# Questions tagged [discrete-data]

Refers to data generated from a distribution that has a countable sample space. The discrete data tag may encompass categorical data, whether nominal (e.g. the distribution of race in a sample of individuals) or ordinal (e.g. socio-economic status), or an actual discrete random variate, such as a set of event counts (e.g. the number of errors on a page of text). Discrete data need not necessarily be integer, however.

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### Multilevel Modeling in Linear Mixed Models versus Generalized Linear Mixed Models

I am analyzing a data set that includes several discrete and continuous outcome variables (DV). For the continuous DVs I intend to use Linear Mixed Models (LMM) processed in SPSS. For the discrete ...
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### Computing a Confidence Interval for E[X] when PMF is given

I am given a Probability Mass Function for a discrete random variable. From the PMF I computed the Expected Value $E[X]$, the Variance $V[X]$ and the Standard Deviation $S[X]$. Here is an example (the ...
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### How to determine the correlation between a discrete variable and a continuous variable? [duplicate]

I have 9 conditions (discrete variables) with each having only two states: occurrence (corresponding to 1) and non-occurrence (corresponding to 0), resulting in a total of approximately 511 ...
3k views

### Is a Poisson minus a constant still a Poisson?

I am working with a process in which I expect my variable to be Poisson distributed. For reasons that have to do with the scale, however, the values I obtain have a minimum of 11. I have noted than ...
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### A set of values ​from a discrete uniform distribution is scaled down by the same factor

Use MATLAB's randi function to generate a set of values ​​that conform to discrete uniform distribution, such as {0,1,2,3,4,5}. If this set of values ​​is divided by an integer 10 at the same time, ...
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### Can a finite decimal number be a discrete variable?

If I have an array {0.1, 0.2, 0.3, 0.4, 0.5}, is this a discrete array? Are the values in it discrete values? (I have this doubt because many materials show that discrete values are usually integers) ...
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### Sampling from a binomial and get stuck in boundaries

I am trying to use the Metropolis-Hasting in order to obtain a sample for X that is a vector of length N of values that go from 0 to K (in this case K=3). So X ~ Binom(K, p) and p ~ Beta(1,1). For ...
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### Imputing a Continuous P-value Distribution from Discrete P-values [closed]

I'm exploring methods to create a continuous-like P-value distribution from discrete P-values. For example, consider the process where a balanced coin is tossed four times per experiment to note the ...
• 143
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### Probability distribution for weights in Gym machine?

Below is the image of weights in Gym, I would like to know what probability distribution that would fit the wear and tear of the weights. Below are my initial thoughts: (1) Has to be discrete ...
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### Error bars on average for discrete limited values close to edge of range

Let's say I have discrete data that can only fall into a limited range - for example rating a product with a score from 1 to 10. How would I go about assigning error bars to the average value of the ...
28 views

### Effectively Visualizing P-value Distributions with Excessive 1.0 Values

I'm dealing with a discrete statistical test scenario where a significant portion of the P-values calculated are exactly 1.0, due to the nature of the test statistic not exceeding its observed value ...
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### Suitable hypothesis test for non-normal, discrete data with repetitions

In the field of cryptography, one is concerned that algorithms execute in so-called "constant time" (more precisely, independent of the input data, or at least the parts of the data which ...
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### using mode or median

A survey is conducted among high school students, consisting of 30 questions designed to evaluate their levels of social media addiction. The responses to these questions are aggregated to calculate a ...
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### Discrete test statistics cannot form a uniform P-value?

I received this feedback on my permutation test design from a collaborator and I'm wondering if his claim is valid. My test statistics are discrete (like counting the number of red marbles found after ...
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### UMP size $\alpha$ hypothesis test for discrete distribution

Let $\left(Z_1, \ldots Z_n\right)$ be an i.i.d. sample with common probability mass function $$p_Z(j)=\vartheta^2 I_{[j=1]}+2 \vartheta(1-\vartheta) I_{[j=2]}+(1-\vartheta)^2 I_{[j=3]}$$ Find a UMP ...
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### Correlation Coefficient between discrete and continuous: is it possible?

Is it correct to measure the correlation coefficient between a continuous variable and a discrete variable? I visualized it and there is definitely no linear relationship the way I see it that is why ...
76 views

### Number of Phones in a word: Numerical or Categorical Data?

I'm trying to model a subset of the MALD dataset (language related) using Gaussian Distribution. MALD: https://link.springer.com/article/10.3758/s13428-018-1056-1 One of the variables I'm working with ...
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### Predictive Modeling of Overseas Filipino Workers' Average Length of Stay: A Comparison of Linear and Poisson Regression Models

i want to find our average length of stay in months with a discrete values however the number of months in the dataset is up to 60 that we can treat as continuous. I would like to determine when is ...
56 views

### Significance in 3x3 crosstab including low values and high N

I am conducting a study of 126 organizations. Each organization has one or more registered domain names. Each domain name needs to conform with specific cybersecurity requirements. Some ...
18 views

### How can I perform a comparison of poisson and linear modelling using one dataset?

my y is average length of stay in months however the number of months in dataset is up to 60 so I can treat it as continuous but my main objective is to identify when can i determine it's better to ...
191 views

### Multiple linear regression homoscedasticity/linearity

My question is about the implications of the violation of homoscedasticity/linearity for multiple linear regression. I have tried to find the answer in multiple sources but could not figure it out. I ...
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### Practically and probabilistically modeling discrete data that can take on a countable (potentially infinite) number of values?

