# 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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### Sample is almost the same as the population

I'm interested in a situation where I have a small list of events, somewhere in the range ten to a few hundred. Each event can be a 1 or 0 outcome. I have a good reason to believe that the factors ...
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### How to simulate sample proportions near or at zero in a Monte Carlo simulation?

I am running a chain of Monte Carlo simulations to estimate uncertainty in some model estimates (which are derived from a series of estimates). An important variables used in one of the steps is a ...
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### Best way to compare changes in proportions

I am reviewing a manuscript so I cannot be specific but the authors had a treatment that was supposed to improve access to care. They had a treated group and a control group. Access to care was ...
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### Relationship between Beta regression of Y on X and linear regression of X on Y. (where Y is a proportion)

I am trying to model the relationship between school district funding and a district's poverty rate. If I treat funding as the independent variable then the dependent is a proportion on [0,1]. This ...
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### Comparing the distributions of proportions in two groups

I'm comparing the total dog population in a region with the number of dogs in rehoming centres in that region. The data are below. The number of cases is the number of dogs that have been in rehoming ...
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### R: generalised additive model on proportional data

Introduction I am analysing temporal population data on the amphipod Orchestia gammarellus. At several moments each year, all animals were collected from a small spot, and several life history traits ...
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### Sample size for the normal approximation of the Binomial distribution

I am reading about the familiar hypothesis test for proportions, using the normal approximation for large sample sizes. Some people say (write) that the condition for using the approximation is np>5 ...
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### Sample size needed to prove equal proportions

We are trying to prove that three groups have the same proportion of some effect. We are struggling with formulating the null hypothesis, and whether or not the sample size is big enough. The ...
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### Proportion Test: Z-test vs bootstrap / simulation - different results

I'm learning hypothesis testing, and going through the following example: The CEO of a large electric utility claims that 80 percent of his 1,000,000 customers are very satisfied with the service ...
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### Test for yield and disease incidence in block design

I need to analyse a set of data coming from an agricultural experiment, with the intention of assessing the incidence of a certain disease in potatoes under three different treatments (plus blank). I'...
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### How to calculate the error of percentages

Is it correct to calculate the standard deviation of percentages/proportions as you would for four numbers (i.e. non-percentages)? Thanks for your help @user2974951 @whuber and @asdf. Yes, you're ...
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### Find significance between two group proportions

My question is the following: what statistical test would I use to compare the proportion of participants between two groups. For example, if in 2009, 20% of participants ( population was 55) to a ...
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### group sequential design for one proportion

I would like to create a group sequential design for a one proportion to test H0: p=0.97 vs H1: p=0.98 with alpha=0.3 and beta=0.43. Above specification provides me the sample size of 120 for a ...
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### GLM for proportion data in r - with many zeros (or ones) [duplicate]

My understanding is that generalized linear modeling (GLM) is recommended for proportion data. However, this seems to run into problems when a set of data is full of zeros (or ones). For example, a ...
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### which stat test?

I am doing a health interventional study in the community. I calculate the "pre-intervention" proportion of behavior of the community before applying the interventions. And after 1 years of various ...
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### Get better confidence interval by drawing multiple samples

Imagine that I have population of size N and I draw a sample of size n from which I compute a proportion $\hat{p}$ of a categorical variable. And I want to get a confidence interval of 95%. So I ...
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### Calculating a Confidence Interval for a Proportion for a Sample of Different Size

I'm interested in a (preferably analytic) solution or approximation to the following problem: Let $s_1$ be a sample from an unknown distribution of size $N_1$ and with proportion of successes $p_1$. ...
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### Comparison of proportions using McNemar's Chi-Square using Pre- and Post- data for two disease conditions

This question follows-up on the post: What is the difference between McNemar's test and the chi-squared test, and how do you know when to use each? I am examining a pre- and post- intervention data ...
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### Test a proportion against unanimity

How can I test a proportion against an expected value of 1.0? Made up example (slightly silly): Dichotomous Yes/No question... Would you like me to hit you very hard on the head with this hammer? ...
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### Distribution for average of multiple binomial proportions

Assume we have a population $N$ and a proportion $p$ of that population with a characteristic of interest. Both $N$ and $p$ are unknown. Furthermore, assume that we have $k$ random samples $(n_i, x_i)$...
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### Modelling percentage and proportion data with GLM's [duplicate]

I would like a simple answer, if there is one, to a question I cannot seem to find on here. What is the best way to model percentages? Say I have a glass that is empty and I fill it with liquid ...
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### Comparing Test and Control Lift in Proportion

I have two groups - a test/treated and control group - for which I am trying to assess whether the lift or percent change in proportion from a pre to post period between the two groups are unequal. I'...
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### Comparing survival rates

The question I have is focused on comparing remission rates at a fixed point in time. For example, I have cancer type A and cancer type B (the two are not mutually exclusive groups) and all patients ...
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### Where is my potential flaw in my Z-test of Proportions?

