Randomness is the lack of pattern or predictability in events. Randomness is often modeled with probability distributions, but can also be generated by deterministic processes.
Questions tagged [randomness]
215 questions
35
votes
3 answers
Are the digits of $\pi$ statistically random?
Suppose you observe the sequence:
7, 9, 0, 5, 5, 5, 4, 8, 0, 6, 9, 5, 3, 8, 7, 8, 5, 4, 0, 0, 6, 6, 4, 5
, 3, 3, 7, 5, 9, 8, 1, 8, 6, 2, 8, 4, 6, 4, 1, 9, 9, 0, 5, 2, 2, 0, 4, 5, 2, 8 ...
What statistically tests would you apply to determine if this…
Cam.Davidson.Pilon
- 11,476
- 5
- 47
- 75
34
votes
7 answers
Why is it bad to teach students that p-values are the probability that findings are due to chance?
Can someone please offer a nice succinct explanation why it is not a good idea to teach students that a p-value is the prob(their findings are due to [random] chance). My understanding is that a p-value is the prob(getting more extreme data | null…
Patrick
- 1,381
- 1
- 15
- 21
31
votes
5 answers
Generating random numbers manually
How can I manually generate a random number from a given distribution, as for instance, 10 realisations from the standard normal distribution?
A-dude
- 450
- 4
- 11
27
votes
5 answers
A statistical approach to determine if data are missing at random
I have a large set of feature vectors which I will use to attack a binary classification problem (using scikit learn in Python). Before I start to think about imputation, I am interested in trying to determine from the remaining parts of the data if…
graffe
- 1,799
- 1
- 22
- 34
27
votes
3 answers
Can non-random samples be analyzed using standard statistical tests?
Many clinical studies are based on non-random samples. However, most standard tests (e.g. t-tests, ANOVA, linear regression, logistic regression) are based on the assumption that samples contain "random numbers". Are results valid if these…
KuJ
- 1,356
- 3
- 15
- 25
24
votes
5 answers
What is wrong with this "naive" shuffling algorithm?
This is a follow-up to a Stackoverflow question about shuffling an array randomly.
There are established algorithms (such as the Knuth-Fisher-Yates Shuffle) that one should use to shuffle an array, rather than relying on "naive" ad-hoc…
Thilo
- 533
- 1
- 5
- 7
22
votes
7 answers
Can someone help to explain the difference between independent and random?
In statistics, does independent and random describe the same characteristics? What's the difference between them? We often come across the description like "two independent random variables" or "random sampling". I am wondering what's the exact…
tiantianchen
- 1,661
- 2
- 18
- 31
18
votes
2 answers
Random walk with momentum
Consider an integer random walk starting at 0 with the following conditions:
The first step is plus or minus 1, with equal probability.
Every future step is: 60% likely to be in the same direction as
the previous step, 40% likely to be in the…
user1566
16
votes
1 answer
Scrambling and correlation in low discrepancy sequences (Halton/Sobol)
I am currently working on a project where I generate random values using low discrepancy / quasi-random point sets, such as Halton and Sobol point sets. These are essentially $d$-dimensional vectors that mimic a $d$-dimensional uniform(0,1)…
Berk U.
- 4,265
- 5
- 21
- 42
16
votes
2 answers
What does it mean to say that an event "happens eventually"?
Consider a 1 dimensional random walk on the integers $\mathbb{Z}$ with initial state $x\in\mathbb{Z}$:
\begin{equation}
S_n=x+\sum^n_{i=1}\xi_i
\end{equation}
where the increments $\xi_i$ are I.I.D such that…
Ye Tian
- 619
- 6
- 19
13
votes
1 answer
Differential Entropy drops when any random variable is normalized to unit variance
Differential entropy of Gaussian R.V. is $\log_2(\sigma \sqrt{2\pi e})$. This is dependent on $\sigma$, which is the standard deviation.
If we normalize the random variable so that it has unit variance its differential entropy drops. To me this is…
Cagdas Ozgenc
- 3,716
- 2
- 29
- 55
12
votes
3 answers
Why do several (if not all) parametric hypothesis tests assume random sampling?
Tests like Z, t, and several others assume that the data is based on a random sampling. Why?
Suppose that I'm doing experimental research, where I care much more for the internal validity than the external one. So, if my sample might be a little bit…
Bruno
- 173
- 8
12
votes
2 answers
Is tossing a coin a fair way of randomising a group into two groups?
So myself and my uncle are having an argument over whether a coin flip is truly random. I argue it isn't because in real terms a coin tosser will always manipulate a coin so the result isnt 50/50 therefore it is not a good choice as a randomisation…
googleplex101
- 187
- 1
- 7
11
votes
2 answers
Will this introduce bias into what should be random numbers?
Assume a data file with 80+ million ones and zeros, randomly generated.
From this file, we want to create a list of random decimal integers.
This is the plan to do this conversion.
Divide the 80 million digits into groupings of 4 binary digits.…
Joel W.
- 3,096
- 3
- 31
- 45
11
votes
3 answers
What is the probability of n people from a list of m people being in a random selection of x people from a list of y people?
If I am selecting 232 people from a pool of 363 people without replacement what is the probability of 2 of a list of 12 specific people being in that selection?
This is a random draw for an ultra race where there were 363 entrants for 232 spots.…
Sarge
- 365
- 2
- 11