# Questions tagged [differences]

The process of taking the difference between two values to achieve desirable statistical properties. e.g. paired differences t-test, differences between time points in an AR(1) model, and difference-in-differences causal impact analysis.

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### Statistical test to show differences between two categorical datasets

I have two categorical datasets that I would like to compare against each other, but I'm not exactly sure which test to choose and how to go about it. Both datasets show the number of cases for 8 ...
1 vote
47 views

### How to compare cases and controls after adjusting for age differences?

I have a dataset in which I have different measures (a, b, c) and two independent variables: D which is an independent binary variable representing cases (1) and controls (0), and age is another ...
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### What is the difference between a one sample t test of the difference between two groups versus a two sample t test comparing the two groups?

Let us say that we currently have two independent groups $G_1, G_2$ with equal sample numbers $n_{G_1} = n_{G_2}$ and may not have equal variances ${\sigma_1}^2 \neq {\sigma_2}^2$. If the statistical ...
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1 vote
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### Getting relative measure of difference between two numbers - Reference (close to) zero

I'll be writing a program that compares two numbers and based on how different they are, perform, or not perfom an action. It would make sense to have one formula to get a standardized measure that I ...
1 vote
16 views

### Measuring treatment effect when only half the the treatment group appear affected

I have data for a set of customers divided into treatment and control, where the objective is to check the impact of treatment on customer’s bank balance. To this purpose, I computed the percentage ...
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1 vote
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### What is the distribution of similarites between 2 iterations of a binomial variable?

Suppose I have a binary vector $v$ of dimension $n$ with $np$ entries set to $1$ and $n(1-p)$ entries set to $0$ (where $0 \leq p \leq 1$, and $q:=1-p$). Suppose I then generate a random vector $w$ by ...
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### Which test do I need for testing differences in two populations?

I would like to compare the different variables in a life table of two populations and check if the differences are significant. However, I am totally unsure which test is appropriate. For example, I ...
20 views

### How to calculate reliability of difference scores?

I am trying to calculate the reliability of a difference score. Specifically, the data have, for each participant, scores for 10 items in Condition X (1s and 0s), as well as 10 different items in ...
68 views

### Is there a formula for the 95% confidence interval for the Skellam distribution or difference of two Poisson r.v.'s?

I have two independent Poisson random variables and want to assess the confidence bounds for X - Y. I know there is a closed form solution for Poisson confidence bounds, but need the difference. Can I ...
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20 views

### How to compare if multi-class outputs are different?

I am testing different multi-class (16 classes) classification models (ANN, DNN, DL, and so on) and the overall accuracy varies from 0.75 to 0.92. Despite that 0.92 is greater than 0.75, is there a ...
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80 views

### How to calculate mean difference for effect size calculation?

For a two-sample effect size calculation on paired data (or a one-sample test on differences), does it make sense for an effect size to be negative for a hypothetical % increase of a mean? I’m doing a ...
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### Statistical difference between very small distributions

I am evaluating machine learning classifiers with 4-cross validation due to very small dataset. Is there a way to determine if a classifier is better (other than F1 averages) from only 4 performance ...
1 vote
22 views

### How to model a difference score for cross-sectional, hierarchical survey data

What is the best way to model a difference score that is based on cross-sectional survey data, while also taking into account the hierarchical structure of the survey data? I have the following survey ...
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175 views

### A time-series where the average of the difference depends only on the interval

Consider a time-series: $\{X_1,X_2,\ldots,X_T\}$. Then, we can think of the difference like $X_{t+r}-X_{t}$, where $r$ is an integer. Here, I am wondering whether there is any time-series process that ...
• 401
1 vote
41 views

### Error between average of averages and true average [closed]

It is known that the average of averages can yield an incorrect result as compared to the true average. The classroom example comes to mind: if the test results of class A is [50, 60, 100], class B is ...
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### Can I test for a significant difference within one variable?

I collected microplastics falling on an island in a year. The types of microplastics are fiber (F) and miscellaneous (M) particles. I want to know if the number of each that fell are significantly ...
14 views

### Improving an ARIMA model by eliminating AR/ME terms

I've come over the following two statements to manually improve the fit of an ARIMA model by changing its parameters $p,q$. If the AR coefficients sum to nearly 1 and suggest a unit root in the AR ...
• 103
662 views

### Independent Variable vs. Dependent Variable in Statistics

Following are the definitions of independent variable and dependent variable I found on the internet: <1> In statistical modelling, the dependent variable is studied to see if and how much it ...
128 views

### Inverting diff() and BoxCox() in R

i'm doing a project with a non-stationary time series. i used BoxCox trasformation and differences to make it stationary ...
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### One-way Table vs Two-way Table. What’s the difference?

The following is the definition representative of the definitions if you google the difference between the one-way and two-way table: Sometimes we talk about data tables in terms of independent and ...
110 views

### Expected Value of the Difference Between the Powers of Two Randomly Selected Numbers From a Standard Normal Distribution

My question is similar to (and an extension of) this one. I select two values ($i$ and $j$) at random from a standard normal distribution. What is the expected value of $|x_i^n-x_j^n|$ for all integer ...
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1 vote
58 views

### Transform Second Difference Predictions from VAR model back to levels

I am currently working with a VAR model in R using the second difference of some variables (it only becomes stationary after differencing twice). So far I'm trying to see if the model fits one of the ...
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34 views

### Train Test leakage

Imagine the following dataset. 1 --> Person buys this product sometimes 0 --> Person never buys this product: ...
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1 vote
722 views

### How does the Bayesian Information Criterion work for model selection? [closed]

I am aware that we can use the BIC values from different models in order to determine which model predicts the data best. However, I'm a little confused about the criteria used to determine which ...
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162 views

### Joint posterior distribution of differences

I have data $x_1,...,x_n$, $y_1,...,y_m$ and $z_1,...,z_p$ where $$x_1,...,x_n\sim N(\mu_x,\sigma^2_x)$$ and $$y_1,...,y_m\sim N(\mu_y,\sigma^2_y)$$ and $$z_1,...,z_p\sim N(\mu_z,\sigma^2_z)$$ Now let'...
17 views

### Relationship between std dev of difference of 2 random samples of a distribution and the std dev of the distribution

I am studying the analytical variance of a clinical test. In published work I observed two things: 1) when looking at a particular patient, the std dev of repeated replicates was 11.5 points. 2) when ...
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### how to treat values that evaluate to negative infinity with computing a percent reduction

A main limitation for reporting or measuring a percent reductions is having zero in the denominator. For example, if one was counting data on paired subjects and then analyzing the effects of some ...
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281 views

### If B is backshift operator, then how to calculate 1/(1 - B)?

We have known that: when |r|<1, (1−r)^-1 = 1 + r + r^2 + r^3 + r^4 + . . . But for 1/(1-B), since the coefficient of B is 1, the power series 1 + B + B^2 + B^3 + . . . can not converge. In my ...