# 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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### Why do Z-tests use standard error (using the know population standard deviation) and not only standard deviation?

I understand why a T-test uses the standard error, after all we are dealing with the inaccuracy of small samples. $$T = \frac{\bar{x} - \mu}{\bar{s} / \sqrt{n}} = \frac{\bar{x} - \mu}{SE}$$ But why ...
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### Should I use a $\chi$-squared test or a z-test?

I have a dataset with four groups $G_i$ with $i = 1, 2 , 3 , 4$, and in each group $G_i$, a certain number $n_i$ of observations are favorable. I want to check if there are any differences between the ...
1 vote
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### Can evidence of absence be obtained only in one-sided hypothesis tests?

It seems that if a one-sided Z-test returns a p-value $>1 - \alpha$, you have enough evidence of absence to reject the alternative hypothesis in favor of the null hypothesis, because if you were to ...
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### Z Test basic problem

The mean selling price of new homes in a town over a year was \$2,200,000. The population standard deviation is \$200,000 . A random sample of 81 new home sales from this city was taken. What is the ...
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### One proportion Z-test and Chi Square Goodness of Fit should be identical but return different results

My understanding is that a Chi Square Goodness of Fit test and a one-proportion Z-test should have identical p-values and be equivalent (https://youtu.be/-Vssir6yUNQ?si=4-t9Np9h4bedU9xN&t=423). ...
1 vote
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### On the success or failure of an experiment

Recently I've been asked this question and I wasn't really able to give a solid answer from a statistical standpoint. I hope someone can help me :) Statement Let's say that in a given region, in a ...
1 vote
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### 2 proportion Z/T test?

I want to find out if 2 proportions are different or not. For one, sample size is <30. For the other, it's much >30. Can I use the Z test since one size is large? Or do i have to use the t test? ...
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### Did I use z-test correctly in this problem?

The problem: It has been said that it is difficult to distinguish Coke and Pepsi by taste alone, without the visual cue of the bottle or can. In an experiment that I did in a class at Stanford, 10 ...
446 views

### Why are there two formulas for the z-test?

There are two formulas commonly used in the z-test: one involving the standard error (se) and the other involving the standard deviation (std) of the population. The formulas are as follows: ...
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### Confused about when to use z-test and p-value test for hypothesis testing

Can anyone help me solve this confusion? I don’t know why z-test and p-value test for hypothesis testing is used for this, given that the pattern between the two questions are same. Records show that ...
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### Testing homogeniety within a bin of scores given max number of bins

I have a score (ranging from 0 to 1000) which predicts a binary event. The score is based on a regression. Scores are binned. There should be a maximum of $x$ (e.g. $10$) bins. Predicitions within a ...
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### At loss regarding a suitable hypothesis test for proportions in the same population

I'm dealing with a population where there are $5$ categories $A, B, C, D, E$ and I would like to make the claim that $A$ is the most common category in the population (i.e., the most frequent). I ...
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### Comparing success of group 2 and failure of group 1 (cross-tabulation comparison in contingency table)

I'm studying the endowment effect through the exchange paradigm. Participants received an object A or B. Then the experimenter asks the participants if they accept to trade their object with the ...
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### Compare two proportions with a Bayesian analysis

I'm conducting an experiment in which participants receive either an object A or an object B. Next, we ask participants if they want to trade their objects with the alternative object (i.e., object B ...
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### Comparing two proportions within contingency table for small sample size [duplicate]

I need some help for a statistical analysis. I have the following contingency table : I would like to compare p3 and p2, that is the comparing the proportion of event in G2 and the proportion of not-...
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### Which statistical test is more suitable?

In an exam question I was asked to consider the following data related to education loan taken or not for pursuing higher education and formulate a suitable hypothesis and validate it by using an ...
1 vote
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### Comparing groups based on data containing proportions without raw counts

I have 2 object types, A and B For type A, I observe delivery to demographic groups x1, x2, x3, x4.... xn. For type B, I observe delivery to the same demographic groups x1, x2, x3, x4.... xn. x1(a) + ...
1 vote
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### Compairing multiple distributions from repeated measures design to a refrence value

I have 24hrs of temperature measurements taken in one minute intervals for a set of individuals. Thus, there is a non-independent distribution of temperatures for each individual as each measurement ...
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### Can I use the Z-Test with estimators for mean and standard deviation?

I'm trying to select feature columns in a binary classification model. I'd like to remove near-constant columns that don't predict the target column values very well. One way of defining this is the ...
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### Are large samples always needed for a Z-Test?

I have read that you should use a Z-Test when you have a sample size $n > 30$, because this is where your sample distribution becomes normally distributed. The Z-Test equation has more power when ...
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### Can you use a Z-Test with a sample size of 1?

Background I'm performing a feature selection process on a fraud dataset. The dataset is made up of roughly 300 columns and 40,000 rows. It has a single binary indicator for a target. A lot of the ...
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### Significance of a single point, or population of 1

This may sound simple but I'm lost. I have a simple experiment 15 controls and 15 treatments. 13 of the 15 controls were positive, but only one of the treatment samples was positive. This makes the SD ...
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### What is the reason in R prop.test() for 2 proportions to report Wald's confidence interval yet Rao test score? They are not consistent [duplicate]

I calculated the difference in 2 proportions using the prop.test() using some exemplary data I found in internet. ...
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### Why is the confidence interval for difference in two proportions inconsistent with the p-value for this difference in R prop.test()?

