Statistical tests, P values, confidence intervals, and power: a guide to misinterpretations

Misinterpretation and abuse of statistical tests, confidence intervals, and statistical power have been decried for decades, yet remain rampant. A key problem is that there are no interpretations of these concepts that are at once simple, intuitive, correct, and foolproof. Instead, correct use and interpretation of these statistics requires an attention to detail which seems to tax the patience of working scientists. This high cognitive demand has led to an epidemic of shortcut definitions and interpretations that are simply wrong, sometimes disastrously so—and yet these misinterpretations dominate much of the scientific literature. In light of this problem, we provide definitions and a discussion of basic statistics that are more general and critical than typically found in traditional introductory expositions. Our goal is to provide a resource for instructors, researchers, and consumers of statistics whose knowledge of statistical theory and technique may be limited but who wish to avoid and spot misinterpretations. We emphasize how violation of often unstated analysis protocols (such as selecting analyses for presentation based on the P values they produce) can lead to small P values even if the declared test hypothesis is correct, and can lead to large P values even if that hypothesis is incorrect. We then provide an explanatory list of 25 misinterpretations of P values, confidence intervals, and power. We conclude with guidelines for improving statistical interpretation and reporting.

Worth reading.

Thanks to Bren for the heads up.

dv said:

Statistical tests, P values, confidence intervals, and power: a guide to misinterpretations

Misinterpretation and abuse of statistical tests, confidence intervals, and statistical power have been decried for decades, yet remain rampant. A key problem is that there are no interpretations of these concepts that are at once simple, intuitive, correct, and foolproof. Instead, correct use and interpretation of these statistics requires an attention to detail which seems to tax the patience of working scientists. This high cognitive demand has led to an epidemic of shortcut definitions and interpretations that are simply wrong, sometimes disastrously so—and yet these misinterpretations dominate much of the scientific literature. In light of this problem, we provide definitions and a discussion of basic statistics that are more general and critical than typically found in traditional introductory expositions. Our goal is to provide a resource for instructors, researchers, and consumers of statistics whose knowledge of statistical theory and technique may be limited but who wish to avoid and spot misinterpretations. We emphasize how violation of often unstated analysis protocols (such as selecting analyses for presentation based on the P values they produce) can lead to small P values even if the declared test hypothesis is correct, and can lead to large P values even if that hypothesis is incorrect. We then provide an explanatory list of 25 misinterpretations of P values, confidence intervals, and power. We conclude with guidelines for improving statistical interpretation and reporting.

Worth reading.

Thanks to Bren for the heads up.

He’s such a Bayseian fanboy.

chuckle

> We then provide an explanatory list of 25 misinterpretations of P values, confidence intervals, and power.

Nice. I’ve written here before about the problems of not taking enough samples to get a statistically significant answer.

Misinterpretation of statistical tests is much less of a problem than not applying statistical tests in the first place.

The journal he refers to that banned statistical tests was Basic and Applied Social Psychology.

I am not sure what kind of thing it was replaced with … I mean I assume the articles have to come to some kind of conclusion.

mollwollfumble said:

> We then provide an explanatory list of 25 misinterpretations of P values, confidence intervals, and power.

Nice. I’ve written here before about the problems of not taking enough samples to get a statistically significant answer.

Misinterpretation of statistical tests is much less of a problem than not applying statistical tests in the first place.

my stats lecturer says 30 or more is of statistical significance and n= a lot will always give you a significant result

In the engineering (and financial) context it seems to me that the biggest problem is treating the tails of real distributions as though they were a normal distribution, and hence finding that the probability of rare events is effectively zero, when it is in fact large enough to create a significant risk.

The Rev Dodgson said:

In the engineering (and financial) context it seems to me that the biggest problem is treating the tails of real distributions as though they were a normal distribution, and hence finding that the probability of rare events is effectively zero, when it is in fact large enough to create a significant risk.

—

So outliers are the problem…

The Rev Dodgson said:

In the engineering (and financial) context it seems to me that the biggest problem is treating the tails of real distributions as though they were a normal distribution, and hence finding that the probability of rare events is effectively zero, when it is in fact large enough to create a significant risk.

In psychology it seems the major problem is fraud and poor practice…

tauto said:

The Rev Dodgson said:

In the engineering (and financial) context it seems to me that the biggest problem is treating the tails of real distributions as though they were a normal distribution, and hence finding that the probability of rare events is effectively zero, when it is in fact large enough to create a significant risk.

—

So outliers are the problem…

Yes.

Rare problems, but sometimes huge.

tauto said:

The Rev Dodgson said:

In the engineering (and financial) context it seems to me that the biggest problem is treating the tails of real distributions as though they were a normal distribution, and hence finding that the probability of rare events is effectively zero, when it is in fact large enough to create a significant risk.

—

So outliers are the problem…

it’s more than that… the issue is often the assumption that, like Rev says, the distribution is normal; when in reality they tend to be skewed.

It’s then important to understand the impact these low probability (and often high consequence) events can have on engineering or financial performance.

// In psychology it seems the major problem is fraud and poor practice…

of the Sigmund type

S:

(sigmoid colon)

dv said:

S:

(sigmoid colon)

Hahahahahahahahahaha!

Michael V said:

dv said:

S:

(sigmoid colon)

Hahahahahahahahahaha!

Thank you thank you

Today is termite bombing day. Happy Memorial Day all you fuckers!

While that is happening we will be in the workshop trying to find where I have hidden the small tripod.

This afternoon we have the unemployed rocket surgeon coming by to pick apricots.

Excitement plus around here.

Damn, wrong thread.