# 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.

278 questions
Filter by
Sorted by
Tagged with
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 ...
17k views

### 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 ...
3k views

### 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 ...
6k views

### 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?
7k views

### 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 ...
11k views

### 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 ...
6k views

### How can we ever know the population variance?

In hypothesis testing, a common question is what is the population variance? My question is how can we ever know the population variance? If we knew the entire distribution, we might as well know the ...
26k views

### Likelihood Ratio Test and Wald test provide different conclusion for glm in R

I'm reproducing an example from Generalized, Linear, and Mixed Models. My MWE is below: ...
5k views

### 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 ...
3k views

### chi squared test or Z test? [duplicate]

I have an outcome from a biological experiment, where I have counted the number of dead cells upon a mutation. For example, in once case - out of 120 cells we saw 16% of the dead cells, but our ...
842 views

### Simultaneous Z-test for the equality of two proportions (binomial distribution)

Is there a simultaneous test for the equality of two proportions when $k$ binomial properties are being tested? Example: Two groups of large size $n_1$ and $n_2$ are asked if they agree or disagree ...
35k views

### two samples z test in Python [closed]

Does Scipy have a z test to compare the mean of two samples? I searched this page but couldn't find one.
894 views

### What is wrong with one tailed z-tests for a proportion?

After answering How to analyze observed vs expected when expected is just a proportion? by suggesting that the OP uses a one tail Z-test for their proportion data, I got into a debate in the comments ...
2k views

### 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: ...
3k views

### Why would one ever use z-score over a t-score?

Forgive me if this seems like an elementary question, but no amount of googling has turned up a satisfying answer for me. From what I understand, a t-score should be used instead of a z-score when the ...
1k views

### Why is independence required for two- sample proportions z test?

I read in several books as well as in different posts (e.g. here) that independence is required for two-sample proportions z tests. But so far I could not find an explanation why this is the case and ...
111 views

### Can I use a z-test on heteroscedastic data?

Suppose I have two methods that I test over time on the same data. I suspect that the methods degrade over time, and that this degradation is more or less linear. I want to know if one method degrades ...
467 views

### 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-...
675 views

### How do I test difference in Percentages?

I have some survey data and know the number and percentage of "yes" responses. How do I determine if any of the percentage yes regional responses are statistically different from the national yes ...