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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How to find changes in proportions using regression?

I want to test the hypothesis that the expansion of lending institutions changed the goals that households obtained their loans for. In other words, say in 1950 the breakup was: 33% got loans for ...
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How did they power this study? (One sample proportion test)

I was asked to perform a sample size calculation for a study with a single arm and a binary outcome. They have given me an assumed proportion, $p$, and need the upper 95% confidence interval to be ...
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26 views

What's my population? Is this Descriptive or Inferential?

I have a list of employees at a company. I want to show some comparison of some demographics (say, %female) of those who have left the company and those who have stayed with the company. However, I ...
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What method is appropriate? - analysing patterns of attacks by region

I am currently working on a project using a dataset on global terrorist attacks. For each attack there are details on the type of attack which has 7 levels (e.g. bombing, assasination etc.), the ...
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Hypothesis test of 2 proportions, with $np < 5$

We are frequently conducting one-tailed hypothesis tests for 2 proportions ($H_0: p_1-p_2=0;\, H_1: p_1-p_2 > 0$). However, $p_2$ is relatively small in terms of $n, x$ and in some cases we find ...
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how to test equality of proportions at different times

Here is my question. 20 (worm) mothers produce males + females and hermafrodites (many every hour). I want to test if the proportion of males + females born on day #1 is the same as in days #2 and ...
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15 views

Proportion test with null hypothesis p1=x*p2

I'd like to compare the proportion of two sets of binomial data where the null hypothesis is not p1=p2, or p1-p2=x, but \begin{equation} H0: p1=x*p2 \end{equation} I've been computing a z test as ...
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Assign the tree species most representitive of a specific size class

I am replicating another study in which trees were assigned to a class based on diameter. The most representative species of each class was identified for each plot sampled. The classes are sapling ...
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Compare official population distribution with sample?

I have official numbers regarding the population of specific ZIP codes that belong to a certain region, e.g. 90210 has population of 20.000 (just an example). (The set of ZIPs comprises a city and its ...
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61 views

Modeling a proportion using longitudinal data

To illustrate my question I'll make a (very) fictional example. I have a set of 17 year old people that every year report how many cigarettes they smoked and how many miles they ran. Very few of ...
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173 views

Probability distribution for a proportion based on (continuous) quantities

I have a problem related with probability distributions and parameter estimation, which comes from a real case. I would be very grateful if you could help me. Let us suppose that we have a continuous ...
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Is difference in proportions due to sample size?

I am currently working for a project team that is trying to reduce the number of defective parts produced in a factory. Without going into too much detail, the plant has a safety procedure where they ...
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28 views

Comparing rates of success in paired groups of samples

I have $2n$ paired populations, on which I measure a rate of success, let's say $(r_{group}^i)_{group \in (0,1)}^{i \in[1,n]}$ where $r_0^i$ and $r_1^i$ are the rates of success in the $i$-th pair of ...
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Fairness of a Coin

A coin is tossed $40$ times. Define $T$ as the number of tails. i) Define the region of rejection by $|T-20|\geq5.$ Calculate $\alpha,$ the significance level --- $\displaystyle\alpha = P(y\leq15 ...
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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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Sampling comparison groups based proportionality versus real-world frequency

I am looking at differential gene expression (using a t-test) in the context of five Breast Cancer Subtypes. I am working with data in which the distribution of subtypes matches real-world frequency ...
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30 views

How to interpret parameters of GLM with binomial family for proportions

I would like to use glm with binomial family for proportions. However, I am wondering how could I interpret the parameters that is important in my case. In binary logistic regression one can interpret ...
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29 views

Can a proportion confidence interval be thought of as error of estimation?

One interpretation of a confidence interval for a mean is that the most plausible position of the mean (given no more information) is in the middle of the confidence interval, and the plausibility ...
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paired subject design test of proportions

I am analyzing a performance data set and would like to compare across two different conditions. I have three subjects, which were tested over a number of trials. Each trial had a chance of being in ...
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27 views

Comparing differences of ratios in 2 independent populations

I have a setting that I think is quite similar to the one described in What type of statistic should I use to compare ratios in my experiment?. I have two independent populations, which were screened ...
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1answer
36 views

McNemar's Test for repeated sex ratio data

I have proportion data (sex ratio of a dioecious plant) for a population that was measured three times. I would like to know if a McNemar's Test is the most appropriate analysis to answer the ...
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21 views

Post-hoc test for prop.test with 3 samples

I am performing a prop.test() in R for 3 different groups (samples). The result is a p-value that tells me that the observed proportions differ between the groups. --> How can I now find out whether ...
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weight of sample sizes in quasi-binomial GLM for proportion data

I'm studying a colonial organism, and my hope is to compare differences in percent survival between three treatment groups. The results are clear, there is a 55% difference in survival between ...
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87 views

Are different p-values for chi-squared and z test expected for testing difference in proportions?

