Penis Size Probability

I promise that I expect this to be my last post about penis size for a good long while, no worries.  As always, the data comes from a Dutch study conducted by WPS in Amsterdam.  Penis size generally follows what is known as a normal distribution.  This is found often in nature, and generally can be used to analyze any number of measurements, from IQ to height to test scores.  The distribution of an average always follows a normal distribution, in what is one of the most useful patterns in statistics.  My math department loved designing tests to produce a good normal distribution, the astonishingly accurate bastards.  You’ve probably seen it before.  It looks like this.


Basically, most values are around the average, and the farther you get from the average, the fewer values you have.  This is pretty intuitive.  A lot of people are of, for example, average intelligence, and then you have a few super-geniuses like Hawking.  It certainly doesn’t describe everything well, but it’s generally a good place to start, especially for biological phenomenon, like the size or weight of animals, &c.  The normal distribution is so common and so useful that its values have been extensively plotted, so that you can determine how likely it is that a value will be so many standard distributions away.  If you don’t know what a standard distribution is, don’t worry, it’s basically a measurement of how spread out data points are.

Now, using the average and standard deviation, you can find the Z value.  The Z value can then be used to determine how likely it is that a value, in this case, penis size, is as great as or greater than a particular value.  You can find a Z to P Calculator here.  Let me show you how to find a Z value.

Z = (X – µ) / σ , where µ is the average, σ is the standard deviation, and X is the given value.  For our dataset, µ = 5.949″ and σ = 0.765″.

So, let’s say we want to determine how likely it is that a penis is 8 inches or larger.  Z = (8 – 5.949) / 0.765.  Z = 2.68.  If we put this into the calculator, we get 0.0037.  This means that the p-value is 0.0037, or .37%.  Therefore, we’d expect about four out of every one thousand men to have penises that are that length or larger.  One note: this tells you the probability that a value is more extreme than the average, so if you use an X value smaller than the average, you’ll get the probability that a penis is smaller than that size.  If you subtract this probability from one, you can find the probability that a penis is larger.

But we’re not finished!  This becomes a much more powerful tool when you’re finding how likely an average value is.  Let’s say you see a penis size poll, and one hundred men have said their average penis length is seven inches.  How likely is that event?  It’s pretty similar, but we modify Z slightly.  Now, Z = (X – µ) / (σ / √n) , where n is the number of individuals in the sample.  When we used one man, n was 1, so the term disappeared, but now let’s try it with n = 100.

Z = (7 – 5.949) / (0.765/√100).  Therefore, Z = 13.7.  You may recognize this as a value so high that almost no Z table will compute a p value for you, but it’s significantly less than 3*10^-7, which is the p value for Z = 5.  Essentially, it is almost impossible that a random survey of one hundred men should have an average penis length of seven inches.  Now, obviously, people with large penises are more likely to say it than those with small, so self-reporting will bias the results, but it’s still something useful to keep in mind when looking at how large people say their penises are.  (If we include the fact that men tend to overestimate by about an inch, and use 6 inches, we get a Z score of .664, and a p value of 25.33%, which is much more likely.)

Now, the normal distribution isn’t perfect.  Very extreme values are much more likely than the distribution predicts, but it’s a good first estimate.  To help provide a better idea of the “true” p value, I leave you with a quick probability table of penis length.  The first column contains the scenario, e.g. 4″+ refers to the probability that a penis is four inches long or longer.  The second column is the theoretical p value, based off of the Z score.  The third column is the experimental p value.  That is, after looking at the dataset, we find the proportion of penises that are actually longer than a given number of inches, and use that probability.  For example, 6.3% of men in the dataset actually do have a penis that is seven inches long or longer, so the p value is 0.063, or 6.3%.  Since this looks at the actual values we have, it’s probably more accurate than the purely theoretical p value.

Penis Length Theoretical P Value Experimental P Value
4″+ 99.5% 98.1%
5″+ 89.3% 89.8%
5.5″+ 72.1% 77.3%
6″+ 47.4% 50.0%
6.5″+ 23.6% 19.5%
7″+ 8.5% 6.3%
8″+ 0.4% 0.9%
This entry was posted in Interesting Things and tagged , , , , , , , , , , , . Bookmark the permalink.

10 Responses to Penis Size Probability

  1. Very Bangled says:

    8″ not erect? That sounds scary :/


  2. BAP Blog says:

    As a species, we kind of waste a lot of time measuring penises.


  3. BAP Blog says:

    Hah! True. “…potential to study the sociological impact of media portrayal and accuracy over discrepancies in ear sizes and timpanic membranes across racial phenotypes.”

    Liked by 2 people

  4. Pingback: Penis Size Histogram | John Kutensky

  5. Pingback: An Oddity in My Search Terms | John Kutensky

Leave a Reply

Fill in your details below or click an icon to log in: Logo

You are commenting using your account. Log Out /  Change )

Google photo

You are commenting using your Google account. Log Out /  Change )

Twitter picture

You are commenting using your Twitter account. Log Out /  Change )

Facebook photo

You are commenting using your Facebook account. Log Out /  Change )

Connecting to %s

This site uses Akismet to reduce spam. Learn how your comment data is processed.