Questions tagged [interpretation]

Refers generally to making substantive conclusions from the results of a statistical analysis.

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253
votes
16answers
473k views

What is the meaning of p values and t values in statistical tests?

After taking a statistics course and then trying to help fellow students, I noticed one subject that inspires much head-desk banging is interpreting the results of statistical hypothesis tests. It ...
260
votes
11answers
157k views

How to understand degrees of freedom?

From Wikipedia, there are three interpretations of the degrees of freedom of a statistic: In statistics, the number of degrees of freedom is the number of values in the final calculation of a ...
46
votes
3answers
50k views

Interpretation of log transformed predictor and/or response

I'm wondering if it makes a difference in interpretation whether only the dependent, both the dependent and independent, or only the independent variables are log transformed. Consider the case of <...
29
votes
3answers
24k views

Interpretation of simple predictions to odds ratios in logistic regression

I'm somewhat new to using logistic regression, and a bit confused by a discrepancy between my interpretations of the following values which I thought would be the same: exponentiated beta values ...
248
votes
2answers
171k views

Interpretation of R's lm() output

The help pages in R assume I know what those numbers mean, but I don't. I'm trying to really intuitively understand every number here. I will just post the output and comment on what I found out. ...
103
votes
2answers
50k views

Removal of statistically significant intercept term increases $R^2$ in linear model

In a simple linear model with a single explanatory variable, $\alpha_i = \beta_0 + \beta_1 \delta_i + \epsilon_i$ I find that removing the intercept term improves the fit greatly (value of $R^2$ ...
47
votes
5answers
10k views

Interpreting QQplot - Is there any rule of thumb to decide for non-normality?

I have read enough threads on QQplots here to understand that a QQplot can be more informative than other normality tests. However, I am inexperienced with interpreting QQplots. I googled a lot; I ...
34
votes
4answers
42k views

X and Y are not correlated, but X is significant predictor of Y in multiple regression. What does it mean?

X and Y are not correlated (-.01); however, when I place X in a multiple regression predicting Y, alongside three (A, B, C) other (related) variables, X and two other variables (A, B) are significant ...
69
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1answer
71k views

How to interpret coefficients in a Poisson regression?

How can I interpret the main effects (coefficients for dummy-coded factor) in a Poisson regression? Assume the following example: ...
7
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1answer
6k views

Interpretation of interaction term

I have a model: $$ \ln({\rm earnings}) = a+b_1{\rm female}+b_2{\rm white}+b_3{\rm female}\times{\rm white} $$ ${\rm female}$ and ${\rm white}$ are dummy variables. I have interpreted $b_1$ and $b_2$: ...
33
votes
1answer
38k views

What is the intuitive reason behind doing rotations in Factor Analysis/PCA & how to select appropriate rotation?

My Questions What is the intuitive reason behind doing rotations of factors in factor analysis (or components in PCA)? My understanding is, if variables are almost equally loaded in the top ...
39
votes
2answers
89k views

Interpretation of R's output for binomial regression

I'm quite new on this with binomial data tests, but needed to do one and now I´m not sure how to interpret the outcome. The y-variable, the response variable, is binomial and the explanatory factors ...
33
votes
2answers
4k views

Understanding p-value

I know that there are lots of materials explaining p-value. However the concept is not easy to grasp firmly without further clarification. Here is the definition of p-value from Wikipedia: The p-...
22
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3answers
13k views

What does “all else equal” mean in multiple regression?

When we do multiple regressions and say we are looking at the average change in the $y$ variable for a change in an $x$ variable, holding all other variables constant, what values are we holding the ...
55
votes
2answers
14k views

Real-life examples of moving average processes

Can you give some real-life examples of time series for which a moving average process of order $q$, i.e. $$ y_t = \sum_{i=1}^q \theta_i \varepsilon_{t-i} + \varepsilon_t, \text{ where } \varepsilon_t ...
28
votes
1answer
21k views

What is the difference between generalized estimating equations and GLMM?