I calculated the difference in 2 proportions using the prop.test() using some exemplary data I found in internet. ...
1 vote
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### Visualizing how the 2 sample Z test works

In my stats class, we are talking about the 2 proportion $Z$-test, which compares two sample proportions. The test statistic is given as:  Z = \frac{\hat{p_1}-\hat{p_2}}{\sqrt{\hat{p_c}(1-\hat{p_c})...
1 vote
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### Z test for paired proportions when only the two proportions are available

I am familiar with formulae for paired proportions Z test when the crosstabs table is available. However, if only the two proportions are available, I am having trouble to figure out what is the S.E. ...
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### Selecting an appropriate statistical test

I have two sets of data (>10k observations), each having a binary feature describing the activity of every customer within the groups (1=active, 0=inactive). I've seen parametric tests being used ...
1 vote
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### How to check normality of a binary data(True/False) for z proportion test?

One of the three conditions that should be checked before conducting two-sampled z-test for proportions is "check for normality"(link for the source: https://vitalflux.com/two-sample-z-test-...
1 vote
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### Z-Tests tests of Two Proportions for Continuous Data?

Why can't we do z-tests of two proportions for data from a continuous variable? For Example, if I have sample sales data (continuous, dollar) from a company and want to see if the proportion of sales ...
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### Z-test with large sample sizes but small proportions

I'm running an A/B test to determine if a change/treatment we're proposing for our website has an impact on users opting into a specific (niche) category of notifications. To do so, I'm performing a ...
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### Can we use z-test when the population standard deviation is known but the sample size < 30?

Let's say I know the population standard deviation, but the sample size is small (≤30). Can I use the z-test? The reason I ask is that I see two different statements. We can use the z-test, if we ...
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### Is a t-test applicable here in comparing two proportions?

I have 3 categories of tissues examined by microscopy (A , B and C, 12 of each). I want to test whether the proportion of tissues staining by a particular dye, differs in the three categories. Each ...
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### Why is t-test more appropriate than z-test for non-normal data?

(Disclaimer: I am aware that some form of this question has been asked many times on this site, e.g. this, this and this - I was hoping to find a definitive answer to this from Google but I am still ...
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### A/B Testing Question - Power Analysis for Two Proportion Z Test

I'm having a hard time wrapping my head around experiment design and what appears to be a disconnect to experiment outcome analysis. If I am proposing a z test of two independent proportions (...
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### Contradictory results while performing Z-test

Hello Everyone, I'm relatively new to statistics and this community so please bear with me and forgive me if I commit any mistake while asking my question. For starters, here are two hypotheses tests ...
1 vote
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### Comparing two classifiers with two proportion ztest by using balanced accuracy

I'm looking for statistical differences between two classifiers by applying the two proportion z-test formula to them and then performing the hypothesis test. If p1 and p2 are the balanced accuracy ...
1 vote
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### Why are ztest and chisquared test not returning equivalent sample size results?

I'm using the statistical software G*Power to find the minimum sample size needed to detect whether or not the difference in two proportions is statistically significant in an AB test I'm setting up. ...
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### What are the distribution values (mu, sigma) for alternative hypothesis of differences between two proportions? How to calculate?

When comparing two independent proportions (p2, p1) in an A/B test, null hypothesis states that the difference is 0, while the alternative hypothesis states it is something other than 0, let's say mu1....
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### Minimum sample size calculations for two-sample two-tailed proportion z test

I'm struggling to reconcile some minimum sample size calculations. I'm seeking a minimum sample size for two-sample two-tailed proportion z test. I set my parameters as follow... alpha = 0.05 power = ...
1 vote
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### Finding statistical significance difference using Z score test using r

I wonder how to perform the z proportion test to check which COG category of Shewanella_sp_Alg231_23 is significantly high p (<0.05) from other genomes. To undersatnd I have attached a bar braph. <...
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### Testing if the difference of the sum of two distributions is significative

I have two distributions and I wish to understand if the difference of the sum of the elements sampled from these distributions is significative or not. I have set the problem this way: I have $n_{x}$ ...
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### Interpreting coeftest results; z-test; t-test, unfamiliar with the output

I am using coeftest to run z- and t- tests on a few different pieces of data. The output comes in this form: fit <- lm(dest_flood ~ type_flag, data = runsample) coeftest(fit) ...
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### McNemar test or Two proportion z-test?

Consider an experiment where a group of 200 people were asked before and after what is their preference, with possible outcomes being A and B. The research question is: Is there a difference between ...
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### Power analysis of group proportions when sample sizes cannot be guaranteed to be equal

I have a new UX feature, which I need to test out on users on a social media platform. When a user creates a post, he/she can add hashtags to gain community traction. As owners of the platform, we ...
1 vote
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### Two Sample Independent Test for Proportions (z test or t test)

Context: I have two independent samples that I want to compare for equality through an AB test. The metric being evaluated is binary: user clicks or not (proportions). Question: I keep reading that z ...