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Statology
statology.org › home › confidence interval for the difference in proportions calculator
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 ...
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StatsKingdom
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.
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Vassarstats
vassarstats.net › prop2_ind.html
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
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NCSS
ncss.com › wp-content › themes › ncss › pdf › Procedures › PASS › Confidence_Intervals_for_the_Difference_Between_Two_Proportions.pdf pdf
PASS Sample Size Software NCSS.com 216-1 © NCSS, LLC. All Rights Reserved.
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) .........................
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Shef
ssu.shef.ac.uk › diffbinconf › calc
Confidence intervals for difference in proportions
The SSU offers a wide range of statistical services to a diverse client base.
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Statology
statology.org › home › confidence interval for the difference in proportions
Confidence Interval for the Difference in Proportions
June 23, 2020 - There is a 95% chance that the confidence interval of [.0236, .2964] contains the true difference in the proportion of residents who favor the law between the two counties. Since this interval does not contain the value “0” it means that it’s highly likely that there is a true difference in the proportion of residents who support this law in County A compared to county B.
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Sample-size
sample-size.net › confidence-interval-proportion
Confidence interval for a proportion | Sample Size Calculators
Statistical calculators, sample size, free, confidence interval, proportion, mean
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Stats
stats.blue › Stats_Suite › two_sample_proportion_confidence_interval.html
Confidence Interval for Two Proportions
Calculate Confidence Intervals (regular and 'plus four') Comparing the Difference of Two Proportions with our Free, Easy-To-Use, Online Statistical Software.
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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....
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Study.com
study.com › skill › learn › how-to-create-a-confidence-interval-for-the-difference-in-proportions-of-two-independent-groups-explanation.html
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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GraphPad
graphpad.com › quickcalcs › confinterval1
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.
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Calculator.net
calculator.net › home › math › confidence interval calculator
Confidence Interval Calculator
Calculator to compute the confidence interval or margin of error of a sample based on the desired confidence level. It also provides an error bar diagram.
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Statistics LibreTexts
stats.libretexts.org › learning objects › interactive statistics
25: Confidence Interval For Proportions Calculator - Statistics LibreTexts
December 20, 2023 - Write the confidence level as a decimal. For example, for a 95% confidence level, enter 0.95 for CL. Then hit Calculate and assuming \(np\) and \(nq\) are large enough, the correct confidence interval will be calculated for you.
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Stat Trek
stattrek.com › estimation › difference-in-proportions
Confidence Interval: Difference in Proportions
07:54
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
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GIGACalculator.com
gigacalculator.com › calculators › statistics › confidence interval calculator
Confidence Interval Calculator
Powerful confidence interval calculator online for one-sample or two-sample (difference of means) CI: calculate two-sided confidence intervals for a single group or for the difference of two groups. ➤ One sample and two sample confidence interval calculator with CIs for difference of proportions ...
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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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Stats4stem
stats4stem.org › confidence-interval-two-proportions-difference-of-proportions
Confidence Interval
Based on the data, I am 95% confident that the difference in the proportions of defective toys before and after the manager’s claim is between -0.0372 and -0.0068.
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Causascientia
causascientia.org › math_stat › ProportionCI.html
Exact Confidence Interval for a Proportion
If the stated assumption is true, then the confidence limits computed by this calculator are exact (to the precision shown), not an approximation. Some Technical Details are described below. ... Confidence (a.k.a. "degree of belief"), 1 - X, where 0 < X < 1 [default confidence is 0.95 -- i.e., ...
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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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Reddit
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

  1. 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

  2. calculate the confidence interval of each proportion

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

  3. 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.

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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).