I'm running a GEE on 3-level unbalanced data, using a logit link. How does this differ (in terms of the conclusions I can draw and the meaning of the coefficients) from a GLM with mixed effects (GLMM)...
25
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3answers
44k views

Interpreting interaction terms in logit regression with categorical variables

I have data from a survey experiment in which respondents were randomly assigned to one of four groups: ...
18
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2answers
20k views

Interpretation of betas when there are multiple categorical variables

I understand the concept that $\hat\beta_0$ is the mean for when the categorical variable is equal to 0 (or is the reference group), giving the end interpretation that the regression coefficient is ...
84
votes
7answers
46k views

Clustering on the output of t-SNE

I've got an application where it'd be handy to cluster a noisy dataset before looking for subgroup effects within the clusters. I first looked at PCA, but it takes ~30 components to get to 90% of the ...
6
votes
2answers
10k views

In three-way ANOVA, how to interpret the three-way interaction?

I have a significant three-way interaction (with no significant two-way interactions and no significant main effects). To begin with I have followed this up with two two-way ANOVAs (one at each level ...
27
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1answer
51k views

How to interpret coefficient standard errors in linear regression?

I'm wondering how to interpret the coefficient standard errors of a regression when using the display function in R. For example in the following output: ...
39
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4answers
33k views

How to interpret coefficients from a polynomial model fit?

I'm trying to create a second order polynomial fit to some data I have. Let's say I plot this fit with ggplot(): ...
14
votes
1answer
10k views

Interpreting the regression output from a mixed model when interactions between categorical variables are included

I have a question about my use of a mixed model/lmer. The basic model is this: lmer(DV ~ group * condition + (1|pptid), data= df) Group and condition are both ...
41
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3answers
484k views

How to interpret F- and p-value in ANOVA?

I am new to statistics and I currently deal with ANOVA. I carry out an ANOVA test in R using aov(dependendVar ~ IndependendVar) I get – among others – an F-value ...
8
votes
1answer
39k views

Which matrix should be interpreted in factor analysis: pattern matrix or structure matrix?

When doing a factor analysis (by principal axis factoring, for example) or a principal component analysis as factor analysis, and having performed an oblique rotation of the loadings, - which matrix ...
43
votes
5answers
52k views

What is the significance of logistic regression coefficients?

I am currently reading a paper concerning voting location and voting preference in the 2000 and 2004 election. In it, there is a chart which displays logistic regression coefficients. From courses ...
19
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3answers
23k views

ARIMA model interpretation

I have a question about ARIMA models. Let's say I have a time series $Y_t$ that I would like to forecast and an $\text{ARIMA}(2,2)$ model seems like a good way to conduct the forecasting exercise. $$ ...
12
votes
1answer
7k views

Can I interpret the inclusion of a quadratic term in logistic regression as indicating a turning point?

In a Logistic Regression with linear and quadratic terms only, if I have a linear coefficient $\beta_1$ and quadratic coefficient $\beta_2$, can I say that that there is turning point of the ...
10
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3answers
6k views

How to extract information from a scatterplot matrix when you have large N, discrete data, & many variables?

I'm playing around with the breast cancer dataset and created a scatterplot of all attributes to get an idea for which ones have the most effect on predicting the class ...
8
votes
2answers
8k views

How to interpret a box plot?

I have some data in which there are 5 categorical explanatory variables (concern, breath, weath, sleep, act) and 1 continuous response variable (...
30
votes
2answers
78k views

Interpretation of biplots in principal components analysis

I came across this nice tutorial: A Handbook of Statistical Analyses Using R. Chapter 13. Principal Component Analysis: The Olympic Heptathlon on how to do PCA in R language. I don't understand the ...
18
votes
3answers
14k views

Analysis of Kullback-Leibler divergence

Let us consider the following two probability distributions ...
30
votes
6answers
3k views

When are confidence intervals useful?

