A set of data is modelled as being realised values of a collection of random variables having a joint probability distribution in some set of possible joint distributions. The hypothesis being tested is exactly that set of possible probability distributions. A statistical hypothesis test is a method of statistical inference. An alternative hypothesis is proposed for the probability distribution of the data, either explicitly or only informally. The comparison of the two models is deemed statistically significant if, according to a threshold probability—the significance level—the data would be unlikely to occur if the null hypothesis were true. A hypothesis test specifies which outcomes of a study may lead to a rejection of the null hypothesis at a pre-specified level of significance, while using a pre-chosen measure of deviation from that hypothesis (the test statistic, or goodness-of-fit measure). The pre-chosen level of significance is the maximal allowed "false positive rate". One wants to control the risk of incorrectly rejecting a true null hypothesis.
The process of distinguishing between the null hypothesis and the alternative hypothesis is aided by considering two conceptual types of errors. The first type of error occurs when the null hypothesis is wrongly rejected. The second type of error occurs when the null hypothesis is wrongly not rejected. (The two types are known as type 1 and type 2 errors.)
Hypothesis tests based on statistical significance are another way of expressing confidence intervals (more precisely, confidence sets). In other words, every hypothesis test based on significance can be obtained via a confidence interval, and every confidence interval can be obtained via a hypothesis test based on significance.Significance-based hypothesis testing is the most common framework for statistical hypothesis testing. An alternative framework for statistical hypothesis testing is to specify a set of statistical models, one for each candidate hypothesis, and then use model selection techniques to choose the most appropriate model. The most common selection techniques are based on either Akaike information criterion (=AIC) or Bayesian information criterion (=BIC).

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  1. Ahmed1029

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  3. chwala

    Solve the problem that involves Hypothesis testing and Bin (n,p)

    ##p(x≤11)=1-[p(x=12)+p(x=13)+p(x=14)+p(x=15)]## ##p(x≤11)=1-[0.128505+0.266895+0.3431518+0.205891]=1-0.9444428=0.0556## ##⇒p(x>11)=0.9444## ##p(x≤10)=1-[0.042835+0.128505+0.266895+0.3431518+0.205891]=1-0.9872778=0.0127222## Since, ##p(x≤11)=0.0556> 0.05## then it falls on the Accepted region...
  4. ohwilleke

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  5. S

    B Rejection region of hypothesis testing

    From z-table, I get the critical value of z is -1.282 Will the rejection region be z < -1.282 or z ≤ -1.282? If I calculate the test statistics and it has value of -1.282, would I reject or accept null hypothesis? Thanks
  6. P

    How to Determine Whether to Accept or Reject a Hypothesis?

    Summary:: Confused on correction for contunuity I'm confused about one step for questions like this where you have to determine to accept or reject the null hypothesis. Sample size: 50 Number of successes: 23 Significance level: 10% Null hypothesis: p = 0.4 Accepted hypothesis: p > 0.4...
  7. P

    B Stats: Determining significance level in problem

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  8. G

    B Statistics Help : Hypothesis Testing

    Answer : I understnad why x(< or = ) 2 but I do not understand why we use 16 instead of 17 for the second range? When P(X>=16) > 0.005(which is the level of significance). Thank you for all the help given :)
  9. G

    I Hypothesis Testing: Comparing Gaussian Distributions

    Hi, I have some set of data and I want to use Hypothesis Testing to discriminate between two hypotheses: H0: My data follows a Gaussian distribution with a given mean and a given std (the actual values are ugly, so let's say mean = 0 and std = 1). H1: My data follows a Gaussian distribution with...
  10. T

    Showing Rejection Region Equality with Fisher Distribution

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  11. R

    I Multiple hypothesis testing for radar tracking in clutter

    Hello All, The goal is to formulate a multiple hypothesis test for a radar tracking problem when false alarms are occurring and to apply a particle filter on this update step, however I first need to come to/understand the multiple hypothesis formulation in this problem. Say we are interested...
  12. F

    I Can Bayesian Hypothesis Testing Determine the Authenticity of Cables?

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  13. H

    I Why does normal distribution turn into t distribution when variance is unknown?

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  14. M

    MHB Hypothesis testing - Winning a game

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  15. M

    MHB Performance of students - Hypothesis testing

    Hey! :o A teacher wants to find out if the order of the exam tasks has an impact on the performance of the students. Therefore, he creates two versions ($ X $ and $ Y $) of an exam in which the exam tasks are arranged differently. The versions are randomly distributed so that $ n $ students...
  16. H

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  17. K

    B Postulates and pseudoscientific hypothesis difference?

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  18. T

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  19. M

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  20. R

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  21. G

    How Do You Test a Hypothesis Without Sample Variance?

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  22. G

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  23. P

    I Algorithm to create a composite score

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  24. R

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  25. N

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  26. T

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  30. S

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  31. H

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  32. A

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  33. Kerrie

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  34. X

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  35. D

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  36. P

    MHB Which Should You Use in Hypothesis Testing: P-Value or TCV?

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  37. T

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  38. M

    Hypothesis testing for std. deviation (SD)

    Hi, What I know: In a hypothesis test for the mean, we compare a sample mean with a hypothetical sampling distribution of means. And depending on how far it is away from the mean of the sampling distribution, we attribute it the probability of getting that value purely by chance. What I...
  39. B

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  40. P

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  41. Pythagorean

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  42. P

    Hypothesis Testing: Factorial ANOVA

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  43. B

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  44. twoski

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  45. icystrike

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  46. K

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  47. A

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  48. A

    A Question about Hypothesis Testing

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  49. A

    Some questions about hypothesis testing

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