# Basic easy rules for statistics

In a binomial experiment, if we observe $x=0$ positive individual among $n$ individuals, then the proportion of positive individuals is significantly lower than $3/n$ with a type 1 error less than and very close to $5\%$. This fact, sometimes called the "rule of three", is a consequence of the inequalities $$\exp\left(-\frac{np}{1-p}\right) \leq \Pr(X=0) \leq \exp(-np).$$

Do you know other such basic easy rules for statistics? I find them very interesting and useful. This principle is not really a "rule of thumb" because it has a reliable theoretical foundation, but I don't see another tag for this question (I hope it is not off-topic)

-

"Normally, more than two-thirds of the people are average" (meaning within one standard deviation of the mean)? – Dilip Sarwate Jun 8 '12 at 11:42
One very simple one that comes to mind is how the variance of a sample proportion of successes out of $n$ Bernoulli trials is no more than $1/4n$ (which is achieved when the success probability is $1/2$) – Macro Jun 8 '12 at 12:11
Many "rules of thumb" are based on theoretically rigorous analyses or approximations. – whuber♦ Jun 8 '12 at 13:02

## 1 Answer

Check out Gerald van Belle's book "Statistical Rules of Thumb" a very nice little paperback text loaded with examples of rules of thumb and explanations including the "Rule of three" that you mention above.

-
(+1) That seems like a nice book. Not only does he give rule-of-thumbs, but he also motivates them and discuss their validity. – MånsT Jun 8 '12 at 12:13
Nice! I will ask to my boss to buy it :) – Stéphane Laurent Jun 8 '12 at 12:13
Ahah ! I've just send an email to my boss and actually we already have this book :) – Stéphane Laurent Jun 8 '12 at 12:20
Yes, it's a great book. It's fun just to read it. – jbowman Jun 8 '12 at 13:28

1
– Stéphane Laurent Jun 8 '12 at 14:35
show 1 more comment
{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 7, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "github"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "english_confidence": 0.9490627646446228, "perplexity_flag": "middle"}