This is a simple z score calculator that calculates the value of z (and associated p value) for two population proportions.
Further Information
The z score test for two population proportions is used when you want to know whether two populations or groups (e.g., males and females; theists and atheists) differ significantly on some single (categorical) characteristic - for example, whether they are vegetarians.
Requirements
- A random sample of each of the population groups to be compared.
- Categorial data
Null Hypothesis
H0: p1 - p2 = 0, where p1 is the proportion from the first population and p2 the proportion from the second.
As above, the null hypothesis tends to be that there is no difference between the two population proportions; or, more formally, that the difference is zero (so, for example, that there is no difference between the proportion of males who are vegetarian and the proportion of females who are vegetarian).
Equation
Sample Size Calculators
for designing clinical research
This calculator uses JavaScript functions based on code developed by John C. Pezzullo.
This project was supported by the National Center for Advancing Translational Sciences, National Institutes of Health, through UCSF-CTSI Grant Numbers UL1 TR000004 and UL1 TR001872. Its contents are solely the responsibility of the authors and do not necessarily represent the official views of the NIH.
Please cite this site wherever used in published work:
Kohn MA, Senyak J. Sample Size Calculators [website]. UCSF CTSI. 20 December 2021. Available at //www.sample-size.net/ [Accessed 18 October 2022]
Software utilities developed by Michael Kohn.
Programming and site development by Josh Senyak at Quicksilver Consulting
Thanks to Mike Jarrett at quesgen.com for an early version of this site
Graphic design by Emanuel Heim Design
This site was last updated on December 20, 2021.
Instructions: Use this step-by-step Confidence Interval for Proportion Calculator, by providing the sample data in the form below:
Confidence Interval for a Population Proportion
A confidence interval is a statistical concept that has to do with an interval that is used for estimation purposes. A confidence interval has the property that we are confident, at a certain level of confidence, that the corresponding population parameter, in this case the population proportion, is contained by it. For the case the population proportion (\(p\)), the following expression for the confidence interval is used:
\[ CI(\text{Proportion}) = \displaystyle \left(\hat p - z_c \sqrt{\frac{\hat p (1-\hat p)}{n}}, \hat p + z_c \sqrt{\frac{\hat p (1-\hat p)}{n}}\right) \]
where the critical value correspond to critical values associated to the Normal distribution. The critical values for the given \(\alpha\) is \(z_c = z_{1 - \alpha/2}\).
The basis for this confidence interval is that the sampling distribution of sample proportions (under certain general conditions) follows an approximate normal distribution.
Assumptions that need to be met
It is crucial to check for the assumptions required for constructing this confidence interval for population proportion. In this case we need the normality assumption, which is required because ultimately we have a binomial variable involved, so certain assumptions are needed. Typically, we require that \(n \hat p \ge 10\) and \(n (1-\hat p) \ge 10\).
Observe that if you want to use this calculator, you already need to have summarized the total number of favorable cases \(X\) (or instead provide the sample proportion). This is not a confidence interval calculator for raw data. If you have raw data, you need to summarize it first.
Notice that this calculator works for estimating the confidence interval for one population proportion. When you are dealing with two population proportions, what you want is to compute a confidence interval for the difference between two population proportions .
Other Calculators you can use
You are probably interested in calculating other confidence intervals. For example, you can use our confidence interval for the mean , or this confidence interval for variance when mean is known , or you can also this confidence interval for mean regression responses , as well as our calculator for a confidence interval for the variance .
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