I was working through this z-test of proportions example I found online. The online example solutions says that the difference between the groups is statistically significant, whereas I concluded it ...
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### Is lmer or glmer appropriate for nested continuous proportion data

I have a reviewer that wants me to analyze my data along the lines: Con_Ratio ~ Range * Latitude * Longitude + (1 | Genotype/Pair). But I'm not sure if this can be done and how. My experimental ...
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### Are there statistical tests for testing multiple sample proportion?

For categorical variable testing, we have chi-square test. For example, we want to test if a dice is fair (assuming sample has [6,5,7,7,6,5] and ...
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### Time Series of Wound Healing percentages / proportions

I am looking at wound healing over time and have hit a wall with analysis. My data consist of injury cases which are tracked over time. Injury healing is measured as percentage wound area/perimeter ...
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### What statistics test to compare the repartition of multiple choices between two groups?

I made an experiment about UX where the participant has to detect among five differents configurations the one that he prefers. The configurations are slightly different and are presented randomly 3 ...
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### Standard error of a proportion on a 2 x 2 contingency table

Why on a 2 x 2 table such as where $p = \frac{a}{a+b}$ the standard error of $p$ is $$\left(\frac{(a+c)(b+d)}{(a+b+c+d)^2(a+b) }\right)^{1/2}$$ ?
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### Comparing proportions between multiple groups - Fisher's exact test

I have a simple dataset on reproductive success of a certain plant species. Reproductive success was defined as a proportion between number of flowers and number of fruits. We measured on 10 different ...
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### Cochran's Q test with changing proportions

for my thesis I am investigating the change in proportions of children in regular and special education. The information is obtained through an online questionnaire, and I have data for 4 consecutive ...
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### Statistical test for binned proportion data in JMP / MATLAB

I have been trying to determine the proper statistical test for comparing binned proportional data between groups. My data set is individual subjects (4-5 per group) with 76-165 cells per individual. ...
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### Z-score for weighted proportion [duplicate]

I have a question regarding the Z-Score test when it comes to compare two proportions. Usually, one would use this formula to obtain the Z-Score: and then compare it to a Standard Normal ...
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### Testing the goodness-of-fit for the binomial distribution

As specified in the title, I'm trying to understand how to test the goodness-of-fit for the binomial distribution; to this aim, I followed what suggested in this link. Particularly, I'm investigating ...
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### How to report percentage change in proportions?

I want to compare changes in the proportion of fruit purchases over time for a household. For example, in year 1, 4/40 (10%) fruit were apples, in year 2, 12/80 (15%) fruit were apples. When ...
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### How to define sampling unit. t.test vs proportion test

In my particular case I am comparing damaged fruit in several treatment fields vs. several control fields For simplicity: Both treatment and control have 10 bushes each. a cluster of fruit is taken ...
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### Regression when both the predictor and outcome variables are proportions

I am using $X$ The estimated pre-game win probability of a sporting team playing on its Home field (estimated according to a certain model) to predict $Y$ Actual proportion of points scored by ...
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### Frequencies/percentages different from zero - which test?

I conducted an experiment and had participants indicate binary judgments by either pressing "1" or "0" when seeing different types of stimuli. Now I want to test whether the proportions of number ...
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### How likely is a random sample to be significantly similar to the full population?

I am looking for a way to compare the proportions between two data sets of surveys, where individuals can be placed in more than one classification. One of my groups contains the survey results of 10....
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### Calculating sampling proportion's standard deviation given population proportion?

So the question is as follows (paraphrased): A population votes for/against a political candidate. In a sample of 200 voters, let $X$ be the fraction of people who vote for this candidate. ...
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### Interpretation of variable in a probit model

I am struggling interpreting the coefficient of a variable which is expressed as a proportion in a probit model. As it currently stands , I am interpreting the average partial effects of this variable ...
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### Chi squared test: which is the correct null hypothesis?

I'm reviewing some literature in my field, specifically looking at whether physical activity (PA) has any beneficial effects on cognitive performance. The results across the studies are quite mixed. ...
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### Bernoulli / binomial trials for a process with variable probability of success

One of the conditions for a Bernoulli trial (and by extension binomial proportion confidence intervals) is that the probability of success is the same every time the experiment is conducted. In the ...
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### Model proportions as independent variable for binary outcome

I've binary (disease) outcome: 0, 1 with certain independent variables in proportions, and other covariates as - age, sex. There are Packages that model proportions as outcome variable but not other ...
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### Beta regression where fractional response adds up to 100%?

I have a data set of people switching brands. Say #people switching from Brand A to Brand B, C or D. My data looks like this ...
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### z-test of proportions vs chi-squared

A 2-sample z-test of proportions and a chi-squared test can both be used to analyze a $2\times 2$ contingency table. In fact, for $2\times 2$, $\chi^2=z^2$. Why can the same table, being used with two ...
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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 ...
Consider a spatial random process $Z(s)$, where $s$ denotes the spatial location. Our objective is to delineate the zone $\mathcal{Z}$ where the probability that $Z$ exceed a given threshold $\zeta$ ...