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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16
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3answers
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?
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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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2answers
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 ...
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2answers
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 ...
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1answer
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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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2answers
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 ...
5
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1answer
1k views

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%. ...
10
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1answer
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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 ...
6
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1answer
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: ...
4
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2answers
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Likelihood-ratio test or z-test?

Consider the following two logistic regression models: $$ \begin{aligned} &\text{Model A: }&P(Y=1)&=\frac{\text{exp}\left(b_1+b_2X_2\right)}{1+\text{exp}\left(b_1+b_2X_2\right)} \\ &\...
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1answer
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 ...
5
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1answer
4k views

Hypothesis testing for 2 proportions - for A/B testing

I was trying to understand the statistical tests to use during A/B testing and stumbled upon this documentation of the Amazon A/B testing SDK: https://developer.amazon.com/public/apis/manage/ab-...
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1answer
858 views

Test of proportions or chi-squared? [duplicate]

These data are from an A/B test of free trials to conversion. Someone can sign up for a 30 day free trial of the product. If they like it they stay on and become paying customers. By default (A), when ...
6
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2answers
916 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 ...
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1answer
139 views

Is this the correct way to undertake Z-Tests on average user ratings to compare different versions of products?

The below is a partial data set showing the mean user ratings for a number of products, each of which is available in a number of standard versions, e.g. a common feature added to each product such as ...
3
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1answer
193 views

Is there a t-test equivalent to Stouffer's z-test?

I have $k$ pairs of samples from different distributions. For each pair of samples I want to check if the samples are taken from a normal distribution with the same mean and variance. I assume the ...
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2answers
91 views

t-test or z-test: assume normality or s≈σ?

Let's say I have a large sample ($n>30$) with mean $\bar{X}$ and standard deviation $S$. I can calculate only: $T=\frac{\bar{X}-\mu}{S/\sqrt{n}}$. If I want to use t-test for a hypothesis, then I ...
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1answer
302 views

Can I use a two proportion z-test?

I have a response, "Satisfaction" that goes on a scale from 0-10 (where 0=dissatisfied and 10= very satisfied), and I have a predictor variable that also uses the same scale. I recoded the response so ...
0
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1answer
88 views

Is a Z-Test, the right test to compare the mean of several sub groups to a control mean?

I am having some trouble confirming that I am on the right track and I hope someone can help me out. I have a data set with 9 products each of which has received 8 treatments, including the control ...
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6answers
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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 ...
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2answers
848 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 ...
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2answers
368 views

Is there any hypothesis test for two binomial distribution without normal approximation?

Let's say we are running an A/B testing and each data point has a binary response. We would like to test whether the ratio of true are different between A and B. (e.g. ask a yes/no question to both ...
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2answers
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Outlier detection for heavy-tailed data

Applying modified z-score for outlier elimination on some data (Iglewicz and Hoaglin, 1993), I discovered that a big proportion of the data (~10%) was outside the range ...
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1answer
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two samples, hypothesis test of proportions t or z test

I have two samples of documents where one sample contains documents of a certain category and another sample contains documents of another category. I am analysing the occurrence of a certain word in ...
6
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1answer
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 ...
4
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1answer
229 views

Statistical significance of a difference between poll percentages with a small sample?

Analyzing my company’s internal survey results, I was stuck with calculating statistical difference between percentages. I usually used a Z-test as described below, but I am not sure whether it is ...
3
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1answer
108 views

Most appropriate test for A/B testing results

I looked answers for this question but couldn't find anything clear, everyone says something different. I wonder what is the most appropriate method for testing the statistical significance of our A/...
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2answers
1k views

Large overlap between confidence intervals, although z test for difference was significant

I have calculated a z test to examine the difference between two proportions. I found differences to be significant. The formula I used was: $$z = (p_1-p_2)/SE$$ where $$SE = \sqrt{ p ( 1 - p ) ( \...
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1answer
515 views

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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2answers
1k views

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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2answers
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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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1answer
191 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 ...
2
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2answers
919 views

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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1answer
1k views

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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1answer
135 views

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 ...
0
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1answer
420 views

Find if two groups are different where one is a subset of the other

I have a dataset of 3,500,000 categorical observations that can be grouped by an ID. In these categories u occurs 25,000 times. How can I test to determine if a ...
0
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1answer
269 views

Probability that two people get a certain number of heads on 100 coin tosses and all other outcomes with lower probability?

2 people flip a coin 100 times. The first person get 42 heads, the second person gets 58 heads. What is the probability of this outcome and all other possible outcomes that have an equal or lower ...