# Questions tagged [proportion]

A proportion is the fraction of some total that is of a particular kind, either (i) as a count of one type of thing out of a total count, or (ii) as a component of a continuous variable.

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### Why can't I just compare percentages at face value (with different sample sizes)

I'm having the largest brain fart and I feel like this is actually simple so please give me your thoughts if you have any! I've got these 6 types of claims, that can either be approved or denied. My ...
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### Including a predictor variable that is a proportion in panel regression

I built a panel data model using the R plm package, and one of the predictor variables is a proportion. Should I perform any transformation on this variable as it ...
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### Confidence intervals for dependent proportions

I have a strange dataset and I need some help calculating confidence intervals for proportions, with an unorthodox dependence structure. I have been constrained to the following setup, and I have no ...
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### Newbie: Difference between the meaning for the data analysis: proportion of correct responses and probability of correct responses

Very newbie, sorry if the question seems to be not very smart... If proportion of correct respones is defined as Number of hits + Number of correct rejections / Number of trials Is the probability of ...
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### How can you compare changes in a shifting population over time?

How can you compare changes in shifting population over time? For instance, say I have the proportion of retired people in a town at time 1 (T1), then again at time 2 (T2). The "population" ...
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### How to control for n when using proportion for modelling?

I am trying to fit a logistic model on binary variable y, using p as an independent variable. ...
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### What are some of the pros and cons of using percentages as opposed to raw number data?

(NOTE: the question and data explained here is not based on a real experiment; it has been randomly generated for the sake of explanation) Let’s say I wanted to compare 3 different coin types—a US ...
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### Book on probability proportional to size sampling

Can anyone please suggest a book to study probability proportional to size sampling with and without replacement and all its details ? Thank you
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### Horwitz thompson estimates

Let U = (1, 2, 3, 4, 5, 6) be a finite population of size 6. Let $\ S_d$ = {($\ s_1 = (1, 2), \ s_2 = (3, 4, 5), \ s_3 = (1, 2, 6), \ s_4$ =(3, 4, 6)} be the support of the design. Let P($\ s_i$) = ...
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### How to show that $\pi^*_i \pi^*_j - \pi^*_{ij} = \pi_i \pi_j - \pi_{ij}$ in a probability sample?

Let $\pi^*_i \quad i=1,2,\dotsc, N$ be the probability of not including the $i$th unit in the sample and let $\pi^*_{ij} \quad i, j = 1, 2,\dotsc, N$ be the probability of including neither the $i$...
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### Statistical Significance of a Comparison of Percentages

I'm looking at a comparison of percentages pre/during covid and I'm trying to work out how to show if there is a statistical difference between groups. I'm not sure which statistical test to use and/...
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### Multiple Sampling Plan - proportions. What test statistics to use?

Company A implemented a new acceptance sampling plan in 2020. So I need to compare the customer returns data from 2019 vs. 2020. Given these type of data available. What test statistic I am going to ...
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### Can proportions over variables be learned/predicted with Neural Networks using multiple-outputs?

I am interested in understanding how Neural Networks could be used to both learn from and predict proportions. That is, say matrix $X$ is the training features data with $N$ cases and $k$ features. ...
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### Hypothesis testing multiple proportions

Need help on my research! We are introducing a new process in 2021 which might affect customer returns behavior. My data is in proportions which is total number of returns of total number of units ...
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### Which test to use when comparing multiple sets of proportions (with unknown sample size)?

I have two conditions, about 50 samples for each condition, and for each sample - a set of 9 proportions. The proportions are estimates of the proportion of 9 cell types of this patient. Clarification ...
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### Statistical Test for one-sample, multiple choice option from a survey

I have conducted a survey where 410 people were given 14 brands. Of those 14, they were asked, "Which brand do you consider to be the "#1 Trust Brand for Protection". Respondents could ...
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### What is the best way to regress proportions (as both dependent and independent variables)?

I am currently conducting a meta-analysis and have pooled the prevalence of a certain disease. I would like to check for any association of risk factors, such as gender, ethnicity, and disease ...
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### Can I use logit transformed proportion as a independent variable for meta regression, while my dependent variable is also logit transformed?

I am now conducting a meta-analysis for depression in a certain disease. The prevalence of depression is available for the studies (n=21), and I would like to conduct meta regression with the ...
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### What is a noise-resistant method for testing correlations of proportions

I have a friend who is trying to analyse a large Sanskrit corpus with many verbs in. Verbs can occur in the active or the passive, and they can occur in the past tense or the present tense. She wants ...
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### Plotting the results of a fitted mixed model with fractional/proportional outcome?

I have a dataset with repeated measures (3 tests performed by each subject), and a percentage outcome (amount of correct responses on each test), which I fit using glmer: ...
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### When is a hypothesis test appropriate?

For example, when would a hypothesis test bed used?
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### Estimating Population Proportion

I am trying to determine the number of "large" words (10 characters or more) in a dictionary of roughly 235,000 words. I have drawn 100 samples, each of size 100, with replacement. The mean ...
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### Estimating a proportion based on two counts

I need to estimate a proportion based on independent measurements of the numerator and the denominator. Both the numerator and denominator are measured as counts. I know from theory that the ...
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### confidence intervals around proportion on multilevel data

I've posted this question another listserv (statalist) and have not received any responses. Any feedback is welcome. I’m doing an analysis of applications and selections for grants. I do not have a ...
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### Sample size calculation for estimating a small population proportion

I'm having a disconnect on power and sample size estimation. I'm using the sample size calculator here: https://select-statistics.co.uk/calculators/sample-size-calculator-population-proportion/ Im ...
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### Sample size calculation for an estimated probability

I have a primary outcome of observing at least 1 adverse event. I would like to know the sample size for observing and adverse event of probability of 2% or greater, 5% or greater, and 10% or greater. ...
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### How to use proportion data for T-test and ANOVA, respectively (Non-continuous data)?

