95% confidence interval for difference in proportions calculator

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0.95 0.99 · Group Allocation ............................................ Equal (N1 = N2) Confidence Interval Width (Two-Sided) ......... 0.05 to 0.30 by 0.05 · Input Type ...................................................... Proportions · P1 (Proportion Group 1) .........................

Statology

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Confidence Interval for the Difference in Proportions

June 23, 2020 - This means that, for example, a 95% confidence interval will be wider than a 90% confidence interval for the same set of data. Suppose we want to estimate the difference in the proportion of residents who support a certain law in county A compared ...

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statskingdom.com › two-proportions-ci-calculator.html

Proportion confidence interval calculator - normal approximation, Clopper–Pearson, Wilson score interval

Confidence interval calculator for the difference between two proportions with calculation steps, using the normal distribution approximation.

Vassarstats

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Confidence Interval for the Difference Between Two Independent Proportions

The Confidence Interval for the Difference Between Two Independent Proportions · This page will calculate the lower and upper limits of the 95% confidence interval for the difference between two independent proportions, according to two methods described by Robert Newcombe, both derived from a procedure outlined by E.B.Wilson

Statistics LibreTexts

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9.1: Two Proportions - Statistics LibreTexts

January 6, 2022 - It is different from the formula or the TI-83/84 calculator due to a continuity correction that R does. 4. Statistical Interpretation: There is a 95% chance that \(0.0505<p_{1}-p_{2}<0.1182\) contains the true difference in proportions.

Study.com

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How to Create a Confidence Interval for the Difference in Proportions of Two Independent Groups | Statistics and Probability | Study.com

Step 8: Calculate the upper bound of the confidence interval by adding the MOE to the difference between the sample proportions. ... Step 9: The confidence interval is (0.120, 0.380). We are 95% confident that the true difference in population ...

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Confidence intervals for difference in proportions

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Stat Trek

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Confidence Interval: Difference in Proportions

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Previously, we described how to construct confidence intervals . For convenience, we repeat the five steps below. Choose the confidence level. The confidence level describes the uncertainty of a sampling plan. Often, researchers choose 90%, 95%, or 99% confidence levels; but any percentage can be used. Compute the standard deviation or standard error. The standard deviation (SD) and the standard error (SE) for the difference between proportions can be calculated ...

Published February 3, 2025

Penn State Statistics

online.stat.psu.edu › stat200 › book › export › html › 193

9.1 - Two Independent Proportions

Confidence Interval for the Difference Between Two Proportions · \((\widehat{p}_1-\widehat{p}_2) \pm z^\ast {\sqrt{\dfrac{\widehat{p}_1 (1-\widehat{p}_1)}{n_1}+\dfrac{\widehat{p}_2 (1-\widehat{p}_2)}{n_2}}}\) A survey was given to a sample of college students. They were asked whether they think same sex marriage should be legal. Of the 251 women in the sample, 185 said "yes." Of the 199 men in the sample, 107 said "yes." Let’s construct a 95% confidence interval for the difference of the proportion of women and men who responded “yes.” We can apply the 95% Rule and use a multiplier of \(z^\ast\) = 2

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Confidence Interval for the Difference in Proportions Calculator

April 21, 2020 - To find a confidence interval for a difference between two population proportions, simply fill in the boxes below and then click the “Calculate” button. ... You can be 95% confident that the interval [0.0236, 0.2964] contains the true difference ...

reddit.com › r/askstatistics › how to generate the confidence interval for difference between control and test proportions? (my boss is adamant his solution is correct but i disagree..)

r/AskStatistics on Reddit: How to generate the confidence interval for difference between control and test proportions? (My boss is adamant his solution is correct but I disagree..)

September 13, 2023 -

We ran a marketing campaign at work with a control group and a test group. (The test group got a solicitation for a discount of our product; the control group did not.) The results looked something like this

| Group    | Converted | Did not convert |
| -------- | --------- | ----------------|
| Control  |  30       |  387            |
| Test     |  59       |  465            |

So, in this example (not our real data) the test group converted at a 11.3% rate while the control group converted at a 7.2% rate.

My boss wants to make a statement like

The difference is 4.1%. With 95% confidence I think the true difference lies between X% and Y%.

His strategy is to

calculate the standard deviation of each proportion.

ctrl <- 30/(30 + 387)
test <- 59/(59 + 465)
sqrt(ctrl*(1-ctrl)/(30 + 387))  # 0.01265354
sqrt(test*(1-test)/(59 + 465))  # 0.01380879

calculate the confidence interval of each proportion

ctrl +/- 2 * 0.01265354    <-- 2 standard devs gives 95% conf interval
test +/- 2 * 0.01380879

Then he wants to do something like take the difference of the lower bounds and the difference of the upper bounds.. This is where I'm confused and skeptical of his approach.

I know how to calculate the 95% confidence interval by using a simulation, but I suspect there's a formula or R code that'll let me plug and chug.

As a side note, I originally wanted to use the Fisher Exact test for this project, but the confidence interval is reported in terms of an odds ratio and my boss is steadfast on getting a confidence interval for the difference in conversion rates.

