Questions tagged [odds]
The odds of an event is the ratio of the probability that the event will happen (p) to the probability that it will not happen (1-p).
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Interpretation of coin toss: odds of getting a tail in two coin flips
Let's say someone asks me: What are the odds of getting a tail when a coin is flipped twice?
Assuming the coin is fair and tosses are independent, I see two ways of solving this problem:
If we ...
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Use of weights in a binomial model, with the response no longer a proportion
I am studying the factors that influence mosquito feeding behavior. In the experiments, N mosquitoes are exposed to a host for a duration t. At the end of this exposure, we count how many mosquitoes (...
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Convert β to odds ratio?
I would like to convert β-values into odds ratios. It is about table 1 on page 5 in the article
„A revised inventory of Adverse Childhood Experiences“
https://www.semanticscholar.org/paper/A-revised-...
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Beta regression: slope of scaled predictor
I want to fit a beta regression with an scaled continuous predictor, and express the slope in terms of proportion (not at the transformed, log-odds scale). In other words, I would like to express the ...
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Correct interpretation of a logistic regression coefficient
I have a simple confusion regarding the interpretation of logistic regression. Suppose married people are more likely to be employed compared to single people. In here, unemployment = 0, employment = ...
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Risk ratio or odds ratio?
I have a question which may seem stupid. This is for a retrospective cohort study.
I have a table like this for my outcome:
Among the 20,000 patients in group A, 4671 are dead (23.55%). Among 50,000 ...
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How to calculate the increased likelihood of drawing a type of item from a supply of mixed item types after adding more of a specific items type?
There is a board game, The Castles of Burgundy, which has a supply of 40 "black market" tiles, of which 16 are beige, 8 green, 2 gray, 6 blue, 6 yellow, and 2 burgundy.
The game takes place ...
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Scaling odds ratios and converting them to probability
I'm trying to calculate a scaled odds ratio and convert them into percentages for an analysis I am doing.
I have just one independent variable in the model, SAT score. Dependent variable is college ...
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model formulas for glmer
I have a glmer (library lme4) logit model that I conducted in R. I have very basic knowledge in stats and glmm models are completely new to me. My Models in R basically are like this:
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Color sequence odds on roulette [duplicate]
Consider a fair roulette game with 18 red numbers, 18 black numbers and 1 green zero.
At each round, the probability of winning by betting on red or black is 18/37, which is 48.6%.
If we play a lot of ...
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How do payouts for bets change as the odds change?
Say that there's a horse race between the two horses Alice and Bob. People bet on which horse will win. The "house" is taking no money off the top, so basically it's a direct transfer where ...
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Does testing the statistical significance of an odds ratio always produce a smaller p-value than a z-score obtained from the test of two proportions?
I have a question regarding the significance testing of an adjusted odds ratio vs. the significance testing of the adjusted difference between two proportions using a z-score. This is following the ...
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Calculate difference in log odds between two logistic regression models
I would like to calculate the difference in log-odds between the error of two logistic regression models, given the correct answer aka ground truth (depression present${}= 1;$ depression absent${} = 0$...
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Should the odds ratio be used to judge incremental information in psychological scales?
I am looking at the incremental validity of the MMPI-A-RF (a psychological instrument) and MACI (another psychological instrument) in the prediction of the DSM code for depression disorders found in ...
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Score for over/under representations of a variable in sub-group
I have a corpus of book publications split into different clusters. I have information about the nationality of the authors (variable A) and the nationality of the publishing company (variable B).
In ...
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Simpson's paradox detected via multivariable logistic regression?
This is not homework.
This is simple self-learning from real data.
I am fitting a logistic regression model as follows:
$$\text{logit}(p_i) = \beta_0 + \beta_1 race_{i} + \beta_2 x_{2i} + \beta_3 x_{...
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Better odds with $9 bucks on lotto?
I think I have a juicy one! My state's lotto game is 2 dollars, you select 6 numbers between 1 and 40, (odds to get all 6 are 1 in 3,838,380). However, if you pay an extra 1 dollar (so 3 in total) you ...
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How to adjust team win probability based on in in game win probability
I have a formula to calculate each team's win probability based on their win rates and home court advantage. So lets say I use it to determine that team A has 45% chance to win and team B has 55% ...
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Probably that an item was not selected in a sample
I have a population that a sample was taken from, and one "group" was not selected in the sample. I am wanting to find the probability of one group not being selected. I will use red/blue ...
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Scale of y-axis of a plot showing the predicted outcome risk for a continious predictor in a logistic regression model
I was previously informed in another thread that my plot on the y-axis is showing odds and not odds ratios. The following example code and figure depict this.
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What are the odds for winning this drinking game?
Out of pure boredom during the corona period back in 2020 I 'invented' a drinking game which seemed to have a fair outcome, but I am not sure. We were sitting on the couch and after a lot of beer, and ...
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Determining odds of an event happening 6 times more than average
Math/statistics lovers, I need your help. I have always sucked at figuring these out. And it makes me feel horrible about myself.
Assuming an accurate average has been determined, if a given event ...
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Logistic regression coefficients compared to the mean in R
No doubt this is a stupid question but I can't seem to find help anywhere online.
I want to do a logistic regression with 2 independent variables.
Ideally, I would like to see how each variable ...
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Probability of net gain being greater than 0 lottery question
I'm working on some practice exams and I came across a probability question that stumped me.
"In a lottery game, for any lottery ticket bought at random, the chance of winning each prize is ...
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Card Collecting Odds
My friends and I are thinking about participating in an event to collect these cards. There are 8 total cards in the set, and we can buy a pack of 10 random cards at a discount. So we were wondering, ...
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Can we compute the expected value of a football match final score?
I am asked to make predictions for the exact final result of some football matches. To be clear, I do not have to place any bets on them, just guessing the final score.