Long time reader, first time poster. I'm doing an observational study and have gotten into unknown waters in both statistics and R (beginner in both). (1) I have 2-categorical variable (species) and ...
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### How to calculate variance of a proportion?

Say I have two independent random variables X ~ N($μ_{x}$,$σ_{x}$) and Y ~ N($μ_{y}$,$σ_{y}$). I know that I can calculate the variance of their difference with $Var(X-Y) = σ_{x} - σ_{y}$. But I want ...
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### Why does a two-sample proportion test with outcome Y and predictor X give the same result as one with outcome X and predictor Y?

I just noticed, while playing around in Stata, that this is the case, at least with three pairs of variables I tried out, which makes me think there must be some real relation there -- the z-statistic ...
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### Comparing / Sorting Rates with different denominator scale

I have a list of N customers, each has its own performance rate let's call it Xi. In order to compare the performance of each customer Xi (for example finding those best-performing customers), i would ...
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### Which type of regression is appropriate whenever the dependent variable is the saving ratio?

I don't know which regression is best suited to use the saving rate of household income as a dependent variable. The options I have at the moment are Censored Regression (this was brought forward by ...
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### Fisher exact test manual input of observed and expected

I have a 4x4 table and I want to test if observed proportion equal to a given expected proportion I provide. Because the counts between observed and expected are very different, I am interested in ...
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### Comparing two sample proportions where one proportion (p1) is a stratified sample and the other is a convenience sample taken from p1 (p2)

I have taken a stratified sample of vaccination clinics from a population in the US based on a categorization of A, B, C. I have sampled 2k clinics from A, 1k from B, and 1k from C. I am interested in ...
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### Comparing multiple sample proportions between two groups where one group is a subset of the other

I have 2 populations which I want to test if the proportions between group A and B are the same for each location or not by using hypothesis testing. It's very much as this problem described here: ...
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### Confidence Interval for Proportion that is 100%

I am examining differences between groups with two categorical variables. For one category of categorical variable #1 all values are in one category of variable #2. Thus the proportion of category in ...
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### What test to use to compare proportions of answers “Yes”, “No” and “I don't know” in two different researches

I am trying to recreate the results of one research I found, because authors did not mention what test they used. The situation is as follows: They gathered the following counts of answers for their ...
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### Proportionality check for samples at different scales

(I am not a stat guy so kindly excuse my lack of knowledge) There are two systems A & B that are counting vehicles at a particular road junction. System A is expected to capture more vehicles than ...
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### Is this a valid method to test textual difference?

For some research I am trying to reject/ not-reject the null-hypothesis that the proportion of a word is higher in a certain sample of a text than in the rest of the text. The full text is a ...
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### Conducting a meta-analysis of proportions and one proportion is negative

I am conducting a meta-analysis of proportions and plan to first use the Freeman-Tukey double arcsine transformation before meta-analysing the data. However, one of the proportions is negative (-1.3%)....
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Sample Data: ...
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### How do I calculate the effect size with paired samples of proportions?

I am doing a meta-analysis and frequently need to calculate the effect sizes from the data since the effect size I am looking for is frequently not reported directly. I am looking at a paper where ...
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### binomial vs betareg? glm for y=ratio

https://docs.google.com/spreadsheets/d/1e_XOgTv1flSFFleHSwUJJPBzBdd9VPXRaZc2oukwtrE/edit#gid=0[data] I'm using glm to evaluate the response of mammal species to different % of forest cover. My ...
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### Can I use posterior beta parameters from a previous experiment to use as priors for my current experiment?

I am doing a Bayesian comparison between two proportions, H0 being Proportion(Protein)> Proportion(Mixed). Here the Proportion is of no. of times a free-ranging dog(s) ate from a box(Protein, Mixed)...
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### Proper Test for same proportions (multiple categories) on 2 groups, not normally distributed data, different sizes

I have trying to research the proper test for the following problem. I have 2 groups with different sizes n1 and n2. From each groups I am randomly sampling the same % of samples. (so say kn1 and kn2)....
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### unbiased estimation of the variance of $p$ (proportion) of a random sample without replacement

Given a random sample without replacement of size $n$ from population of size $N$ and $p$ is the estimator of the proportion $P$. How could one show that: \begin{equation*} \frac{N-n}{N(N-1)}pq \end{...
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### How to find the credible interval on the difference between the means of two proportions in R?

I have two proportions of the beta-binomial family. x1=41, n1=88, x2=41, n2=90 (x= no. of successes; n=no. of trials). The beta prior shape parameters for the two proportions are alpha1= 20, beta1=26, ...
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### How should I compute confidence intervals for a proportional estimates of a Poisson count?

I'm developing an microbiological assay for enumerating defined mixtures of different bacterial strains that all have similar growth requirements and can't be distinguished by visual characteristics. ...
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### One-sample: difference between two proportions that are parts of the same whole

What is the sampling distribution of the difference between two proportions when they are parts of the same whole. It's relatively easy when one proportion is binomial, the one of the common ways to ...