Linked Questions

1answer
1k views

What are the ''desirable'' statistical properties of the likelihood ratio test?

I am reading an article whose method is fully based on the likelihood ratio test. The author says that the LR test against one sided alternatives is UMP. He proceeds by claiming that "...even when ...
2answers
2k views

How to define a rejection region?

This has always troubled me a bit. When I choose my hypothesis, do I define in some way the rejection region [RR], or, do I do that by choosing the test statistic I want to use? By fixing the ...
3answers
272 views

Is this null hypothesis wrong?

The Wikipedia article Null hypothesis says in its opening paragraph: In inferential statistics, the term "null hypothesis" is a general statement or default position that there is no relationship ...
2answers
328 views

Why do we trust the p-value when fitting a regression on a single sample?

I have code below that builds a linear model for a set of data: ...
2answers
1k views

Choice of null and alternative hypothesis

A firm producing tobacco cigarettes claims that it has discovered a new technique for curing tobacco leaves, that results in an average nicotine content of a cigarette of less than 1.5 mg. To test ...
2answers
279 views

Ambiguity of chi-squared test of association; how can the conclusion change using the ''same'' sample?

Recently I have been struggling with the following two questions regarding the chi-squared test of independence / association during reading an article. Is the chi-squared test able to detect no ...
3answers
244 views

Null hypothesis for the one- and two-tailed test

From the Online Stat Book, Chapter 11.5: The null hypothesis for the two-tailed test is π = 0.5. By contrast, the null hypothesis for the one-tailed test is π ≤ 0.5. Why is that so? The null ...
2answers
286 views

The rationale behind the “fail to reject the null” jargon in hypothesis testing?

In hypothesis testing with a Null and the Alternative hypothesis (assuming that these two cases are mutually inclusive of all the possible "truths"), we usually base our hypothesis selection criterion ...
2answers
201 views

Appropriateness of one-sided hypothesis tests when testing medical treatments

I am working on some research where we are studying the effectiveness of two different types of brand new (i.e. never been studied before) treatments (call them high and low treatment levels) on death ...
4answers
175 views

consequences of rejected/accepted hypothesis

A and B are some statements such that A implies B. I test the null hypothesis that A is true. If my test fails to reject A, does that result say anything about B? Analogously, if instead I test the ...
2answers
191 views

What fraction to use in the formulation of a hypothesis test ? - Population fraction versus sample fraction

Imagine that I am studying racial discrimination. In particular, whether a white candidate (for a job) is chosen more often than an equally qualified minority candidate. I ask people to choose ...
2answers
201 views

ANOVA for Regression

When using ANOVA to compare means, I understand the null hypothesis is u1=u2=u3.... as we need to combine all groups into a single group when assuming their means are the same. But for ANOVA for ...
0answers
216 views

what “rejecting a null hypothesis” actually means?

I have a sample dateset consists two variables as "Score"(independent continuous) consists score of students in maths and school(dependent categorical)having 3 categories as "S1","S2","S3". I'd ...
1answer
148 views

Probability of significant result in a second sample given first was significant

It's an example mentioned in Amos Tversky and Daniel Kahneman's Belief in the Law of Small Numbers: Suppose you have run an experiment on 20 subjects, and have obtained a significant result which ...
2answers
90 views

Definition of alternative hypothesis

Which of these properties is required of the alternative hypothesis, by definition, in the general case: a) If the alternative hypothesis is true, then the null hypothesis would necessarily tend ...

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