To do that I was thinking about ...
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What does it mean if the exponential of the coefficient in a logistic regression model return infinity
I have fitted a generalised linear model in R using the GLM command
m = glm(A ~ B+C+D+E , data = data, family = binomial(link = logit))
When trying to interpret the models output to find the odds of ...
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Better to pick first or last?
If 8 balls placed in a bowl and 1 had a prize and 8 ppl are choosing in order each ball. Is it better to go first or last without putting balls back in once each person takes one out?
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Difference between odds and odds ratio? Interpreting logistic regression coefficients [duplicate]
I was wondering what the difference is between odds and odds ratio in logistic regression. I understand that formally, odds is the probability of success over the probability of failure, however, I ...
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Mean of geometric distribution is odds?
Context: I mean the $P(X=k)=(1-p)^k p$ not the $P(Y=k)=(1-p)^{k-1} p$. Apparently the mean of the 1st kind of geometric is $\frac{1-p}{p}$ instead of $\frac{1}{p}$ for the 2nd kind of geometric. I ...
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Very different sizes of parameter estimates in lmer vs glmer (binomial) versions of “same” model (R)
In a 2-level glmer analysis the assumptions did not hold, so I created a binary outcome variable instead and run the same model setup on that (most Y values were 0’s and 1’s originally). With regards ...
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Getting probabilities from odds
Simple question here.
Consider an urn with balls of three colors. 50 % of the balls
are red, 30 % black, and the remaining balls green. The experiment is to
draw a ball from the urn.
What is the ...
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Numerically stable log-odds of intersection of independent events
Suppose we have independent events $E_1,\dots,E_n$, and define $E = E_1 \land \cdots \land E_n$ to be the conjunction (logical-and) of these events. Let $p_i=\Pr[E_i]$, $p=\Pr[E]$.
If we are given ...
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How can I calculate the odds of exposure for >1 outcome group, combined, using the rms::lrm function. Predict? Contrast?
I have been using a logistic model from rms::lrm to estimate the odds ratio of a binary exposure on an outcome, using splines [time] as Frank Harrell recommended. I ...
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Probability of Winning a Prize from a raffle with Multiple Winners with Multiple Entries
So let's say there's a raffle to win 500 prizes for a raffle and you can have multiple entries. There are currently 200,000 entries and I have 200 of those entries. Each person can only win once as in ...
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What is the effect size `h` in `pwr::pwr.p.test` in `R`?
The R package pwr has a function for calculating the required sample size for a one-sample proportion test (I assume a z-test ...
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odds ratio for two variants of covid [duplicate]
I need to calculate the odds ratio for mechanical ventilation and death in relation to
different early COVID-19 symptoms for two COVID variants - delta and omicron. How should I do it? I want to ...
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What is the intuition behind the odds scale?
What is an intuitive explanation of the odds scale?
In a logistic regression such as $$logit(p) = \beta_0 + \beta_1 x$$
we often interpret $\beta_1$ by looking at the odds ratio, $e^{\beta_1}$, which ...
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Interpretation of continuous variable in an odds ratio for logistic regression
I have an odds ratio of 1.02 for x variable (Age, a continuous variable measured in units "1 year"). My response variable is Y. I would interpret this as for every increase in Age by 1 year ...
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Log of the odds in Logistic Regression
In simple logistic regression i noticed that many researcher neglect the constant part of the logistic regression equation.
Log(odds) = a + b Gender (say that 0 = Female and 1 = Male)
So the log of ...
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Intuition of the log odds linearity assumption for logistic regression
I'm currently having trouble understanding the assumption of logistic regression that the input variables must be linearly related to the log odds. Specifically, what actually happens to the model ...
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D&D Probability question: why am I wrong?
In Dungeons and Dragons, the primary die used for success or failure is the D20, or 20 sided die. A 1 is a critical failure, and a 20 is a critical success. When one has advantage, one rolls 2 dice ...
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Interpretation of Odds Ratio (OR) in Fisher's exact test
I've tried using R operating Fisher's exact test to test for independence of the 2 datasets below and struggling to interpret the Fisher report. Please have a look at the data and the Fisher's test ...
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Probability your name will be drawn out of a hat without replacement
Let's say you put your name in a hat with 7 other names (n=8). Only 4 names will be drawn from said hat. Each name will be drawn one at a time, without replacement. What is the probability that your ...
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Flipping Coins : Probability of Sequences vs Probability of Individuals
Here is a problem I thought of:
Suppose I am watching someone flip a fair coin. Each flip is
completely independent from the previous flip.
I watch this person flip 3 consecutive heads.
I interrupt ...
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Chances of four people being drawn together
There are eight people in a golf group. There is going to be a draw to split them into two groups of four. There are four people within the group who would like to be drawn together. What are the odds ...
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What are the odds of 8 being drawn out of a group of 10 digits 5 times in 8 tries? [closed]
I am wanting to know the odds of something happening. What are the odds of 8 being drawn out of a group of 10 digits 5 times in 8 tries?
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meanBEINF vs predict(model, type = "response') in BEINF GAMLSS. and determining odds of predictor variable coefficient
A variation of this question has been asked, but certain items remain unanswered -
I am modeling the proportion of mortality (Prop) using a single continuous predictor variable which is temperature (...
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How does Shapley obtain values in the probability space in tree classifiers?
By default, the Shapley values for a tree explainer (e.g. based on xgboost) are in the log odds space (where they are additive). However, there's a functionality in the package to obtain values in the ...
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Transforming linear mixed model effect estimate to odds of a predetermined increment of change
I'm studying patient reported outcome in relation to treatment modalities in cancer. To assess the effect of a specific treatment (yes/no) on a specific outcome (normalised to 0-100, repeated measures ...
