# 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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### Given two non-overlapping confidence intervals, calculate confidence interval for difference between means [duplicate]

Let's say we have two means with a confidence intervals calculated, a±b and c±d, such that (a+b) < (d-c), e.g. the two confidence intervals are non-overlapping. How would I calculate a confidence ...
61 views

### compare these three numbers whether they are significantly different or not [closed]

I have three measurements of a soil property. They have the same unit but only these 3 numbers. I want to compare these three numbers whether they are significantly different or not. What test is ...
10 views

### Multivariate forcasting when variable observations are not contemporaneous: lag logic

I am looking at various VAR models for several time series, doing one-ahead forecasts. Within each period of observation there are sub-periods. Variable x is ...
19 views

### How is standard error affected by multiplication?

If I have some measure, suppose the difference of two means, and then I multiply it by 100; how will the standard errors be affected? Will they be multiplied too? or will they be completely different?
6 views

### Standard error for Rate differences

I have a database structured like this: ...
33 views

### Retrospective cohort study and case control study

What study would best suit looking at the association between low birthweight and later academic performance? Note - 1000 low birth weight children and 3000 normal birthweight children were included ...
83 views

### Differencing estimator in two-way fixed effects model

Consider a simple linear panel regression model with two-way fixed effects: $$Y_{it}=\alpha_i+\mu_t+X_{it}'\beta+u_{it}, \quad i=1,...,n, \ t=1,...,T,$$ where $n$ and $T$ represent the total units in ...
13 views

### 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 ...
15 views

### Changing the range of data before relative difference computation

I have a correlation coefficient obtained from measurement and a correlation coefficient obtained from theoretical model. I am searching for a difference metric to show how well these two correlation ...
14 views

### Do I need to normalise/standardise my data, or is percentage change ok?

I'm doing some analysis of two data series, both of which are currency (GBP) over time. My hypothesis is that there's a relationship between the two series. One series is aggregated spend data, the ...
20 views

### How to calculate relative lift in Difference-in-Difference

In difference-in-difference finding the absolute difference is pretty straightforward difference = (Test{Post} - Test{Pre}) - (Control{Post} - Control{Pre}) But if ...
26 views

### How to apply second order differencing to time-series regression?

I have the following regression where the dependent variable is I(2), i.e. I need to apply the second order difference to make it stationary. Now the question would be whether I have to apply the ...
46 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 ...
18 views

### Should i make correlation matrix of (1) first difference logarithm, (2) logarithm or (3) the natural numbers?

I am currently working on a project where I am looking at how prices are affected by changes in the exchange rates. For an example, I want to see how a change in my currency (Norwegian Kroner) affects ...
21 views

### Developing intuition on what difference between consecutive points means

As an example, let's take var_a and var_b: var_a <- c(0,10,10,9,12,10,10,0) ...
164 views

### Which statistical test should be used for comparing frequencies of a categorical variable levels by another categorical variable (figure provided)

I would like to show that marital statuses differ between different educational levels. Which statistical test should be used for this purpose? And how should I write it under my methods? METHODS: ...
14 views

### How do I add back the seasonal trend?

I worked on to predict the future values of my model but as they had a seasonal trend I had to do a lag differencing of lag=7. But now how do I add back that trend to get original values.
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### Over Differencing a Time Series

Consider the simple white noise process, $Z_t = a_t$. Discuss the consequences of over-differencing by examining the ACF and AR representation of the differenced series, $W_t = Z_t - Z_{t-1}$. Answer: ...
21 views

### How to calculate the percentage difference for multiple values

If I want to calculate the percentage diffidence for two values (v1 and v2), I would use [(v1-v2)/(v1+v2)/2]*100. But I do not know how to do this if I have three or more values (v1,v2, v3...). Not ...
32 views

### Differencing in a simple OLS regression

I am attempting to do a simple OLS regression on time series data from 1990 to 2019, and there a trends in my variables GDP capita (dependent variable), oil prices etc which I am able to difference. I ...
25 views

### Checking significance in differences between groups (gaps in income between genders and education levels)

I wonder if you could give me a hint on how to find out whether there is a significant difference in the income gap between genders and their education level. The picture below shows education levels (...
17 views

### Differences in Differences - Athletes, injuries and salaries?

I am preparing the dataset to perform a DiD analysis. The dataset is panel and collects information from 2000 to 2007 on a group of athletes of a specific league. I would like to verify if the ...
198 views

### Why this OLS fitting will converge to (0,-0.5)?

In this AR1 model, if we fit y with diff(y), regardless the true coefficient, when N is large, it seems the model will converge ...
43 views

### Time series difference operator

I have a question regarding the difference operator of SARIMA models. I am attempting to write out $SARIMA(2,1,2)(2,1,1)_{24}$. This seasonal ARIMA model has therefore 2 difference operators. I have ...
24 views

### What is the link between the order of the AR process and the order of the Augmented Dickey-Fuller test in case of first differences?

