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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Statistical comparison between binomial distributions, two groups and many trials

I have a data set with two groups. I have multiple trials with different Ns in each trial, and different numbers of trials for each group. In each trial, for each ...
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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), ...
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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. ...
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18 views

Test of single proportion - how do i know population proprotion?

I have a study where I did a sample size calculation using N=2800, CI=95%, margin or error = 3.5% to yield n=613. In the study (auditing of charts), I wanted to look at the error rate in my sample. I ...
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38 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 ...
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Proportion test with null hypothesis p1=x*p2

I'd like to compare the proportion of two sets of binomial data where the null hypothesis is not p1=p2, or p1-p2=x, but \begin{equation} H0: p1=x*p2 \end{equation} I've been computing a z test as ...
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33 views

Comparing Means: Multiple Dependent Variables

I am using school-level data to compare mean scores for two groups (Group A schools and Group B schools), as measured by a series of indicators: 1) grade-level exam percentile, 2) percent of male ...
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52 views

Sample size estimation for test for proportions

I'm interested in finding out if a particular activity increases the chance of a particular segment of prospects converting to a client. I would like to be able to detect a 5% difference in overall ...
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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 ...
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Exploring a two-way interaction in multi-level regression, why do I get significant contrasts when the confidence intervals overlap on the graph?

I'm exploring a significant two-way interaction in a multi-level random-effects regression. The graph (below) appears to show the interaction is driven by differences at low X, and that at high X the ...
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32 views

Comparing differences of ratios in 2 independent populations

I have a setting that I think is quite similar to the one described in What type of statistic should I use to compare ratios in my experiment?. I have two independent populations, which were screened ...
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33 views

Z-test with a lot of null values

I have a question concerning the validity of my email tests. I'm testing different email variations (between 2 and 4 variations usually) with different groups of members (hundreds of thousands ...
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36 views

Strange two sample z test result in experiment

I performed an experiment on a virtual population wanting to see whether Vitamin C can positively affect performance on an IQ test. I gathered 80 people and grouped them into two groups of 40. ...
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132 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 $$ ...
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11 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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3answers
131 views

“The test statistic is reported as a z…”

I was reading a neuroimaging paper in which the authors compare the effect of a chemical compound on a measure of brain connectivity. They measure the value of connectivity for each brain voxel under ...
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49 views

1 sample z test of proportions

We are trying to work out whether what we currently do is accurate. We want to work out if a proportion (% scoring 5 on a 5 point scale) are significantly below a target score. Normally a 1-sample ...
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1answer
72 views

Significance of continuous variables

I have a table with several numerical continuous measurements and an indicator column catastrophy ...
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45 views

Statistics on tastings

Some people at my workplace have had some fun lunch discussion as of late, concerning some people's alleged ability to taste the difference between things one thought one shouldn't be able to taste a ...
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231 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 ...
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99 views

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 ...
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98 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: ...
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154 views

Why is P value interpreted under null hypothesis? [duplicate]

P value is explained very nicely in the link . But still i have not understood Why is P value interpreted under null hypothesis?
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Which statistical test should I use to compare two samples?

I have two groups and must conduct hypothesis testing by using an appropriate stats test. Seeing as I have 26 participants in each group, do not have the standard deviation (or any other information ...
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36 views

What type of test should be used?

What kind of test would I use to find the answer to this? Is there evidence that cereals promoted in an in-store circular have a higher average number of units sold per store than cereals not ...
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3answers
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Hypothesis testing - speeds before and after

I have the following data: ...
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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.
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Accuracy Assessment: Do I still have to use any other test statistics?

I have a training set and a separate test set. In both sets, I have extracted two different parameters and I have compared the predicted values of these parameters to the actual values. So, I have ...
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117 views

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 ...
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53 views

Hypothesis testing with multiple variables

I'm trying to understand the process behind testing both A/B site changes for statistically significant increases in conversion rate, and also how then to expand this to testing multiple variables. ...
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Z test could be a good choice ? and z-test for multiple samples?

I've two samples with mean value $\mu $ and standard deviation $\sigma$ (normal distribution). Can I use a Z-test to compare them ? Also if I don't know the sample size ? If I've five samples to ...
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110 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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Formulating a Z-test (or any other suitable test ) for survey data

I have a particular survey data related to a particular job. Out of a population of 90 people in this job, 36 people are in the lowest income group. 19 out of 36 people want to quit that job. I want ...
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44 views

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 ...
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How do we perform a two-tailed z-test when we *do* know the population mean of the intervention sample?

I am in the process of working through the Udacity course Intro to Inferential Statistics. In Lesson 9: Hypothesis Testing, the following example is given. Say that we record survey data from all ...
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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 ...
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1answer
361 views

Are pupils in a school independent and identically distributed when compared to a national population?

I am interested in the way in which data are analysed in education. In England, pupils' reported test results are compared to national test results using z-tests. These results are then used to judge ...
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43 views

Obtaining Cohen's d from z-test statistic

After an ANOVA, I run post-hoc tests with the glht function in the multcomp package. glht ...
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248 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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226 views

Power calculation of study using 2 sample z-test

This is not homework! I have two very different answers for a power calculation I have done on the below data - ...
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1answer
144 views

Difference between “common index” and “no common index”

I have been looking at the G*Power tool for Statistical Power Analysis but I am confused by the difference between two of the z-test options. ...
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582 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
223 views

Comparing sample proportion to population proportion

I have a data set consisting of a number of different hospitals. I am trying to compare the proportion for hospital X to the overall proportion in the data set (which includes hospital X). Should ...
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149 views

Alternative to Chow test for equality of estimates, when the data for the 1st group is not available

My goal is to compare published regression weights estimated from a sample in another country, with those of the same model established on our data.There is ample evidence on the web that a Chow test ...
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242 views

Xlstat and Pearson correlation coefficient: how are p-values calculated?

Someone asked me questions about his outcomes from Xlstat. Since I do not know this software at all, here is the question: How are p-values for Pearson correlation coefficients calculated ($H_1: \rho ...
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1answer
93 views

How can you derive the sample size to obtain a particular type II error rate?

I often see that the sample size for a $z$-test to achieve a particular type II error rate $\beta$ (at a given significance level, $\alpha$) is: $$n = ...
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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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733 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: ...
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2answers
269 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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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: ...