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10 votes

What does it mean for observations to be uncorrelated and have constant variance?

Random variables VS observations. Strictly speaking, there are random variables (which take values in $\mathbb{R}$) and realizations of these random variables (which are elements of $\mathbb{R}$). ...
Idontgetit's user avatar
10 votes
Accepted

What does it mean for observations to be uncorrelated and have constant variance?

These are assumptions made for certain models to ensure certain properties, like valid test statistics. There's a great overview here. The key word here is assumption. These need not hold up in real ...
Frans Rodenburg's user avatar
9 votes

Correlation for Small Dataset?

Estimators based on sample statistics are not very reliable indicators of the population quantities they estimate when sample sizes are very small. In short, the sample correlation $r$ could be very ...
Glen_b's user avatar
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7 votes

What does it mean for observations to be uncorrelated and have constant variance?

$y_i$'s are not just real numbers. They are random variable. Specifically, the simplest linear model assumes $$y_i = x_i^T\beta+\varepsilon_i,\quad \varepsilon_i\overset{iid}{\sim}\mathcal{N}(0,\sigma^...
Voyager's user avatar
  • 305
7 votes

Correlation for Small Dataset?

In line with the answer @Glen_b in the worst case (true correlation is zero) you need 300-400 observations to well-estimate $r$, e.g., to within a margin of error of 0.1 with 0.95 compatibility. For ...
Frank Harrell's user avatar
6 votes
Accepted

Does it make sense to describe change in Pearson's correlation coefficient in percentage terms?

It's not helpful or even always valid to talk about percentage change in correlations. Let's note that in principle a correlation could be exactly zero, in which case percentage change from zero isn't ...
Nick Cox's user avatar
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5 votes

Correlation for Small Dataset?

I agree with all of Glen_b's points. What could you try? First, is there any substantively sensible way to combine some of the sets of 10? That is, not a method based on statistics, but on what you ...
Peter Flom's user avatar
  • 125k
4 votes

Correlation for Small Dataset?

I'm somewhat more positive than the other two answers, but it all depends on (a) how your data actually look like and (b) what you will then do with the correlations, and whether there are good ...
Christian Hennig's user avatar
3 votes
Accepted

Association between more than 2 categorical variables

You can do chi square with more the two variables. Or, indeed, with only one variable. There may be problems with sparse cells, but that would affect other methods too. You could also look into log ...
Peter Flom's user avatar
  • 125k
3 votes

How to generate 2 correlated Beta random variables

How can you simulate correlated beta distributed variables? This question has attracted a lot of views, suggesting (future) readers might still be interested in the titular question. I would like to ...
Frans Rodenburg's user avatar
2 votes

Why is correlation obtained from nlme different from Pearson correlation?

The correlation values provided by the lme function for your mixed model represent the correlations between the estimated coefficients (slopes) of the model. These ...
Robert Long's user avatar
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1 vote
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Pearson chi square and correlation

"chi squared test value is 4.664 And asymp sig is 0.97 so the data are independent". I don't agree with this statement. You do not know that the data are independent. You have failed to find ...
Jeremy Miles's user avatar
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1 vote
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Regression with dependent observations of only one individual

My Y variable will likely be binary (agrees/disagrees) or on a Likert scale (1-5) I'd recommend the Likert scale since it's more informative. For analysis you can use an ordinal logistic model. https:...
Lukas Lohse's user avatar
  • 2,862
1 vote

I would like some insight into what I have been working on here

Summarizing comments into an answer: When a potential customer opens the door and allows the salesperson into the house, then the salesperson must take the time to make the sales pitch. If the pitch ...
EdM's user avatar
  • 95.8k

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