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 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 ...
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Statistical test for one sample proportions

I am carrying out a study into the handedness of racehorses. There are clockwise and anti-clockwise racecourses. I want to test to see if 1) horses are more likely to win if they are left handed on ...
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41 views

Testing variables in meta-analysis

I am conducting a meta-analysis of cognitive-behavioural interventions on self-esteem and I could use some assistance navigating through the statistical procedures. I have extracted pre-post scores ...
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30 views

p-values in sign test

If we are given a list of $n$ independent measurments $\{0,0,1,0,1, \dots, 0,1,1,0,1\}$ of binomially distributed random variable $X$, we can use the sign test to check, whether the difference between ...
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38 views

Implicit assumption in z-test of difference in proportions?

In reading through the literature on z-tests for difference in proportions, I often see it stated that the null hypothesis only tests whether p1 = p2, not whether p1 = p2 = any specific value for the ...
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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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32 views

How to measure extraneous and confounding variables?

The test-re/post/test methodology entails establishing a baseline, introducing a condition and measuring the effect size. The condition is known. But whether or not it yielded some changes, is what ...
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65 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 ...
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60 views

How to test if a sample proportion matches a population proportion, should I use the z-test or the t-test?

For (a), $H_0 = 0.75$ and $H_a \ne 0.75$. For (b), how can I get an answer with a $z$-value? Why can't I use a $t$-value to answer this question? Is the idea: $p \pm Z (p(1-p)/N)^{0.5}$?
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How do I test difference in Percentages?

I have some survey data and know the number and percentage of "yes" responses. How do I determine if any of the percentage yes regional responses are statistically different from the national yes ...
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1answer
52 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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Z-test question: why variance between population and sample assumed as equal?

Example from wiki: 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 in ...
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Comparing binomial outcomes from prediction algorithms in R

I've written a simple model to predict the outcome of soccer games based on some input. The outcome is either "H","D",or "A", short for home team, away team, or draw. I'm comparing the results of this ...
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240 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 ...
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Chi post-hoc OR Z cell comparisons: do 2 proportion z-tests indicate most significant factors?

Attached is an example of some data I'm working with. I'm testing the occurrence of a rare behavior, while controlling for both education and the "bin" variable. The observed sample size is 129. This ...
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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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35 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 ...
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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 ...
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58 views

Can someone explain what 'comparative error rate' is?

I have a set of rates of conversion for two different groups of ads. The rates are calculated by dividing conversion/impression (or, more simply, purchased/seen ad). I did a t-test for the ...
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85 views

Contradiction between confidence intervals and Z-test

I've got the problem with Z-test and confidence intervals. Z-test rejects null hypothesis (proportions are equal), but confidence intervals are intersect. Let us consider 2 companies. The proportion ...
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Can I do a z-test if population standard deviation is unknown?

Edited: Suppose I'm trying to compare a sample of 45 articles drawn from a population of 5,000 to see if there's a significant difference between the sample and population means. The population ...
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Chi square test vs z test

I have got results for a survey and was wondering which test I should use to show there is a significant difference in my results. It is a survey on apple charger breakages and other phone charger ...
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Difference in hypothesis testing using p-value and confidence interval

I have a simple problem The sample population is 384 people and $12$% of it have a disease. The hypothesis is that $5$% of the real population have a disease. So, $H_0: \mu = 0.05$ and $H_a: \mu \...
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What happens if I use Z-test instead of T test?

I know that when sample size goes large, they basically give the same result. My question is that what happens if I use z-test instead of t-test when sample size is not large. I guess the type I ...
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Z-test or t-test: Which is more appropriate for this situation? [duplicate]

We are monitoring the performance of a network using several KPI's. We want to detect if there are any anomalies for a KPI X within last hour for which we obtained (usually) 30 values from the last ...
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Finding if the coefficients are significantly different from each other

I have a dataset which is segmented into two independent groups. I used multinomial logistic regression to estimate the coefficients corresponding to explanatory variables in both the groups. The ...
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39 views

How to test if proportions are the same across categories?

I am working with collision data and want to run a few tests. I thought a chi-square was what I wanted, but it doesn't let me say what I want to. Then I thought a z-test of two proportions was what I ...
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How to test a sample proportion against a known population value?

Say someone makes the argument "people who wear blue shoes steal more bananas." Then as proof they say, "the total population of blue shoe wearers is 30% of the population. Out of a random sample of ...
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A/B testing on Revenue: what test to use

For testing on ecommerce websites: If you do an A/B test and not only look at conversions, but also want to track if there is a significant increase in average order value and/or total revenue: what ...
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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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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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226 views

Calculating p-value from beta and se_beta

I have a set of beta and se_beta values that I would like to calculate p-values for. I know this should be possible via a z-test, but I don't understand how it works and how to implement it. Any help ...
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Proportion z test for predictive model

I have deployed two models, the baseline one which only includes historical data of a stock market index and the twitter model which includes both historical data of the index as well as significant ...
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Testing the Validity of a Test Statistic (incorrectly)

In this post @Wolfgang shares a few lines of code to test in a simulation the ability of a particular test statistic to perform as expected, measured by the percentage of type I errors. He shows by ...
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Z-test and confidence intervals for mutual information

Given two discrete random variables $X,Y$, I would like to obtain confidence intervals for the Mutual Information $I(X;Y)$ and a p-value for the null-hypothesis that $X,Y$ are independent. I would ...
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2-Proportion Z-Test

I want to compare, with 2-proportion Z-Test, the number of student visits to school nurse office in Q1 of 2015 to Q2 of 2015. What do I use for sample size for Q1 and Q2 when it’s different each ...
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Why does changing the null hypothesis change the confidence interval?

Using my stat calculator, I don't see why if I do two different tests with everything the same but the null hypothesis, the confidence interval is different. For example: Has a different CI from ...
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What follows if we fail to reject the null hypothesis?

What conclusions can we draw if $p>\alpha$? Does not rejecting the $H_0$ mean anything?
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Z-test and sampling distribution

The basic trick behind the z-test is the "sampling distribution". The "sampling distribution" is the distribution of all means of all samples. So what we are interested is: if the population means ...
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One variable multiple treatments

I'm drawing a blank on how to analyze this data. I've got one drug/treatment type (variable) with multiple answer options (4 to be exact) and I'd like to compare the answer options for significance. ...
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229 views

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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1answer
101 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 ...
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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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34 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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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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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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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 ...