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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80 views

How to test the increase of proportions

Let say I've a contigency table as : score <=2 [3-4] >=5 no_event 248 796 288 event 71 419 285 I computed the ...
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2-Sample Proportions z-test vs Fisher's Exact Test

I want to evaluate the difference in proportions in declined applications and exceptions from policy from one quarter of data to the next. My sample sizes are generally not small (several hundred to ...
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406 views

T tests on proportions - Wrong, but how wrong?

Background: In psychology, and probably a number of other disciplines, it's common practice to test between-groups effects on a binary variable, such as accuracy, by aggregating data within ...
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278 views

Pooled variance for post hoc tests for contingency table $\chi^{2}$ tests

The 2-by-2 contingency table test provides an alternate hypothesis testing approach to the $z$ test for proportion difference. Conveniently enough, a 2-by-k contingency table test provides an omnibus ...
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58 views

Statistical Test for Evolution of a Population Proportion?

The problem I am faced with is as follows - there is some population proportion $p$ of people with a certain characteristic that is evolving over time. We take new samples every day (without ...
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263 views

What to do when predictors are proportions that sum up to one?

I have a situation as the one described in the links below: Interpreting proportions that sum to one as independent variables in linear regression Predictor variables sum up to 1 but not necessarily ...
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275 views

Why don't we use the n-1 correction for standard error of sample proportion?

From my understanding, when we construct a confidence interval for a sample mean with a sample size of n, we try to estimate the standard deviation of the sampling distribution $$σ_{\overline{x}} = \...
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3k views

Two-Sample Hypothesis Test for Difference Between Two Proportions: Pooled vs Unpooled? How to Choose?

When are you supposed to use the pooled formula vs the unpooled formula? My understanding is that you use the pooled formula when testing a hypothesis where the null hypothesis is $H_0 = 0$ and the ...
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59 views

How can I account for range restriction when meta-analytically aggregating differences based upon bounded measures such as mean proportions?

Background and Problem In the past, I have read or conducted meta-analyses that aggregate effects based upon mean proportions. For example, in a typical psychological experiment dealing with human ...
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Testing differences between slopes by examining proportions rather than interactions

In a recent article published in Nature Genetics, Francioli et al. argue that the relationship between paternal age and mutation rate depends on what part of the genome you're looking at (intergenic ...
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1answer
191 views

How to Compare more than two Averages of Proportions or Means of Proportions

My experiment deals with $60$ subjects, one third of them belong to type A subjects, $i=1..20$, another third to type B, $i=21…40$ and finally type C, $i=41..60$. Each of these $60$ subjects from the ...
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1answer
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What distribution does $\frac{\hat p -p_0}{\sqrt{p_{0}(1-p_{0})/n}}$ have?

Suppose we're testing whether more than $100p_0$% Bernoulli trials are successful at the $\alpha$% significance level. We take a sample of $n$ Bernoulli trials and find that $\hat p$ trials are ...
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Counter-intuitive result from Cochran Armitage trend test and glm binomial

My question is motivated by the Q&A at How to test the increase of proportions. The question is how to test for a trend in proportion between events and non-events given an ordinal risk of 3 ...
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Formula for sample size for hypothesis test for difference in proportions confusion

For a hypothesis test for difference in proportions: Source A (some Stanford professor): The sample size for both groups is $$\frac{2\bar{p}(1-\bar{p})(Z_\beta+Z_{\alpha/2})^2}{(p_1-p_2)^2}$$ $$\bar{p}...
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1answer
145 views

Comparing multiple proportions across groups for time spent on activities

I have a stacked column chart comparing time spent on 3 activities (here illustrated as A, B and C) by novices and experts. The proportions will always add up to 1; the participants could not do ...
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117 views

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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89 views

Confidence interval of proportion of a proportion

Let's say we have $N$ users. Some of them could be hackers and some not. Only for a random $p_u$ percent (e.g. 1%) of users have we actually investigated manually to know which ones are hackers and ...
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111 views

Confidence Interval for a proportion, with false negatives/positives

I have a fairly simple problem but haven't been able to find any resources with the solution. Let's say we have a population of N subjects. We get a sample of size n, and within that sample we have k ...
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129 views

why use an odds ratio instead of a proportion

I would appreciate your advice regarding a 'work' query, in that nobody at work can agree on what appears to be a very simple statistical analysis. I have changed some of the details to protect ...
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62 views

Is 5 in 100,000 the same as 50 in 1000,000 from a Bayesian perspective?

I am learning about bayesian reasoning and I was having a discussion with a friend about it. My friend asked me this question, which I couldn't answer (this is not a homework, I am an adult learning ...
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3k views

Understanding output of prop.test in R

Specifically, I wish to understand the meaning of the confidence interval. An example: ...
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922 views

Using chi-squared or Fisher's exact with replicates

I want to compare proportion data (sex ratio) between two treatments. There are 19 populations for each treatment (i.e., 19 replicates). The specifics of the data is that it is the proportion of ...
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114 views

Multiple binary responses per participant in a 3 x 2 factorial ANOVA

As part of my thesis in linguistics, I'm currently analysing whether emotions influence the use of adjectives in speech. In my experiment, each participant (N = 90) produced multiple independent ...
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306 views

test statistic for change in proportion over time?

