# 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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### Can I statistically describe a single case/outlier vs. a distribution?

I have a dataset consisting of body weight and corresponding age for a bunch of healthy subjects (grey triangles below). I fit a nonlinear function to this data and graphed a 95% prediction interval. ...
2k views

### Z-Test Versus Chi-Square Test

I need to test whether response rate for Test B is larger than response Rate for Test A (i.e. AB Test). Null Hypothesis: is Response Rate (Test B) <> Response Rate (Test A). Alternative ...
58 views

### What distribution does $\frac{\hat p -p_0}{\sqrt{p_{0}(1-p_{0})/n}}$ have?

Suppose we're testing whether more than $100p_0$% Bernoulli trials are successful at the $\alpha$% significance level. We take a sample of $n$ Bernoulli trials and find that $\hat p$ trials are ...
372 views

### Required size of control group for two-proportion z test

How do I determine, pre-experiment, the minimum size of a control group that would be needed to satisfy the requirements of a two-proportion z-test? $p_i=\frac{k_i}{n_i}$ is the proportion of ...
2k views

### Why t-test of correlation coefficient can't be used for testing non-zero?

t-test of a correlation coefficient is used for testing the sample correlation against population correlation of zero. To test an assumed value of the population coefficient other than zero, we should ...
893 views

### Permutation for large sample sizes (and z-test)

I was trying to do a permutation test on a large amount of temperature observations in R. Approximately 1700 temperature observations (g1) from one place and 2 ...
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### When to use Chi-squared and when Z test for categorical variables?

The problem is: There was a survey conducted among 1137 adults from California, Nevada, and Oregon. They were chosen randomly and they answered to the following question “Do you think Marijuana ...
240 views

### lower tail z-test

This is an exercise from Freedman, Pisani and Purves’ Statistics, 4th ed. (p. 552/8) An investigator has independent samples from box A and from box B. Her null hypothesis says that the two boxes ...
38 views

### Good resources for derivations of statistical significance tests

I am looking for a good resource to deep dive into mathematical derivations of statistical significance tests such as z-test one-sided two-sided t-test pair-wise t-test etc. I can find many ...
550 views

### Test difference of population proportion and weighted sample proportion

I want to test for differences of the known proportion of the population vs. the proportion of a sample. The sample is weighted by sampling weights. The sum of weights is equal to the size of the ...
401 views

### Z-test question: why variance between population and sample assumed as equal?

Example from Wikipedia: Suppose that in a particular geographic region, the mean and standard deviation of scores on a reading test are 100 points, and 12 points, respectively. Our interest is ...
166 views

### Compare two population means at different time point

I am trying to determine the change in the size of a population during a 20 year period using two scenarios. I run the model for each scenario 100 times under different random seeds and then take the ...
638 views

### How would I determine statistical significance for ad impressions?

I'm programatically adding keywords to bid on. Some keywords will trigger ads and impressions, and some impressions will trigger clicks. Clicks / impressions = CTR (click-through-rate). Clicks cost. ...
40 views

### How to compare two PROPORTIONS if you don't have 'n'?

Have data in this format: | A | A' | B | B' | |-----|-----|-----|-----| | 0.4 | 0.2 | 0.4 | 0.3 | | 0.3 | 0.3 | 0.3 | 0.5 | | 0.1 | 0.2 | 0.6 | 0.2 | Note ...
899 views

### Deriving the power formula of the one-sample proportion test

I have to derive the power of the z-test in testing $$H_0: \pi=\pi_0 \text{ versus } H_1: \pi>\pi_0$$ Denoting by $p$ the sample proportion, the power equals  Pr\left[\frac{p-\pi_0}{\sqrt{\frac{...
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### Difference test for beta–binomial variables

Let $X \sim \textrm{Beta–Binomial}(\alpha_1, \beta_1, n)$ and $Y \sim \textrm{Beta–Binomial}(\alpha_2, \beta_2, n)$ and write $\mu_1 = \frac{\alpha_1}{\alpha_1 + \beta_1}$, $\phi_1 = \alpha_1 +\beta_1$...
178 views

### Most appropriate tests for online advertising significance data

We are running ads and want to construct two Excel formulas, one calculating the p-value for every other ad vs the one with the highest CTR (click through rate) and another that compares the CPA to ...
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### Could z-test test percentage difference between means of two sample groups?

Problem: I have two sample groups(A and B), each with more than 30 samples. I want to know if the mean of A is 5% more than mean of B. Is z test a proper way to go here? Online I found most of z test ...
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### Testing a linear combination of coefficients: t-test or z-test?

I am running a Seemingly-Unrelated-Regression (SUR) for 80 banks using Stata’s -sureg- command. local subsetvar HSBC-UBS ...
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### Statistical Significance of survey

I recently conducted a survey comparing the generated responses of 2 chatbots. Each participant was asked to complete two tasks: Select a generated response as "best" between 2 generated ...
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### can a whole population sample be considered a random sample? I want to do a z test for 2 population proportions

I want to do a z-test for 2 population proportions to test if the two populations have different probabilities of developing a condition like it says here https://www.socscistatistics.com/tests/ztest/...
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### Not sure about T test's sample size

I have a dataset that has when a user clicked over a period of 31 days in an app. Its possible that all users won't have 31 days of clicks as they might not be using the app on a particular day. The ...
25 views

### Test for a difference in an outcome across 2 groups

I have a dataset of hospital visits across multiple hospitals. One group of hospitals had a special program ‘A’ whereas the other group did not have this program. For each group, I have a percentage ...
73 views

### Comparing multiple models across multiple groups or populations

Say I have a series of different regression models (e.g. 8 different models) which I conduct using data collected at a series of multiple locations (same predictor same response variables) and I have ...
124 views

### Assumptions on the variance of the null model in one-sample Z-test?

Apologies if the answer to this is obvious, but I can't understand why the usual interpretation of the p-value (probability under the null model of obtaining a test statistic at least as unlikely as ...
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### Z-test for comparing two estimator values?