I realize that in general ( for an AR(p) process ), you should include p-1 lagged differences in the ADF specification (when testing for non-stationarity). I was recently told, however, that when ...
28 views

### Comparing two frequencies

Say I have two samples and I am measuring the amount of times a molecule appears in each. In sample 1, this particular molecule appears 200 out of the 1000 total molecules measured. For sample 2, it's ...
25 views

### First difference estimator inconsistent

This is a simple issue but I seem to need some illustration . If I have a first difference model as in : $$y_{it}-y_{it-1} = (X_{it}- X_{it-1})'\beta + (U_{it}- U_{it-1}) \ \ t=2,..T$$ which I am ...
172 views

### Sample size calculation - repeated measures, two groups

We want to calculate sample size for detecting the difference between mean depression scores of two groups of patients after three months of treatment - i.e. those who received a specialized mental ...
48 views

### Whan calculating the significance of a difference, when do we use separate variances and when do we use pooled variance?

When you check if the difference between two sample proportions is significant, some sources (like Khan Academy) recommend using a pooled variance, while others (for instance statistics for dummies) ...
19 views

### Time series I(0) and I(1) - how do I use it in a model?

I am analyzing two time series with the goal to run a VAR-Model. Now I ran a KPSS-test to test if the time series were stationary. The result is now that one time series is I(0) while the other one is ...
11 views

### power, correlations and difference scores

Would it make a difference for a statistical power calculation whether the correlations are obtained using the simple measures or whether they are difference scores? Would you need more participants ...
181 views

### How to reverse log difference?

I am currently doing log differences to a dataset and I want to revert back to the actual values. I'm trying to understand why at the end we need to multiply by the original value (and why we do not ...
30 views

### First-differences regression of a cointegrating system: forecasting and interpretation

I am working with a time series regression. In particular, both my dependent and independent variables are I(1) and they are co-integrated. I was wondering the following: If I run a regression with ...
34 views

### Interaction effect in logistic regression

I have applied logit model, where my dependent variable is Emp (Employment) 1 if employed otherwise 0, and used level of education and Health status as independent variables where: Education consist 6 ...
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### Drastically different results from summary.lmerModLmerTest vs anova.lmerModLmerTest

I am beginning in linear mixed model with lme4. Recently, I have encountered a problem where results obtain from summary.lmerModLmerTest and anova.lmerModLmerTest are drastically different. My model ...
85 views

### Can I apply both differentiation on lag 2 and two differentiations on a time-series?

I'm working with time-series and I have seem two approaches from different teachers. One of them used the following code in Python: ...
48 views

### Basic mean question

Learned today in stats this cool piece of information: If you wanted to optimize the $(y-\overline{y})^2$ or differences squared, of some data. Where $\overline{y}$ is a constant y = number, then you ...
26 views

### Formula for sample size for hypothesis test for difference in proportions confusion

For a hypothesis test for difference in proportions: Source A (some Stanford professor): The sample size for both groups is $$\frac{2\bar{p}(1-\bar{p})(Z_\beta+Z_{\alpha/2})^2}{(p_1-p_2)^2}$$ \bar{p}...
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### Measuring magnitude of proportional difference between two items: cannibalisation and halo effects of products relative to promotions

I am trying to understand cannibalisation/halo effect between products when a promotion event occurs for one product and not another, this data is based in time, and the promotion status occurs at ...
194 views

### Seasonal term not significant after differencing

I am working with a time series (weekly frequency), $\{y_t\}$. I have 250 points in total. The time series is not stationary according to KPSS test (it is stationary according to ADF) at 5%. In any ...
63 views

### Summary statistics for two populations

I have two populations: part-time worker in the health industry (IND=17) and part-time worker in the financial industry (IND=12) For those two populations I have several variables (demographic ...
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### How can I separate the abundance factor of the incidence results?

I must calculate the incidence values for Watermelon Mosaic Virus in different seasons within of habitat. This incidence data comes from infection detection of some plant sampled in different habitats ...
48 views

### Is there a word in statistics for "mean divided by absolute difference"?

For two values, let's say a and b, I calculate a mean of two numbers divided by absolute difference between them. i.e. ...
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### Problem with differencing trend-stationary processes?

I have read somewhere (possibly in Hayashi's Econometrics text) that it can be problematic to work with differenced trend-stationary processes. I have not been able to find the exact source again and ...
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### Get predicted (leveled) value of y from a differenced regression in time series

Suppose I have two time series variables (x and y) which have unit root (non-stationary). I would like to regress y against x, but because they are non-stationary, I first stationarized them by ...
6k views

### What is the difference between econometrics and statistics?

It's never been very clear to me what distinguishes econometrics from statistics. My preliminary understanding was that statistics is data-focused whereas econometrics always starts from theory. But ...
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### How to pull in-sample fitted models towards out-of-sample optimum during training?

A common problem in prediction problems is getting a model fit on in-sample data to predict out-of-sample data with decent accuracy and precision. Assuming that we break a part of the in-sample data ...
29 views

### What is the expectation of absolute difference

Given: E(|X-R|) =2.5 E(|L-X|)= 3 where X, R, L are assumed to be normally distributed and independent. Standard deviations of |X-R| and |L-X| are known. what is E(|L-R|) ?