As an example, let's say that we have observations of the price of some good at various points in time and would like to predict the distribution of the price of the good one point in the future from ...
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### Is it valid to take the midpoint of discrete outcome variables that express a range e.g. (1-20%, 21-40%) then calculate the mean of those midpoints?

I work in a health service and have a PhD student who was told by my boss (her primary supervisor) to measure clinicians' responses concerning what proportion of their clients had a certain condition ...
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### Extrapolating a Discrete Distribution to a Continuous one

Say I have a list of the letter grades of a class (meaning some number of As, Bs, Cs, Ds and Fs). Is there any way for me to take this discrete distribution and extrapolate it to the most likely ...
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### Mean of the means / ANOVA with percentages

I subjected aliquots of 4 replicates (microorganism cultures) to 3 different treatments + control. In each treatment, I : 1- counted the number of cells whose colour changed in 100 cells of each ...
180 views

### How robust is multinomial logistic regression to having a multi-label problem shoehorned into it?

Consider a situation where there can be membership in group $A$, group $B$, both groups, or neither group. If we wanted to predict group membership probabilities from some covariate information, this ...
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### Empirical Bayes grid approximation: How to prevent the prior from overwhelming the likelihood when there are many more samples in the prior?

I am trying to construct a grid approximation of the probability that an event will occur on the discrete interval 0 - 10, the spacing is 0.01. The probability that any single event on the interval is....
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### Distribution of the mean of samples taken from two different distributions

Consider you have some distributions $Z_1$ and $Z_2$ of which you select $n_1$ samples from $Z_1$ and $n_2$ samples from $Z_2$. We now add up these samples and take the mean. The question becomes, ...
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### Does the number of bins influence the "measures of similarity" among histograms?

I have calculated several "measures of similarity" among histograms and discrete probability distributions (such as Cosine similarity, Kullback-Leibler divergence, Jensen-Shannon distance, ...
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### Can I trust the results of a t test on 4 point Likert scale data which hides outliers?

I want to use an unpaired two-sample t-test of random samples of $n=40$ each. The sample data is from 4-point Likert scale assessments. I understand the t-test is not very robust to outliers, which I ...
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### Is my variable a discrete random variable, ordinal, or categorical?

I work in trauma research. We use a injury grading system that is fairly unique. Using a system developed in the 60s-70s - the Abbreviated Injury Scale - injuries are graded for six distinct body ...
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### Energy of a signal contained within a given band

Suppose I wish to compute the energy contained in a given frequency range using FFT. So, first, I compute FFT and take the squares of the absolute values of $x_k$. Can I then use discrete integration ...
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1 vote
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### FFT: zero-padding and mean subtraction

When computing FFT of a finite-time discrete sample with a non-zero mean, I get two different results depending on the order of operations: whether I zero-pad and then subtract the mean or subtract ...
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### Generating samples from a categorical proposal distribution with specific output (sample) structure

I'll caveat this question with that I do not think what I want to do is possible but suggestions in the right direction would be most helpful. Now my data consists of vectors of length six, where each ...
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### Discrete time survival analysis or Cox regression?

In an RCT, I want to find out whether the treatment (treatment vs control) has an effect on the uptake of aftercare (yes/no + time). I have five measurement points, which are not equidistant (i.e., ...
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### Sample size calculations for a pair-dependent discrete outcome

How do we calculate sample sizes (and power) for an outcome that is discrete and is only measurable between two individuals of a group? Suppose we have $n_A$ individuals in group A, and $n_B$ ...
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### Numeric variable that can't be applied to all my observations, causing NA's [duplicate]

Suppose I have a numerical discrete variable that does not apply to all my observations, i.e. 'years_married'. Not all the people in my dataframe is married, so they have an 'NA' registered in this ...
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### How does a machine learning model distinguish between ordered discrete int and continuous int?

Lets say I am classifying if a user will like a Airbnb listing or not (binary classification model) I have 2 features: Number of house rules the Airbnb host has. Since this is a count, this is a ...
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### Models for a discrete numerical response with only 5 distinct values

I have a response variable that takes on only 5 distinct values: -15, -5, 0, 5, 15. These values are obtained in a clearly categorical manner, meaning: if event A happens, then the outcome is 5, if ...
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### How to sample from a distribution with discrete variables with a known average?

My motivation is to produce carcasses of animals in an ecosystem. The animals have discrete sizes in kg (75, 216, 700, 2500, 5000, 8500, 25000). I also have the estimated percentage each animal ...
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### What kind of transition probability matrix indicates dependence/independence?

Suppose we have two discrete random variables $X$ and $Y$, both of which take values from $\{1,2,...,k\}$. $Y$ is generated from $X$ via a transition probability matrix (also known as the stochastic ...
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