# Questions tagged [runs]

Runs refers to repeated occurrences of one outcome. For example, in repeated tosses of a coin, there will be runs of heads and tails. In the sequence HHHTHT there are 4 runs (one of length 3 and 3 of length 1).

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### Wald-Wolfowitz runs test on white noise

I am looking for ways to inspect whether a time series is different from white noise. I could inspect directly whether the mean is zero, the variance is constant and the autocorrelations at all lags ...
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### Runs Test for a single individual

I understand the issue around inability to generalize to a population, but in this case I am interested in whether the data indicates randomness of performance in a single individual. Specifically, I ...
1 vote
275 views

### In an A/B test, how can you check if assignment to the various buckets was truly random?

Trying to figure out how I can confirm that my A/B Test assignment is truly random. I know the runs test is used to test for randomness. Is it possible to use the runs test to check if my A/B Test ...
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1 vote
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### Distribution of l occurrences in a row in the limit of infinite trials

The events: Let each event have two possible outcomes: $A$ with probability $p$; $B$ with probability $1-p$ The events are independent Problem: In the limit of the number of trials $N$ tending to ...
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1 vote
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### Theory of 'Runs' and probability

I want to know how did author compute the probability of eleven runs if all arrangements are equally probable. My attempt to answer my own question: This example indicates wide applicability of the ...
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### Expected number of runs when there are $n_1$ objects of one kind and $n_2$ objects of second kind. Flaw in Argument?

Suppose there are $n_1$ objects of one kind and $n_2$ objects of the second kind. These objects appear randomly in a sequence. I want to find the expected number of runs in the sequence. Attempt: ...
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### Joint distribution of longest run and number of runs in a sequence of $n$ coin tosses?

A coin with probability of heads $p \in (0, 1)$ is tossed $n$ times. What is the joint probability distribution of the number of runs and the longest run? Schilling (1990) discusses the distribution ...
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1 vote
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### LR test for overlapping return data using bootstrap

I wish to test a null hypothesis as in Christoffersen (1998) to see whether a sequence of Value-at-Risk forecasts $Q_t(p) \in \mathcal{F}_t$ possesses correct conditional coverage. Here $p \in [0,1]$ ...
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### How to run test for randomness on a ternary cyclic sequence?

I would like to do a run test for randomness on a ternary sequence ($x_n \in \{0,1,2\}$) where a run is said to continue if the value increases by 1 cyclically (i.e. $(x_{n+1}-x_n)=1 \text{ mod } 3$). ...
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### Probability of n successful runs [duplicate]

My background the past while has been project management so I haven't really had much work with stats the past decade or so, so please forgive the terminology if it is wrong. I'm working on a problem ...
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### What are the necessary steps required for conducting a Wolfowitz runs test of randomness, given that I have all the necessary data?

I am writing a part in my thesis about the random-walk theory of price changes. I plan to set up a runs test of randomness to show whether the price changes do follow a particular random pattern. I ...
1 vote
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### Is it normal to get more variance in k folds cross-validation of an algorithm than in k repetitions?

Is it normal to get a lot more variance in k folds cross-validation of an algorithm than in k repetitions of the same algorithm (neural network) on the same dataset? ...
276 views

### Deriving the average and variance of number of runs in runs test

NIST states that the average and variance of a number of runs in the "runs above and below median" test as  \overline{R} = \frac{2n_a n_b}{n_a + n_b} + 1 \\ s^2 = \frac{2n_a n_b(2n_a n_b - n_a - n_b)...
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### maximum randomness and non-randomness

Two questions about randomness of data-sequences: Using a variant of run test like Wald–Wolfowitz to check randomness hypothesis for a one-sample data sequence, which yields a P value denoting the ...
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### How can I use the distribution of run lengths to test if a sequence is generated from flips of a fair coin?

I have a very long sequence (in the tens of thousands) of binary outcomes from some data-generating process. I believe that these outcomes are iid Bernoulli trials with p = 0.5, equivalent to flipping ...
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1 vote
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### Including streaks/runs in (generalized) linear mixed model context

The data and model used so far: I have longitudinal count data on 16 pens (8 with treatment A, 8 with treatment B). Each pen houses the same number of animals, and the pens may be considered as ...
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1 vote
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### Upper and lower limits for numbers of runs

On this website about statistical process control there is a chart which gives the upper and lower limits for the number of runs in a set of data for the data set to be considered taken from a process ...
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### Runs test for randomness for k elements

Say I have a sequence of length $n$ of $k$ different elements, s.t. $n > k, k > 2$. I want to show this sequence is random, based on the number of runs. I found this paper by AM Mood which ...
1 vote
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### Null hypothesis of the Wald-Wolfowitz runs test

From Wikipedia The runs test (also called Wald–Wolfowitz test after Abraham Wald and Jacob Wolfowitz) is a non-parametric statistical test that checks a randomness hypothesis for a two-valued data ...
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### In general which runs test is more powerful?

There are several tests for randomness, one is runs up and down, another is run against mean or some other values, of cause, Bartel's rank test can also be used. There are studies shows where Bartel'...
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