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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 don't we need to use a t-distribution for difference of proportions tests? [duplicate]

In difference of proportions tests we use a Z-distribution. And in Chi square tests which I understand are in practice the same test use the square of the Z-distribution, the Chi square distribution ...
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Statistics to show the differences in population of the sample and city and by sex

Hoping for some help. I am trying to run some statistics for demographics from the results of a survey. I have male/female percentages as a result of the survey (45.1/54.9) compared to male/female ...
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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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Intuition on Linear Discriminant Analysis and Z-Test/T-Test

I am trying to get into Linear Discriminant Analysis without getting too much into linear algebra and also having a lack of geometric fantasy. To obtain an intuition of whats going on, I just want to ...
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36 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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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 ...
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1answer
24 views

Find if two groups are different where one is a subset of the other

I have a dataset of 3,500,000 categorical observations that can be grouped by an ID. In these categories u occurs 25,000 times. How can I test to determine if a ...
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P-value and confidence interval in MVT testing

Context: website A/B testing When calculating P-value and confidence intervals for each variation in an experiment with more than 2 variations (control, variation 1, variation 2 ...) should there be ...
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chi2 + z-test not yielding the same results?

With a 2x2 contingency table, I believe a chi2 test should be equivalent to a z-test -- from Wikipedia: "Two-by-two contingency tables: When the test is applied to a contingency table containing two ...
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methodology to analyze differences between groups

My dataset (n=2,000) shows total daily sales and I can plot a trend and show via a s-test that the average number sales is different in 2016 vs 2017. I also have the information in the data indicating ...
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1answer
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What hypothesis test should I use to compare the overall performance of two different athletes in a 100m race?

I am sourcing data from IAAF's website to test my hypothesis - Athlete A is a better athlete than Athlete B (comparing their times in the Olympics). Since I would be sourcing the data from IAAF's ...
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34 views

Help regarding calculating z statistic and p value

I am trying to solve a problem but couldn't see any way around it. So far, here is the progress $\mu_{pop} = 10 $ $\sigma_{pop} = \sqrt12$ $\mu_{sample} = 12$ $z = (\mu_{sample} - \mu_{pop})/(\...
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One-Sample z-Test

this is a really simple problem but I'm still in doubt about the solution. There's a population of workers and the goal is to see whether the rate of illegal workers has dropped to 20%. I have a ...
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Why does it says data should be normally distributed for analysis, when different test follow its own distribution (i.e. t, Z, F)?

Why does it say data should be normally distributed for statistical analysis when different test follow its own distribution (i.e. t, Z, F)? What does normality have to do with this?
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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 ...
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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 ...
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Statistical significance of a difference between poll percentages with a small sample?

Analyzing my company’s internal survey results, I was stuck with calculating statistical difference between percentages. I usually used a Z-test as described below, but I am not sure whether it is ...
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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 ...
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54 views

How to do hypothesis testing for two different counts?

I have the following problem: in year A, we observe that a company sold N_A of its product, in year B, we observe that the company sold N_B of its products. How do I do hypothesis testing that the ...
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Simple question about difference of two proportions testing

It is usually explained in biostatistics textbooks that to do a z-test for the difference of two proportions, it is necessary that p*n and (1-p)*n are both equal to or above five for both samples. ...
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Calculate Z score from the Confidence level [duplicate]

How to calculate Z score from the confidence level. I have this small table, but I need the values for all confidence levels (integers from 0-100). Is it possible to somehow calculate the values or ...
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What is wrong with one tailed z-tests for a proportion?

After answering How to analyze observed vs expected when expected is just a proportion? by suggesting that the OP uses a one tail Z-test for their proportion data, I got into a debate in the comments ...
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297 views

Z-score computing for two sample proportion comparison

Assume I aggregated the following results: ...
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1answer
277 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 ...
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most appropriate statistical test z/t test or Chi square/Fischer exact - Cognition test between genders over period of training?

My data is from four years of students with an equal number of boys and girls of the same age per year chosen. The purpose of the test is to evaluate the influence of training on a certain cognition ...
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238 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 ...
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1answer
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Hypothesis testing question — how to define the null hypothesis to draw a conclusion

Here is a hypothesis testing question I'm trying to work out but am struggling with how to draw a conclusion, maybe I'm not defining the null hypothesis correctly. The question is as follows: Test ...
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1answer
41 views

Can I use a Z test?