If I understand correctly a confidence interval of a parameter is an interval constructed by a method which yields intervals containing the true value for a specified proportion of samples. So the '...
19
votes
1answer
15k views

Interpreting 2D correspondence analysis plots

I've been searching the internet far and wide... I have yet to find a really good overview of how to interpret 2D correspondence analysis plots. Could someone offer some advice on interpreting the ...
17
votes
2answers
16k views

Interpretation of ordinal logistic regression

I ran this ordinal logistic regression in R: mtcars_ordinal <- polr(as.factor(carb) ~ mpg, mtcars) I got this summary of the model: ...
8
votes
2answers
29k views

Anova from R output interpretation

I have a question on how a statistician would normally interpret an anova output. Say I have anova output from R. ...
13
votes
1answer
12k views

Why does the standard error of the intercept increase the further $\bar x$ is from 0?

The standard error of the intercept term ($\hat{\beta}_0$) in $y=\beta_1x+\beta_0+\varepsilon$ is given by $$SE(\hat{\beta}_0)^2 = \sigma^2\left[\frac{1}{n}+\frac{\bar{x}^2}{\sum_{i=1}^n(x_i-\bar{x})^...
14
votes
1answer
3k views

The difference between with or without intercept model in logistic regression

I like to understand the difference between with or without intercept model in logistic regression Is there any difference between them except that with the intercept the coefficients regard the log(...
66
votes
5answers
52k views

How to interpret an inverse covariance or precision matrix?

I was wondering whether anyone could point me to some references that discuss the interpretation of the elements of the inverse covariance matrix, also known as the concentration matrix or the ...
29
votes
6answers
164k views

Interpretation of Shapiro-Wilk test

I'm pretty new to statistics and I need your help. I have a small sample, as follows: H4U 0.269 0.357 0.2 0.221 0.275 0.277 0.253 0.127 0.246 ...
14
votes
4answers
21k views

“Moderation” versus “interaction”?

I have come across these two terms which are used interchangeably in many contexts. Basically, a moderator (M) is a factor that impacts on the relationship between X and Y. Moderation analysis is ...
7
votes
1answer
6k views

Creating and interpreting Bland-Altman plot

Yesterday I heard of the Bland-Altman plot for the first time. I have to compare two methods of measuring blood pressure, and I need to produce a Bland-Altman plot. I am not sure if I get everything ...
4
votes
1answer
3k views

Interpretation of power and detectable difference

I know power is the likelihood of correctly rejecting the null hypothesis, but I just want to check that my interpretation of it with the detectable difference is correct. Consider a 2 sample test ...
21
votes
2answers
34k views

How to interpret parameters in GLM with family=Gamma

I have a question regarding parameter interpretation for a GLM with a gamma distributed dependent variable. This is what R returns for my GLM with a log-link: ...
27
votes
3answers
3k views

Can't deep learning models now be said to be interpretable? Are nodes features?

For statistical and machine learning models, there are multiple levels of interpretability: 1) the algorithm as a whole, 2) parts of the algorithm in general 3) parts of the algorithm on particular ...
21
votes
3answers
51k views

How to interpret main effects when the interaction effect is not significant?

I ran a Generalized Linear Mixed Model in R and included an interaction effect between two predictors. The interaction was not significant, but the main effects (the two predictors) both were. Now ...
20
votes
2answers
99k views

What happens when I include a squared variable in my regression?

I start with my OLS regression: $$ y = \beta _0 + \beta_1x_1+\beta_2 D + \varepsilon $$ where D is a dummy variable, the estimates become different from zero with a low p-value. I then preform a ...
13
votes
3answers
44k views

Intercept term in logistic regression

Suppose we have the following logistic regression model: $$\text{logit}(p) = \beta_0+\beta_{1}x_{1} + \beta_{2}x_{2}$$ Is $\beta_0$ the odds of the event when $x_1 = 0$ and $x_2=0$? In other words, ...
30
votes
4answers
38k views

How do you Interpret RMSLE (Root Mean Squared Logarithmic Error)?

I've been doing a machine learning competition where they use RMSLE (Root Mean Squared Logarithmic Error) to evaluate the performance predicting the sale price of a category of equipment. The problem ...
21
votes
5answers
22k views

What is a block in experimental design?

I have two questions about the notion of block in experimental design : (1) What is the difference between a block and a factor ? (2) I tried to read some books but something is not clear: it seems ...