# Questions tagged [inference]

Drawing conclusions about population parameters from sample data. See https://en.wikipedia.org/wiki/Inference and https://en.wikipedia.org/wiki/Statistical_inference

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### Find the significance of a variable in a linear model when another correlated variable has a stronger opposite effect

I have a linear model $Y = AX_1 + BX_2 + e$ where $e$ is noise, $Y$ is the dependent variable, $A$ & $B$ are coefficients, and $X_1$ & $X_2$ are variables. Suppose that we know in the real ...
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### Overall analysis of multiple trends of 2 variables

I have multiple sets of trends which show how the concentration of 2 quantities vary with respect to each other over number of observations. Each set is independent from each other and the duration ...
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### Regression inference: Exclude factors

thanks for everybody who was reading through this. In the meanwhile i was checking in detail every line in the code. The most recent changes visible here are correct. So this question is solved. I ...
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### Example of a Discriminative Bayesian Model

While reading through the differences between Generative vs Discriminative; Bayesian vs. Frequentist, I was able to classify the probabilistic models into a table. On further searching on Google, I ...
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### Computing The Center Of Multiple Data Points and Infering Related Data?

Intro: I'm building a freefall measurement device which uses multiple LEDs and analog photo senors to detect falling spheres and in turn compute the acceleration of gravity. Problem: The spheres ...
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### Finding values a and b to get PMF with certain mean and standard deviation

Suppose that the proportion θ of defective items in a large manufactured lot is known to be either 0.05 or 0.15, and the prior pmf of θ is as follows: ξ(0.05) = a and ξ(0.15) = b. Suppose also that ...
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### Type 2 error graphical representations

What is the statistical meaning of type 2 error in graphical terms. Why it is represented under alternative hypothesis curve not under null hypothesis curve.
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### estimating fixed-effects and interactions

I have read and understood the use of mixed-effect models for repeated measures. I would like help correctly specifying the type of model for my experiment. I recruited 3 types of subjects to listen ...
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### Question related to hypothesis testing

Topps, the collectible baseball cards manufacturer, claims that each pack of cards has 10 cards. In a sample of 50 packs, it was found that there were 9.75 cards per pack. Do these results support ...
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### Theoretical standard error when sampling from a single sample different results

When researching the standard error of the mean I found a code block on this forum that looked like this: ...
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### Fishers Exact Test construction

I have a series of binary opinion questions asked of a random selection of people visiting a website. e.g. "Do you support the Death penalty" etc. I also have a number of demographic binary ...
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### Likelihood problem. compute MLE

I wanted to ask you an opinion about this exercise. I don't understand how compute sufficient statistic in this case important point, to compute the log and derivate and find my MLE.
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### Interpretation of Chi Square Goodness of Fit Test

Suppose you run a chi square GOF test on a categorical variable with 2 levels and you reject the null (p= p0). If phat > p0, can you conclude that the population proportion is not only not equal to ...
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### Potential bias in a study design

I am trying to design a study regarding Diabetes. I have patients with test results of some indicator about their situation - sugar levels, but not in the classic sense that you may know. Every ...
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### Preparation for modeling: how to deal with a huge number of variables

The domain I'm operating in is Healthcare. So I have a lot of variables like visits to the doctor, prescribed drugs etc. - each one has a time dimension (5-6 years) and a "measure" dimension like ...
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### Is this summary about Bayesian inference for Normal distribution right?

I summarize this based on http://www.cs.ubc.ca/~murphyk/Papers/bayesGauss.pdf However, there are some questions about this. When the mean and variance are both unknown, can I set the prior of of ...
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### Empirical Density in R given posterior distribution

I am trying to solve the problem where I have calculated posterior distribution f(p|x) = Be(23,8) and prior f(p) = Be(1,1), given the n = 29 and x = 22. representing the comparison by using ...
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### Calculating sample mean of laptop batter for normal population

I have been learning statistics for last few months as I am cross training into Data Engieer role at work and I came across this exercise that I am not sure how to solve and was wondering if anyone ...
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### Some questions related to the asymptotic properties of lasso

A couple of questions have been bothering me. Let's assume, the number of variables is fixed and only n can grow (I only focus on low dimensional datasets): Is the lasso always is root n consistent ...
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### Can we make hypothesis test for a few variables while controling some other variables in a regression model?

My colleagues want to test some predictors in a regression model with the response of disease onset. Let us say we want to know whether pre-diagnosis, bmi, and hormone level have significant ...
690 views

### How to modify Fisher's exact test if sample size if larger than 20?

I have a 2x2 contingency table with the following values: $$A = 20, B = 10, C = 200, D = 300$$ As you can see, the sample size is much larger than $20$, the recommended sample size if one were to use ...
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### Matching with partially-observed covariates?

Context I have a randomized controlled trial where units $i \in N$ have one of two possible values (A or B) on variable x such that $x_i \in \{A,B\}$. Assume equal numbers of observations for all ...
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### What criteria differentials an A/B/C/etc… test with a Multivariate test with respect to webpages?

