22 votes
Accepted

Can an irrelevant variable be significant in a regression model?

Here is a good example. Suppose you are interested in modelling the effect of ice cream sales on incidence of shark attacks. Now, clearly there is no association; buying ice cream in no way affects ...
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8 votes

Can an irrelevant variable be significant in a regression model?

I think a variable can be irrelevant and significant at the same time. But, how do I explain that? This can be explained by using the concept of type I errors. Below is an example by repeating a t-...
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8 votes

Can an irrelevant variable be significant in a regression model?

"Relevant" and "irrelevant" are not well-defined statistical terms that everyone agrees on. Case in point: the answer by @Demetri Pananos interprets "relevant" as "...
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  • 2,732
7 votes
Accepted

Linear relationship seems to depends from one value: would bootstraping help?

First off: If I extend this argument, would removing other value also impact the relationship? Almost certainly yes. The regression line slope depends on all observations, so removing any point will ...
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5 votes
Accepted

Asymptotic normality of OLS estimators in practice

"I can trust the standard errors of my coefficients and their accompanying p-values" .... well, yes, at least in the limit as $n\to\infty$, as long as it's only the distributional assumption ...
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  • 261k
4 votes

Correct Interpretation for One-tailed Hypothesis with Inverse Result

There are several possibilities: If you have made a mistake using software and tested against an alternative in the wrong tail from what you intended, then it is best to do the correct test. If the ...
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  • 50.7k
4 votes

Correct Interpretation for One-tailed Hypothesis with Inverse Result

The whole point of statistical hypothesis testing is to set a sharp line to decide when an effect is large enough to "reject" the null hypothesis. In much of science, such sharp cutoffs aren'...
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4 votes

How do I test for significant change when looking at a metric such as "average products added to cart in per session"?

This is like, THE QUESTION, in AB testing. There are a bunch of ways to answer this, each of which have their pros and cons. I'll give my thoughts here for posterity. The t-test Perhaps the most ...
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3 votes
Accepted

Election result - how to say if we can determine a winner?

Statistical significance is a way of talking about the uncertainty associated with using the results of a random sample to make predictions about the characteristics of the larger population that ...
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3 votes

Hypothesis Testing when the aim is to claim that the two population mean (or any other statistic) are same

If your aim is to claim evidence that two (or more) populations are similar, for example, have similar means, then you are unequivocally looking for some variation of equivalence testing. In a two-...
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  • 26.6k
2 votes

Is it logical to look for a correlation between average and percentage?

The biggest risk of looking at statistics of the aggregates is ecological fallacy (example here). Group-level aggregates do not necessarily are suitable for inferring individual-level characteristics. ...
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  • 115k
2 votes

How to use t-test with percentages

It's much better to work with the underlying numerators and denominators to use a model for binomial outcomes instead (e.g. some form of logistic regression - note: talking about some "test" ...
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  • 23k
2 votes

Can an irrelevant variable be significant in a regression model?

Complementary to Demetri's nice answer (+1): Aside (unmeasured) confounding, we might have spurious associations that are not the same an unmeasured confounding. Two variables ...
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1 vote

What statistical test is suitable to summarise patient time in hospital with health condition

A regression analysis could be useful in this case. You can estimate a multivariate linear regression model. Patient time in the hospital will be your dependent variable. Age and health condition (...
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1 vote
Accepted

What test to implement for a regression where points are biomdally distrbuted (i.e. two peaks)?

Two thoughts. First, don't try to force the data into a single quadratic form. If you want to model a nonlinear relationship between an outcome and a predictor, use a flexible method like a regression ...
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  • 64k
1 vote

Within group variation

How do you want to construct the null hypothesis for such test? Does the ANOVA setup consist independent groups or repeated measures? If you want to test whether the population variance for a ...
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1 vote
Accepted

How to test a linear regression against a NULL expectation?

Since Y is calculated from X, I calculated the null by shuffling X from the original sample, calculate Y, the slope between them. Repeat 1000 times. Find the average slope. Use the equation of the ...
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  • 115k
1 vote
Accepted

Post-hoc tests for unexpected outcome of binomial models

The extra "significant" predictor in the second model, utt_IKI, is involved in an interaction with utt_speed. It can ...
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  • 64k
1 vote

How to use t-test with percentages

Yes, you can use a t-test (aka Welch test) for percentage data, or alternatively a proportion test. Note that the proportion test comes in two variants, with and without continuity correction. Which ...
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  • 3,111
1 vote

Question on statistical significance in single vs multiple linear regression

Here are two examples illustrating two non-exhaustive but hopefully still instructive situations. Example #1 We simulate a dataset with two continuous predictors, x1 and x2, and a continuous response ...
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  • 2,732
1 vote

For bivariate linear model, if the residuals ARE normal, but the data is NOT normal, can I make inferences about the slope coefficient?

Yes! The usual linear regression model does not assume that X is normal. The assumptions are independence, homoscedasticity, linearity and normality of residuals.
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  • 2,536
1 vote

What is the proper way to report confidence intervals (or std, variance) for machine learning - especially wrt the loss and the accuracy?

Well, as I see you have something like 2 populations, where [ones/whole_population] 6/30 & 17/30 are computed as weights, being weighted average... but you didn't prove the Normality of your ...
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  • 11
1 vote

Comparing proportions between 10 groups

For each subject, you have a count of number of nouns and non-nouns. That gives you a 10x2 contingency table, so you could use the chi-squared test. One problem with this approach is that it does not ...
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1 vote

What is the best method to statistically test two areas?

I would start with a Poisson rate regression, it is generallt better to model counts than the rates directly. Assuming you have counts on ward level, the response is count of obese children and the ...
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1 vote

Can ANOVA be significant when none of the pairwise t-tests is?

The smallest p-value of the t-tests depends on the maximum spread of the different group means (so only two means are important). The p-value of the ANOVA test depends on the variance of all the ...
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