# 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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347 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 ...
1k views

### 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 ...
127 views

### Statistical significance of a difference between poll percentages with a small sample?

Analyzing my company’s internal survey results, I was stuck with calculating statistical difference between percentages. I usually used a Z-test as described below, but I am not sure whether it is ...
2k 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 ...
90 views

### 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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### 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 ...
109 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 $p_1$. ...
149 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}} = \...
85 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 ...
72 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 ...
102 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 ...
61 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 ...
2k views

### Understanding output of prop.test in R

Specifically, I wish to understand the meaning of the confidence interval. An example: ...
808 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 ...
96 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 ...
55 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 ...
265 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 ...
625 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 ...
183 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: ...
172 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 ...
164 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 ...
701 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 ...
114 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 ...
203 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 ...
11k 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: ...
20 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 ...
31 views

### Hypothesis test involving proportion of proportions

I have 100 different coins, each with probability $p_i$ of being heads - but these $p_i$s are unknown. I flip each coin $n_i$ times, and see that it lands on heads $x_i$ times. So the proportion of ...
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### 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 ...
35 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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### 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 ...
35 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 ...
29 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 ...
100 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 ...
242 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 ...
46 views

### 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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### 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 ...
460 views

### 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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### What are the chances of seeing a photo 2 days in a row?

I've installed a photo slideshow on a small TV in our kitchen, which displays a randomly chosen family picture amongst 3'700, once every 20 seconds. My wife frequently observes "but I saw that one ...
433 views

### Test difference of population proportion and weighted sample proportion

I want to test for differences of the known proportion of the population vs. the proportion of a sample. The sample is weighted by sampling weights. The sum of weights is equal to the size of the ...
95 views

### How to compare the marginal variation of two groups with a big difference frequency between them?

I have two different groups (A) and (B) and I would like to compare the marginal variation of the frequency for each time of both groups but, each one of them has a different frequency for a given ...
28 views

### Can I use a Chi Squared test if one participant contributes more than once to the same cell

I have an experiment that can be thought of in this manner: I have two rooms and in each room I have two buttons: one red and one blue. One of the rooms is painted blue and the other is painted red. ...
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### Aggregated Count Data-Days in the last 30- Negative Binomial vs Beta Binomial vs Binomial Regression

I need help choosing between the binomial, negative binomial, and beta-binomial distributions and understanding the rationale of why I would choose one over the other, as well as understanding how it ...
422 views

### Compare pairs of proportions for three groups

I have a interesting problem, where patients are categorized in three groups, namely Severe, Moderate, and ...
52 views

### What should the estimated proportion be for the population when the sample proportion is 1?

I am auditing insurance claims for fraud. In my random sample, all the claims are fraudulent. Could I say for the population that the estimated proportion of fraud is 1? I know how to compute a ...
131 views

### Is this an appropriate use of a GLM? and if so how do I predict a specific outcome?

I am hoping that someone might be able to provide me with some assistance. A colleague of mine was told to use a GLM of family binomial and a logit link function for some of the data they submitted in ...
320 views

### Compare two dependent variables of proportions

I have a group of 20 subjects that is measured twice (pre- and post-treatment). Each time the measurements are proportions. Values range between 10% and 40%. Both variables are not normally ...
64 views

### Paired or unpaired median proportion?

I have measured the presence of a disease (present/absent) in pupils at 10 different schools. Then, disease severity was determined as mild, moderate and severe in those pupils with the disease (the ...
63 views

### How to test whether multiple independent proportions are different from a given value?

I have a dataset of count data: the number of times a behaviour was performed by either of two individuals in a chamber (a focal individual and a partner), with multiple independent tests across ...