Stats novice here. This is my problem: I have 7 samples corresponding to the years 2006-2012, representing emergency department [ED] visits. For each ED visit, X=1 if the visit had diagnostic ...
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637 views

Testing the difference between multiple paired proportions with different sample sizes

Is there a hypothesis test similar to the paired t-test for testing if the difference between a number of paired proportion estimates is significantly different from zero? The data consists of 2 lists ...
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1k views

Zero-and-one inflated beta regression vs. binomial GLMM?

I appreciate some help with deciding whether I should (and how to) construct a zero-and-one-inflated beta regression model. I want to use R to test the hypothesis that there is a ...
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184 views

Appropriate test (in R) for proportion data that aren't normally distributed, aren't based on counts, and include 0's and 1's?

I'm studying differences in tree health among 5 species of trees across 3 different green infrastructure types. Here are the first few lines of data: ...
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204 views

Can I use OLS with robust standard errors to analyze proportions?

I have a response variable that is a proportion. It is not the outcome of a series of Bernoulli trials, so there is no numerator/denominator, just the proportion. I'd like to assess the relationship ...
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753 views

Appropriate GLM when response variable is proportion, but not binomial

The response variable I'm dealing with is the proportion of a total area that is suitable habitat for a species of interest. So although the response variable is bounded between 0 and 1, my intuition ...
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584 views

Power Analysis: Comparing GLM to binomial proportion test

I am trying to run a power analysis using simulated data to compare the power of a glm versus a binomial proportion test to detect differences in proportions. For example, suppose you have some ...
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123 views

Generalization of Chernoff bound to Bernoulli schemes

I have this (I think) simple problem, which I guess is just a generalization of the Chernoff bound to Bernoulli schemes. Assume I have a bowl with N balls with R different colors. The balls are not ...
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206 views

Appropriate statistics for proportions where categories are composites of independent binary variables?

I have data in the form of three digit binary numbers (i.e. 100, 101, etc.) scored for each individual in my samples taken from two populations I wish to compare. The three numbers represent ...
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12k views

How can I calculate the standard error of a proportion?

I made a comparison of hatch success between 2 populations of birds using R's prop.test() function: ...
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841 views

Plotting Multiple Proportions With Standard Error

The Data: The observed probability (proportions) of three mutually exclusive events for five species. What is the best way to plot these data in R along with their standard errors? I'd like to avoid ...
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14 views

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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17 views

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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28 views

Meta-analysis on percentage of total calorie intake

We are looking at a number of studies which have profiled nutrient information which contributes to total daily calorie intake. For example, fibre might make up 5% of daily total calorie intake. My ...
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25 views

Visualizing distribution of sample proportions that takes into account of the sample proportion uncertainties

I have calculated several sample proportions in my dataset that stem from an unknown population distribution - likely a beta mixture. I would like to perform some exploratory analysis to visualize the ...
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23 views

Test for changes in proportion through times?

I want to test for a change in proportions through time, and see that there are a number of unanswered questions related to this. I have a dataset of counts that belong in one of three mutually-...
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1answer
26 views

In a meta-analysis, can you back calculate estimated group proportions from risk difference?

In a meta-analysis of the risk difference, does it make sense to apply the weights & back calculate the expected proportions in each group? For example, if you had the following: ...
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25 views

Proportion Test on Proportion Data

I'm attempting to analyze the results of a game where one player is eliminated each round. I want to try to evaluate whether a player who wins an advantage in the first round of the game (usually one ...
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26 views

Which statistical test for two group proportions over two time periods? 100% sampling, capped membership. Independent groups over time

I'm comparing the number of male and female hires at a city in the 1980's to the number of male and female hires in the 1990's. I'm looking for whether the percentage of females increased ...
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58 views

I have a proportion DV with true 0 and 1. Which mixed modelling approach (in R) is most recommend?ed?

Hope this isn't too much of a dumb question. I've been searching for a definitive answer, and now I've got choice paralysis. I have a proportional DV (accuracy) with true 0 and 1 values averaged for ...
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23 views

Regression alternatives for proportional data that do not rely on the 0 - 1 interval

I'm currently analyzing data consisting of change in cognitive performance and how it is related with a physiological variable (enzymatic activity) in a group of people. As all people were assessed ...
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725 views

Comparing proportions across three groups, multiple levels

I have three groups. For simplicity's sake, lets say they are "cats", "dogs", and "mice". I have been asked to compare the proportions of each that are "grey", "white", or "brown". So lets say my ...
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57 views

Measure for variability of proportional data

I have a list of expected values (E) for the proportions of 20 amino acids in protein sequences.In a particular set of protein sequences these proportions differ from the expected values. In a subset ...
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1answer
50 views

Sample sizes: stratified random vs simple random sampling

In general, how does the total sample size for stratified random sampling compare with sample size for simple random sampling? The variable involved is binary: yes-no. The population parameter to ...
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40 views

Comparisons of multiple related proportions

Here's the setup. I am testing the sensitivity of my method compared to a baseline method. I have tested this at a number of sample sizes, and I'm recording the proportion of rejections I get in 1000 ...
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77 views

Bayes factors in R for correlated proportions (such as a “Bayesian McNemar's test”)

Is there any way to get Bayes factors in R for correlated proportions (i.e., paired sample)? For example, the same group of 90 people is measured with one technique, then with another; once there are ...
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697 views

When to use Chi-squared and when Z test for categorical variables?

The problem is: There was a survey conducted among 1137 adults from California, Nevada, and Oregon. They were chosen randomly and they answered to the following question “Do you think Marijuana ...

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