Can i use a Z test for 2 proportions for the following data? I have 2 samples - male (N=33) and female (N=51) Within the male sample no-one tested positive for a particular attribute. 33 Tested ...
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Can I use z test for a sample that have no outliers?

but I am not sure whether population is normally distributed, standard deviation of population is known. I am measuring national accounts of different countries. Population consists of 183 countries(n=...
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23 views

correct test for comparing proportions across groups

I have 2 overall groups A, B. In both A and B, I have 3 individuals, each scoring a certain percentage on a test. If I want to compare the scores across group A and B, is the correct process to sum ...
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272 views

Sample mean Margin of Error and C.I [closed]

I have data on the mean assembly costs for the first n=36 days of production. It is assumed that the following data follows a Normal distribution: ...
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164 views

What is the Appropriate Test to Compare Pearson's Correlation Coefficient?

Let say I have this simplified data set which contains four variables (2 categorical, and 2 numerical types): ...
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62 views

Reason for the appropriateness of the z-test for linear regression slope check

I know that the z-test can be used to compare the slopes of two regression lines (lines fitted to two separate data sets). What I do not understand is WHY we can use the z-test for that? Therefore I ...
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What is the method for solving an equation in which a data set is compared with a “standard” with a known mean and variance?

For my homework, I have been asked to solve the following question: Suppose Wal-Mart had to pave over a valuable wetland to make room for a new Super-Store and associated parking lot. In obtaining ...
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80 views

Calculate power of t test?

I was wondering how you would calculate the power of a one sided and two sided t test and whether it differed from the z test. I know for a z test it is $p(z < z_{alpha} - abs(u_{a} - u_0)/(s/sqrt(...
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Should I be using Z-tests or T-Tests for my scientific data?

I've conducted a survey for my thesis where I ask a series of questions of the format: A statement relating to the experiment Then the participants answer ...
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1answer
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z-test for one population proportion hypothesis with a small sample size

I have asked a "yes/no" question to a small group of people (n = 22). From the 22, 14 answered "yes" and 8 answered "no". I'd like to find out, with 90% confidence, if the majority of my population (> ...
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336 views

Comparing distribution of sample proportions to population proportion

I'm trying to find out whether there is a statistical method for comparing a distribution of sample proportions to a distribution of population proportions. For example if I have only two groups, A ...
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308 views

Which statistical test should I use (comparing two cohorts)?

So I am doing some research in the field of Medical Physics, in particular radiation treatment with photons and protons. Now, I have two cases I am unsure about. 1) Here I have several patients. ...
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141 views

algorithm for testing a variable

I want to test if a quantitative variable is different in 2 groups. As for what I understood so far, here is the algorithm I should use : if the length of my 2 subgroups are >30 --> z-test else, ...
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245 views

How do I interpret a negative Z-test (two tailed for 2 proportions)?

I used my calculator to do a two tailed Z test for two proportions. Here's the data I input: X1 is 834 n1 is 3610 X2 is 145 n2 is 495 I chose p1 not equal to ...
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73 views

What would be appropriate test to compare two lists of dichotomous variables?

Colleagues, can't wrap my mind on simple question, please help! I have two products and list of their attributes. My respondents make an answer which product on each attribute they prefer. Finally ...
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1answer
1k views

Z-test for One Population Proportion

I am completing a series of questions for this problem and I think I am following but one throws me off. The problem is a common one: In a study of smokers who tried to quit smoking with nicotine ...
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2answers
323 views

Is there a non-parametric equivalent of the t-test for a small sample size?

I have weather stations collecting data (temperature, humidity, solar radiation, wind, etc.) inside and outside low-tech greenhouses. Four of the weather stations are inside, and one is outside. I am ...
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232 views

How to test statistical significance between percentages obtained at two intervals from single sample

I conducted a study on faculty improvement programs, whether they had an impact on teaching practices of faculty members. Sample size was 15. One of the categorical variable observed was 'Is the ...
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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 &...