I'm trying to test the difference in proportions using the z test method and chi-squared method, but am getting very different answers. Is that normal? My data: ...
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Prop.test alternative

I want to test if the proportion estimated by (600/100000) is less than 0.6. With prop.test(600, 100000, p=.6, alt="greater", correct=FALSE), p-value = 1. With ...
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41 views

Is Chi-square the right test to use when comparing multiple proportions

In my analysis, I have 4 groups: FLU-P (symptoms with virus) FLU-N (symptoms without virus) HCY-P (healthy with virus) HCY-N (healthy without virus) I am looking at the level of antibody ...
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Test of two proportions from the same survey

I was wondering which test I should use for comparing two proportions from the same survey. Example: A survey of 1000 people ask two question. "Do you smoke everyday?" and "Do you drink alcohol ...
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Statistical test for comparing two response options in the same survey item

Is there a way to determine whether the proportion of respondents that endorse one response option of a question is different than the proportion of respondents that endorse another response option of ...
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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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Analyzing Social Behavior in Bats

I had a question about what might be the best way to approach one of my datasets. I had been using one method, but a recent talk with one of my professors made me think that perhaps it wasn't the best ...
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Correlated Proportions shown in a Mosaic Plot. What is the fitted model that generates residuals?

I have a 2-by-2 table of correlated proportions where I am plotting the positivity of two diagnostic methods applied on a sample of 216 individuals: ...
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15 views

interrater reliability for proportional (not count) data

My experiment has the following form: a rater assesses a visual image and records a single value, p, which is his estimate of the proportion of that image composed of a single color. Thus, the data ...
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96 views

Deriving the power formula of the one-sample proportion test

I have to derive the power of the z-test in testing $$ H_0: \pi=\pi_0 \text{ versus } H_1: \pi>\pi_0 $$ Denoting by $p$ the sample proportion, the power equals $$ ...
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Significance test for percentages

I have a test in which a person can choose to be in one of three chambers, and I want to compare two different population of people according to the time they've spent in each location. What is the ...
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Comparing Proportion of Positive Tests

A condition or disease (D) is measured using two different methods (A and B) in a sample of 1,000 individuals from a population. Using method A, the percentage of positive cases is 25%, whereas method ...
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316 views

SPSS - making percentage variables

I need to transform a fairly large data set in order to analyse a certain variable as a percentage. I have seconds that I want to convert to their percentage value but by grouping variables. ie. ...
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R power.prop.test and power equation in the difference between proportions

I am looking into the formula built into the R function power.prop.test{stats} and I am stuck trying to understand the following calculation: ...
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How to test a difference in proportions… over many iterations?

I'd like to compare results between two set-ups (let's call them A & B) whose outputs are the proportions of a quantity allocated to three options let's call them (1,2 & 3). The null is that ...
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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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Can I run a multivariate quasi-binomial analysis of proportion data?

I am trying to best analyse a set of foraging ecology data with >10 behaviour categories (DVs) and 3 levels of IV (season, sex, age). The time which an animal spent engaged in a behaviour was recorded ...
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Distribution of proportions relative to sum of random variables

Let $X_1,...,X_n$ be iid lognormally distributed variables and $X_{sum} = X_1+...+X_n$. What is the distribution of $\frac{X_k}{X_{sum}}$ for each $k$ in $1..n$? What are their density functions? ...
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Why not use always a binomial exact test to compare two proportions instead of chi square?

I am trying to figure out what test I should use in the following scenario: I know that there is a lot of room for improvement in a specific area at work - being extremely critical, let's say that ...
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Association between two proportions using p-value

I have two proportions and I need to see if they are associated somehow. The null hypothesis is that they are equal. I'm using R. So I get the pooled proportion: ...
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1 sample z test of proportions

We are trying to work out whether what we currently do is accurate. We want to work out if a proportion (% scoring 5 on a 5 point scale) are significantly below a target score. Normally a 1-sample ...
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44 views

Statistics on tastings

Some people at my workplace have had some fun lunch discussion as of late, concerning some people's alleged ability to taste the difference between things one thought one shouldn't be able to taste a ...
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68 views

Using proportional data with a binomial error structure in R… a worked example needing answers!

I am trying to test if the proportion of herbivores in spider's diets is related to the proportion of herbivores in their grassland, but am struggling to understand if I should be using a binomial ...
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142 views

Solving formula for confidence intervals on two proportions

I'm interested in comparing two independent proportions from two samples. The formula for doing so is available in the Internet (e.g. here). So far, so good. But my main purpose is not to build a ...
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Website Conversion: how to calculate confidence interval for tomorrow's conversion rate

Let's say I have a website with certain number of visits per day and conversion events: ...
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39 views

Testing small proportions

My data is made up of 4 groups, each with a large and identical sample size of 20,000. The number of successes in each group is fairly small: ...