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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What is the intuitive explanation of the Z-statistic formula?

I am wondering if somebody could explain to me why the Z-statistic formula (for hypothesis testing) is derived as it is. Correct me if I'm wrong about my deductions: the numerator portion of the Z-...
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t-test for means of daily conversion

Let's say I'm a/b testing a new site version and want to know if it improves conversion. I realize that conversion is a proportion so I would use a Z-test for this. But then I am thinking - it is ...
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G*Power: Sensitivity Z-test, Compute non centrality parameter given alpha and power

I am using the Z test: Generic Z test, sensitivity tool. I have a distribution of values of the normal population sample with a mean and SD so I thought the non centrality parameter would give me the ...
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the role of MDE in a/b test analysis

I have a question about the role of the minimum-detectable-difference (MDE) in power analysis before the experiment is run and in post-experiment analysis. To clarify: suppose I am testing the ...
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Checking Statistical Hypothesis Testing

Let my dataset with $n=100$ samples have the sample mean $\bar{x} = 2.012$ and a standard deviation of $\sigma = 1.057$. Suppose that the data follows a normal distribution with variance $\sigma^2=1$....
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One sample t test or one sample z-test

I have a question as to whether the one-sample t test or the one-sample z test is appropriate in a sample of n=17 BUT with a known population variance. I would usually use a one-sample t-test for ...
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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 ...
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22 views

Accounting for different factors during construction of hypotheses

I am a beginner in statistics (we are using statistics in a Data Science introduction course) We are learning about hypothesis testing and we have been asked to write Python code to perform ...
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determining if ordering is random

Here's the question I was asked: look at the ordering of multiple choice answers a, b, c, d in a test of 100 questions and determine if their ordering is random - or uniform - pardon the terminology. ...
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z-test in statsmodel with known variance/std

To my knowledge: If I have a small Gaussian distributed data set and I know the true variance $\sigma$ of the data then the z-test is only appropriate if the standard deviation of the estimator is set ...
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51 views

How can I check if nominal and ordinal data is normally distributed (for z-test of proportions)

This section deals with concepts and procedures for testing inferences about proportions that involve the normal distribution. Following a discussion of the concepts related to tests of ...
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Am I right in calculating confidence interval?

Task: In voting 20% of people among 1000 voted "yes", how many "yes" voted will be among 1 million responders? My approach: Ground truth is distributed normally with ...
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Comparing proportions of 3 groups using chi square and z-test

I was wondering if my plan for analyzing my data was appropriate: I am trying to compare proportions between samples from 3 populations (N= 53, 54, and 56). I ran a chi squared test and found a ...
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what type of statistical test should i conduct?

I have data of past 3 years where i have every day sales of my product in my country. Now i want to conduct a test that can observe the difference in sales because of holiday period(almost 7 to 14 ...
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two sample z test in r

I am dealing with a dataset like this below ...
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50 views

When can we use a z-test instead of a binomial test?

I read from https://www.spss-tutorials.com/binomial-test/ and noticed that "So when can we use a z-test instead of a binomial test? A rule of thumb is that P0*n and (1 - P0)*n must both be > 5, ...
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Calculation of critical values

Are the critical values for the two-sample t-test with unequal variances calculated the same as for the two-sample z-test?
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Null hypothesis or alternative hypothesis

Actually I'm a bit confused how to choose my NULL hypothesis and how to choose the alternative one. suppose I have a sample of salary with mean 112,000 and I want to check if the population has mean ...
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I'm comparing multiple demographics across multiple samples, Chi-square test or 2 sample t-test

I would like to compare the demographics of people my company serves with the demographics contained in a subset of the American Community Survey 2017 data. The first set (n=35751) of data is a person-...
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56 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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Are there any problems with using an average of percentages for a 2 proportion z-test?

Let's say I have a 2 groups of test scores (ranging from 0% to 100%), and I wanted to compare their means to see if there was anything significant. I know I can average the test scores to obtain a ...
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How do I calculate sample sizes for multiple proportions, while maintaining a certain ratio of the sample sizes?

I am trying to perform z-tests for multiple proportions, while maintaining a certain ratio of the samples. For example, let's say I'm trying to compare 3 populations, and I want to maintain the ...
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14 views

Null hypothesis test for proportions without minimum requirements? [duplicate]

I have a typical dataset: sample A (method A) which has 200 samples and 25 failures. sample B (method B) which has 240 samples and 0-10 failures. Note that 0 failures is possible. Null hypothesis is ...
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36 views

Comparing z-values

If a test-statistics is expressed in z-values (instead of, for example, t-values), would it be appropriate to use those values for some further inferences? For example, to average a pair and another ...
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Statistical comparison of 3 relative survival values

I have to compare relative survival (have 5-year estimates with SEs and patients number per group) across 3 time periods. Cannot use log-rank etc as (probably) it is impossible to operate with raw ...
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What A/B test calculator can I use to calculate the minimum same size for uneven split between control and treatment groups?