My supervisor asked me to compare values of Pohar Perme estimator of net survival in two regions of the country using Z-test. Am I right that we cannot use Z-test for comparing these estimator values? ...
59 views

### Normality assumption for t/z tests

I have what is probably a silly question regarding normality assumptions for t/Z tests. As I understand, t/z tests require that sample data was obtained from populations following a normal ...
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### z test for sum of two percentages as greater than 100

I have a data set in which participants made a choice between two options--option A and option B. Participants were assigned to either choose an option or reject an option (so, there are two ...
1k views

### Determining samples sizes for an A/B test using z-test and chi-square test

Assumptions I consider an A/B test where there is a control group and a variant group. Each observation can either be true (converted) or false (not converted). I evenly and randomly split the ...
368 views

### One sample proportion test for weighted data

I have a sample of observations (n) representing individual evaluations (positive/negative) of pieces of text (n texts). Each individual can evaluate more texts (thus there are m individuals with m &...
92 views

### comparing 2 population proportions

What are the methods to compare proportions from 2 independent populations i know we can use the z-test or t test for comparing 2 proportions what about Miettinens & Nurimens Liklihood Score ...
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### SPSS Categorical Data: Residuals in Crosstabs

I would like to know what's the difference between the standardized residuals and the adjusted standardized residuals in cross-tabs cell display in SPSS? The following definitions are the ones that ...
71 views

### Why do we use the equal-means assumption in estimating the SE in a z-test but not a t-test?

When we perform a z-test for the difference in proportions between two groups of binary data, we use the fact that under the null hypothesis the proportions are assumed equal in order to estimate the ...
171 views

### Power of simulated data (Monte Carlo) and sample mean

Let's say I have sampled all adult males (N=30) and females (N=25) in a group. There is a property (z) that emerges from pairing male A with female B. I run a Monte Carlo simulation of size 25 (every ...
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### Student t-test and z test are equivalent as $\nu \rightarrow \infty$

I would very much appreciate if someone can give me an idea of how to solve this exercise. I need to show that the t-test and the z-test are equivalent when $\nu$ (degrees of freedom) tends to ...
185 views

### Sample Sizes and Z-Test for Proportions

I am investigating animal behavioural states using Markov Chains, and want to test differences in the transition probabilities between my control and impact groups. However, I’m worried about small ...
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### Compare pairs of binomial populations

I have data from smokers people in different countries and through different years. $X_i$ can be viewed as a Bernoulli R.V. where $X_i=1$ if the person smokes and 0 when it does not. The smokers in ...
69 views

### Joint proportion test on binomial panel data

I'm trying to run a hypothesis test on panel data, where in each period $t_i$ an event $X\in \{0,1\}$ either does or does not occur for each of the entities in the panel. I'm trying to determine ...
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### How to interprete logistic regresion using Eviews having dummy variables

i need your help with logistic regression analysis. My dependent variable is a dummy variable: 0 fails 1 successful. Method: ML - Binary Logit (Newton-Raphson / Marquardt steps) variables and ...
339 views

### Appropriate Correction for 2 proportion test? --with example--

Below is an example of frequency data between observed and expected proportions. Can I simply run a 2-Proportion z test here? Or, would I be violating assumptions? If I were to run dozens of z tests (...
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### Two-proportion z test: is it best for my problem, and can I pool data from multiple "replicate" populations?

I am examining populations (cultures) of yeast cells and scoring them for a particular trait. The data is categorical; within a population, a yeast cell either has the trait or it does not. I wish ...
78 views

### Using a general linear model to perform z-test

I am trying to perform a z-test with a brain-imaging software. I was told that the best way was to use a general linear model with one subject in one group and the rest in the other group. Using this ...
16 views

### Best statistical test for aggregated group rate vs individual rate?

I'm looking to test the difference between an aggregated group weight (weighted average) vs an individual group rate? For example: Let's say we have 4 companies: A - 35/60 = 58% B - 120 / 400 = 30% C -...
11 views

### Determine which independent variables are relevant by examining probability distributions?

I am looking to simulate patient outcomes from a data set that contains patient data such as age, diagnosis, some clinical variables, survival time after treatment and so on. My plan was to use a ...
14 views

### I have calculated relative risk in SPSS with 95% CIs via a 2x2 table, but how do I then calculate the p value?

I have calculated relative risk in SPSS with 95% CIs via a 2x2 table, but how do I then calculate the p value? I thought I could use a two-tailed z test but can't seem to work it out
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### Why does a two-sample proportion test with outcome Y and predictor X give the same result as one with outcome X and predictor Y?

I just noticed, while playing around in Stata, that this is the case, at least with three pairs of variables I tried out, which makes me think there must be some real relation there -- the z-statistic ...
38 views

### Hypothesis Testing and Z-test for happiness at work

I'm doing a school project and decided to look closer into this COVID-19 thing that is obviously going on at the moment. I have a hypothesis that people in teams (at work) are happier at work after ...
49 views

### Propotion test vs T-test

Proportion test - Helps to identify if there is significant difference in proportion across the samples.(i.e. the values are in proportion and denominator is in sample size of entire proportion) ...