I'm a software engineer with a weak background in probability and statistics. I want to determine whether the position and color of the "Purchase" buttons affects my conversion rate. I want to create ...
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### What is the intuition behind loss functions in regression? Can I create one? What rules should I follow?

My question arises after reading this link, which presents 7 methods of regression, we know that each of these methods is determined by a loss function, my question is What is the intuition behind ...
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### Differences between methods of reporting variance

I am a neuroscience researcher without too much background in statistical theory. I have multi recordings from different samples and I want to precisely report the variation across the samples, and I ...
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### Utilization vs Percentile

My objective is to have high utilization of the resources by keeping only the required number of resources alive. Low utilization means the resources were not used effectively, while high ...
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### Multi Level Dependent Variable Statistical Test

I have a multi level dependent variable. The dependent variable is Tenure -  less than 1 year, 1-2 year and above 2 years. The independent variable is AHT. I need to conduct a statistical test ...
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### Shrinking Mean with Noisy and Skewed Dataset

I am having difficulty inferring the proper measure of central tendency in a noisy, right skewed dataset. The mean for each group is higher than is expected and the coefficient of variation is very ...
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### Linear regression for inference when logging regressor and target

I'm looking at the relationship between population density (X) and ad impressions (y). These features aren't normally distributed so I log both to create a linear relationship. The relationship looks ...
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### testing median value of top x% of sample value against median of top x% of of population

I have a random sample from population. I want to prove/un-prove that median/mean value of top x% of random sample represents the median/mean value of top x% of population. I have two questions: ...
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### Representative Sample - Air travel passengers and gender ratio

I have a question regarding the ways to build a representative sample for a research study focusing on air travel passengers in 3 different world regions (NA, EMEA, APAC) I think I should use the ...
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### Why do ridges in parameter space make things hard to estimate?

In this answer https://stats.stackexchange.com/a/279111/151862 Glen_b says The reason is that the d.f. parameter [of a t distribution] is very hard to estimate well from data, particularly if you'...
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### Stuck on rejection region for Likelihood ratio test [duplicate]

Assume $X_1$ .. $X_n$ ~ iid beta($\theta$,1) I'm supposed to construct a Maximum likelihood ratio test for: $H_0$: $\theta$ = $\theta_0$ $H_1$: $\theta$ != $\theta_0$ But I'm stuck at the last ...
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### How to choose a suitable $p$-value?

I encountered this problem: Suppose $Y$ has the following PDF $$f(y)=\frac c{(1+y)^2}\cdot I(0\le y\le \theta),\quad\theta>0.$$ A single value $y$ is observed from the distribution. ...
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### How to infer “groupings” of data points separated alone one dimension? [duplicate]

I have the following data: ...
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### Probability based on average/historical data

I have ten years of data, which I have averaged. Is it possible to calculate the probability that a future point will be less than a threshold based on my data? For example, say the average is 0.065. ...
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### Why do we use $n-2(k+1)$ when we are testing for differences in regression functions across groups?

I bumped into my econometrics book (Wooldridge 6th edition) over testing whether slopes and intercept are the same for two different groups (men and women, white and black etc.). It says that the ...
37 views

### Square of a contrast

If Yi (i=1,2,....n) are normally distributed with common variance v then consider the contrast C = Sum(AiYi) such that Sum (Ai)= 0 Now i know that C^2/Sum(Ai^2) is a vchi ...
117 views

### Good books on predictive modeling (for alpha signal research)

In terms of books on predictive models, I find ESL (elements of statistical learning) trying to cover too much and serves more like a reference, instead of explaining and developing the theories for ...
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### How to explain the closing of a performance gap in a descriptive trend analysis?

I haven't used inferential statistics in a few years, so I am blanking on a simple question. I ran a descriptive trend analysis on assessment results for a school district, disaggregated for group-...
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### Variable elimination - can I start from the middle of the network

I read that while doing inference in Bayesian network with variable elimination, any order will do. Say I want to have the below network, where every random ...
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### MP critical region for discrete random variables

Let $x$ be a discrete random variable with probability mass function $p(x)$, where $x$ belongs to $\{-1, 0, 1, 2, 3\}$. To test $H_0\!: p(x) = p_o(x)$ vs. $p(x) = p_1(x)$, where for above mentioned ...
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### same competition ratio, but different size

I am trying to give my student an advice about which application would be better to choose. The student is preparing for the public police officer test, and there're two options. This test is only ...
### Simple method to estimate $\sigma^2$ from i.i.d. samples of $y_i \sim N(\theta_i, \sigma^2)$
This is a normal means model: given $N$ i.i.d $y_i \sim N(\theta_i, \sigma^2)$ or equivalently  y_i = \theta_i + \varepsilon_i\, \text{ where }\varepsilon_i \text{ are i.i.d } \sim N(0, \sigma^2)...