I have only come across A/B test calculators that give the minimum sample size per variation for 50-50 split between control and treatment. I am running an A/B test for conversion rates with a 80/20 ...
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What test to use to compare two proportions (and calculate effect size and confidence interval)?

There are many related questions here and elsewhere, but I found no satisfying answer. There are plenty of related tests and concepts: Z-test, chi-squared test, G-test, McNemar's test, Fisher's exact,...
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why can you perform t-test with the critical values of normal distribution? [duplicate]

I have estimated parameters and I want to check if they are significantly different from zero by using t-test. But since I have a large sample, I know I can compare the values with the critical values ...
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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 ...
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1answer
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If sample standard deviation is biased, why do we use it in typical mean tests? [duplicate]

If sample standard deviation is biased, why do we use it in typical mean tests? Why do we not use an unbiased estimator by dividing the sample standard deviation by C4?
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One sample T test or Z test?

Given is an internet provider stated that the expected speed is at least 90 Mbit/s and the standard deviation is at most 5 Mbit/s. How there is a sample given with a sample mean of 88.36 and sample ...
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How to identify the difference in significance of two different z test for two proportion test?

I have two cell types (A and B) in a tissue. I have 5 replicates of RNA sequencing data in control and treatment condition for cell type and B separately. We are interested in identifying genes which ...
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40 views

one sample z-test standard error

Let's say I make the claim that 9 out of 10 dentists recommend a tooth paste. Next, I can ask 1000 dentists, and let's say that I find 700 / 1000 acually recommend it. so here $p_o = 0.9$, and $p = ...
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Required sample size to reach adequate power of a test

We got two types of treatment (type 1 and type 2). In our opinion, type 2 treatment has a higher performance and we would like to show this with research. We assume that type 1 treatment has a maximum ...
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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 ...
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Proportion Test: Z-test vs bootstrap / simulation - different results

I'm learning hypothesis testing, and going through the following example: The CEO of a large electric utility claims that 80 percent of his 1,000,000 customers are very satisfied with the service ...
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31 views

Significance of the difference between means

I am running an experiment on students in two of my classes. There is an online class vendor that promises higher test scores with only 2-3 hours more work per week. I decided to give one of my ...
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56 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? ...
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1answer
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Help with calculating number of animals for a fetal surgery experiment

Rather odd question. I'm a surgical resident who is currently a research fellow in a lab studying fetal surgery. Our plan is to test a glue which we believe will help seal a uterus after we open it to ...
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126 views

siginificance testing of cosine similarity between word pairs from word embedding

I want to perform a significance test between two pairs of word embedding generated using Skip-gram model, as to how significant their cosine score is from mean similarity score. In order to do that I ...
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Accounting for factors that could be driving a difference between two means

just restarted data analysis so I've lost my edge quite a bit. Anyway, I've come across a problem and Im a bit stumped. I have a dataset for adverts. I want to measure the uplift in conversion ...
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Where is my potential flaw in my Z-test of Proportions?

I was working through this z-test of proportions example I found online. The online example solutions says that the difference between the groups is statistically significant, whereas I concluded it ...
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In a card game, how to check if hand patterns are fair?

I'm playing contract bridge and the boards are dealt by a machine. Last time, one of the player suggested the boards are not dealt at random and I want to check that. At contract bridge, each player ...
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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. ...
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Mean Sickness Absence at different company sites statically significant ? T-Test, Z-Test?

I'm relatively new to stats so apologies if this is rather trivial but I cannot find an answer (I work in the workforce information dept of a largish company). We have 10 sites, and I calculate the %...
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254 views

2 sample Z test for non normally distributed data

I'm trying to analyse the impact of a marketing campaign and I'm looking to identify the most appropriate statistical test. I have one group of customers who received the campaign (approx 100,000 ...
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45 views

One-Sample Test for differences between questionnaire-answers

For a rather large sample (>800 participants) I have answers from a questionnaire, containing multiple Yes/No-Questions. What I want to find out is, if the proportions of yes & no's differ ...
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Standard normal intuitive understanding

What does it mean for a standard normal to have mean 0 and standard deviation 1? I'm having trouble understanding - what is a "normal variable"?
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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 ...