# Questions tagged [z-test]

The z-test is a statistical test for hypothesis testing that uses the standard normal distribution as the sampling distribution of the test statistic. A common example is the test for the difference of two proportions.

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### What follows if we fail to reject the null hypothesis? [duplicate]

What conclusions can we draw if $p>\alpha$? Does not rejecting the $H_0$ mean anything?
64k views

### What is the relationship between a chi squared test and test of equal proportions?

Suppose that I have three populations with four, mutually exclusive characteristics. I take random samples from each population and construct a crosstab or frequency table for the characteristics ...
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### Choosing between $z$-test and $t$-test

Background: I'm giving a presentation to colleagues at work on hypothesis testing, and understand most of it fine but there's one aspect that I'm tying myself up in knots trying to understand as well ...
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### Why use a z test rather than a t test with proportional data?

When testing the difference between 2 proportions why do we use a z-test rather than a t-test? Further, is there a simple way to conduct an omnibus test for significant differences between more ...
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### At What Level is a $\chi^2$ test Mathematically Identical to a $z$-test of Proportions?

BACKGROUND: Skip safely - it's here for reference, and to legitimize the question. The opening of this paper reads: "Karl Pearson’s famous chi-square contingency test is derived from another ...
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### Independent samples t-test: Do data really need to be normally distributed for large sample sizes?

Let's say I want to test if two independent samples have different means. I know the underlying distribution is not normal. If I understand correctly, my test statistic is the mean, and for large ...
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### is the z-test for difference of proportions valid for massive samples with tiny proportions?

Let's say I want to run a difference of proportions test where each side has n=23,000 but their proportions are 0.21% and 0.34%. ...
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### Wald Test and Z Test

The "z" hypothesis test is derived from the fact the mean estimator $\hat\Theta$ is distributed normally. If we don't know the variance, we just estimate it ($\widehat{se}$). The Wald test, derived ...
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### Interpretation of p-value in comparing proportions between two small groups in R

I wish to compare proportions between two small groups. In group 1, 2 of 18 students received honours. In group 2, 9 of 21 received honours. This is a small sample, so if I use the t-test: ...
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### Two-sample test of proportions

In my research, I aim to compare websites and need to identify if the websites differ significantly from each other. I have divided the website into two categories. I have sampled 45 websites in the ...
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### What do the remaining columns (after column 2) in a Z table mean

In the Z table , I can understand the first 2 columns. The first column is the Z value, the second column is Prob(X<=Z). But what do the remaining columns mean?
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### Understanding formulation of hypotheses in difference between two sample means (z test)

Introduction When testing a sample against a population, one has one of the following sets of hypotheses: Two-tailed test: $H_0: \mu=\ldots$, i.e. "no difference", and $H_1: \mu\neq\ldots$ Right-...
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### 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 ...
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### Appropriate use of z test comparing two proportions

(Apologies for the cross-posting from math.stackexchange.com; I wasn't aware of this site until just now). I would like to test the performance of two algorithms. The second is a variant of the first....
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### Should we apply z-test or t-test for testing the difference between two sample means?

Below is a sample question from Wayne Daniel's Biostatistics 9th ed. This is a question under the subchapter - "Sampling from normally distributed populations where population variances are known". ...
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### Hypothesis testing question -- how to define the null hypothesis to draw a conclusion

Here is a hypothesis testing question I'm trying to work out but am struggling with how to draw a conclusion, maybe I'm not defining the null hypothesis correctly. The question is as follows: Test ...