Top answer

1 of 1

For users of old reddit: The table and code in the question might not work if you use old reddit (at least for some setups). This might save you some effort: Group | Converted | Did not convert | Control | 30 | 387 | Test | 59 | 465 code under 1: ctrl <- 30/(30 + 387) test <- 59/(59 + 465) sqrt(ctrl*(1-ctrl)/(30 + 387)) # 0.01265354 sqrt(test*(1-test)/(59 + 465)) # 0.01380879 and under 2: calculate the confidence interval of each proportion ctrl +/- 2 * 0.01265354 <-- 2 standard devs gives 95% conf interval test +/- 2 * 0.01380879 On the CI for the difference in proportion: The use of two confidence intervals in Step 3 is not correct. You can form an approximate confidence interval for the difference in proportion by adding the squares of the standard errors of each proportion and taking the square root (giving the s.e. of the difference), and using a z interval based off that. There are other approaches but that should work fine. Since you're using R, you can skip that and just use prop.test which by default gives the same chi-squared value as chisq.test (i.e. it also uses Yates' continuity correction, though doesn't say so in the output), but then it also gives an interval for the difference in proportion: conv<-matrix(c(30,59,387,465),nr=2) rownames(conv)<-c("Control","Test") colnames(conv)<-c("Converted","Did not convert") conv prop.test(conv) The output for the last two lines should look like this: > conv Converted Did not convert Control 30 387 Test 59 465 and > prop.test(conv) 2-sample test for equality of proportions with continuity correction data: conv X-squared = 4.0192, df = 1, p-value = 0.04498 alternative hypothesis: two.sided 95 percent confidence interval: -0.079515385 -0.001790562 sample estimates: prop 1 prop 2 0.07194245 0.11259542 so with those settings, the 95% CI does not overlap 0. You can turn off the continuity correction in the usual way (i.e. just as with chisq.test).

Statistics How To

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Confidence Interval: Definition, Examples - Statistics How To

June 26, 2025 - For this example, type “95”. Click “OK. “ · Microsoft Excel will return the confidence interval for the mean and the margin of error for your data. For this sample, the mean (Xbar) is 149.742 and the margin of error is 66.9367. So the mean has a lower limit of 149.742-66.936 and an upper limit of 149.742+66.936. That’s it! Warning: A 99 percent confidence interval doesn’t mean that there’s a 99 percent probability that the calculated interval has the actual mean.

Pacific Northwest University

pnw.edu › wp-content › uploads › 2020 › 03 › lecturenotes8-10.pdf pdf

4.5 Confidence Intervals for a Proportion

Chapter 4. Statistics (LECTURE ... of Error", "CI lower", "CI upper") ... Chapter 4. Statistics (LECTURE NOTES 8) and critical value for 95% = (1 −α) ·...

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r - Confidence interval for difference between proportions - Cross Validated

Top answer

1 of 3

My original answer that was accepted by OP assumes a two-sample setting. OP's question deals with a one-sample setting. Hence, @Robert Lew's answer is the correct one in this case.

Original answer

Your formulas and calculations are correct. Rs internal function to compare proportions yields the same result (without continuity correction though):

prop.test(x=c(19,15), n=c(34,34), correct=FALSE)

    2-sample test for equality of proportions without continuity correction

data:  c(19, 15) out of c(34, 34)
X-squared = 0.9412, df = 1, p-value = 0.332
alternative hypothesis: two.sided
95 percent confidence interval:
 -0.1183829  0.3536770
sample estimates:
   prop 1    prop 2 
0.5588235 0.4411765

2 of 3

In this case you have to use a one-sample test, as this is a single sample. Your question boils down to whether males (or females) are one half. Here's how you'd do it using prop.test():

prop.test(x=19, n=34, p=0.5, correct=FALSE)

    1-sample proportions test without continuity correction

data:  19 out of 34, null probability 0.5
X-squared = 0.47059, df = 1, p-value = 0.4927
alternative hypothesis: true p is not equal to 0.5
95 percent confidence interval:
 0.3945390 0.7111652
sample estimates:
    p 
0.5588235

Datastatpro

datastatpro.com › confidence-interval-calculator.html

Confidence Interval Calculator | 95% CI, Margin of Error & Sample Size

Calculate 95% confidence intervals for means, proportions, and differences. Free CI calculator with margin of error, sample size recommendations, and bootstrap methods. Excel compatible with APA formatting.

Penn State Statistics

online.stat.psu.edu › stat415 › book › export › html › 813

Lesson 5: Confidence Intervals for Proportions

And, of the \(n_2=61\) children ... age 19 than children who had received preschool instruction. Yes, Minitab will calculate a confidence interval for the difference in two population proportions for you....

Statscalculators

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Difference in Proportions: Confidence Interval

This calculator will compute the confidence interval for the difference between two population proportions with a specified level of confidence.

GraphPad

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Confidence interval of a proportion or count

Enter the total number of subjects, objects or events as the denominator. For the numerator, enter the number of subjects, objects or events who had the first of the two outcomes.

Western Users of SAS Software

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1 Constructing Confidence Intervals for the Differences of Binomial

The joint distribution of the responses is given by · 𝑓(𝑥1, 𝑥2, 𝑛1, 𝑛2, 𝑑, 𝑝2) = ൬𝑛1 ... d is the parameter of interest and p2 is a nuisance parameter. Let 𝑑̂ = 𝑝̂1 −𝑝̂2 be the observed difference. The lower and upper confidence 95% confidence intervals ...

Fiveable

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Confidence Intervals for the Difference of Two Proportions - AP Stats Study Guide | Fiveable

August 22, 2025 - Calculate the standard error for ... the desired confidence level: zα/2 · Calculate the lower and upper limits of the confidence interval: p̂1 - p̂2 ± zα/2 * SE...