All Questions
Tagged with hypothesis-testing binomial-distribution
277 questions
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Head First Statistics Book: error in hypothesis test?
Chapter 13 in the book Head First Statistics deals with hypothesis testing. Its example is like the below:
A drug (called snorecull) cures snore at a rate, 0.9. Then, one gets
the below results.
...
1
vote
1
answer
154
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Binomial test for finding ratios
I have tried reading about the concept here:
https://www.ncl.ac.uk/webtemplate/ask-assets/external/maths-resources/statistics/hypothesis-testing/hypothesis-testing-with-the-binomial-distribution.html
...
- 113
0
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0
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29
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Jeffreys' test for a single event
Assume $x\sim B(p,n)$ and using Jeffreys' prior the posterior distribution of $p$ for $x$ events and $n$ observations is $$\text{Beta}(x+\frac{1}{2},n-x+\frac{1}{2})$$ I am reading about a Jeffreys' ...
user406757
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61
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Are 2 samples from the same binomial distribution?
I have 2 samples drawn from binomial distributions. My null hypothesis is that the 2 samples are from the same distribution. How to reject the null hypothesis with p < 0.05?
Concrete case:
Sample #...
- 111
1
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2
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66
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Test whether my new method's type I error rate correctly matches chosen alpha
I am testing two different methods for hypothesis testing, bootstrapped likelihood ratio tests, and likelihood ratio tests assuming an asymptotic distribution. I would like to see if the number of ...
- 425
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0
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29
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What is the correct sample size for the purposes of this test?
$X_i$, $i = 1, \ldots, n_X$, are i.i.d. from some distribution; and $Y_j$, $j = 1, \ldots, n_Y$, are i.i.d. from some other distribution. Consider all pairs $(X_i, Y_j)$. The number of pairs is $n=n_X ...
- 1,251
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0
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21
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Rejection region in LRT test
Let's say I have $X_i \sim Bi(1, \theta$) and want to test $H_0: \theta \geq \theta_0$ vs $H_1: \theta < \theta_0$.
I've found that $\lambda = \frac{\sup_{\theta \in \Theta_0}L(\theta)}{\sup_{\...
- 101
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0
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34
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Binomial Test for data with normally distributed messurement error
I have a series of measurements and I want to perform a binomial test to see if the chance of exceeding some value $a$ is less or equal to some $p_0$. The measurement has some error which is normally ...
- 63
0
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1
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43
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Analogue of fisher's exact test for one group?
I understand that Fisher's exact test applies to testing whether the proportion of an outcome in one group, $p_1$, differs from the proportion of the outcome in another group, $p_2$. This could be ...
1
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1
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77
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Statistical test for binomial draws with unknown number of trials
I have two binomial random variables $X_1 = \text{Bin}(N, p_1)$ and $X_2 = \text{Bin}(N, p_2)$; same number of trials but different probabilities of success. Suppose that the number of trials $N$ is ...
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3
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Binomial test to establish a pass criterion
I'm sorry for the following -probably- stupid question.
I'm performing a psychological experiment and I have no idea about how to establish how many control items one has to pass to be included. My ...
- 175
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0
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72
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Sample size required for normal approximation - null hypothesis or estimate?
Consider a simple hypothesis test with a binomial distribution $Bin(p,n)$:
$$
H_0: p = p_0, \\
H_a: p \neq p_0
$$
and my estimate for $p$ is $\hat{p}$.
If I wanna do a normal approximation, a common ...
- 143
1
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0
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64
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UMP size $\alpha$ hypothesis test for discrete distribution
Let $\left(Z_1, \ldots Z_n\right)$ be an i.i.d. sample with common probability mass function
$$
p_Z(j)=\vartheta^2 I_{[j=1]}+2 \vartheta(1-\vartheta) I_{[j=2]}+(1-\vartheta)^2 I_{[j=3]}
$$
Find a UMP ...
- 133
1
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1
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121
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Why are the p-values for a binomial test very different from the p-values for a chi-squared test?
I am testing if a coin is fair by throwing it n-times and having n/2 + sqrt(n) heads.
However, I get very different p-values ...
- 13
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0
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21
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Bivariate problem, what is the best model for this? Scoring probability depending on distance
I have been directed here from the main stackoverflow site, where i described my problem: here.
Basically i have a set of sports data containing shots with their distance to the goal and the result (...
2
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1
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772
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What is the connection between Binomial and Jeffreys Test?
Normally, I am testing the calibration of a probability of default model with the binomial test. The ECB is suggesting the Jeffreys Test.
Are they related in any way? Is the Jeffreys test superior to ...
- 333
2
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1
answer
27
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Hypothesis testing with binomial test vs Chi2
Is it valid to test the following hypothesis with a binomial test? Or should a chi2-test be applied in this case?
A factory produces different products (A-G) with different rates of production errors ...
- 257
1
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0
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60
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Testing if Binomial Data [closed]
Suppose that I have the following data: $4,0,4,2,1,8,4,1,3,3,5,4,6,1,3$. How do we check if the data comes from a binomial distribution, say Bin($p,8$) for some $p$ or from some other distribution on $...
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Verification of my results
For an experiment where I simulated n=10000 games of chess with random moves I obtained the following results:
White won = 1674
Black won = 1721
Draw = 6605
Now I am interested in testing whether ...
4
votes
1
answer
78
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Binomial proportion test
I'm really confused about a basic test for a binomial proportion. Specifically, the p-value. If $n=20$ with $y=17$ successes, I want the p-value for $H_0: \pi\leq 0.7$ vs. $H_A: \pi > 0.7$. I've ...
- 555
1
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1
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88
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Doubt in calculation of critical region in two-tailed test
Consider the following question:-
A tetrahedral die is manufactured with numbers 1, 2, 3 and 4 on its faces. The
manufacturer claims that the die is fair. All dice are tested by rolling 30 times and ...
- 13
7
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1
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214
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How to perform a 2 sided binomial test with the alternative being larger
Given data for two groups:
Group A: $\left\{ (n_1, s_1), (n_2, s_2), \ldots, (n_k, s_k) \right\}$.
Group B: $\left\{ (n_1, s_1), (n_2, s_2), \ldots, (n_l, s_l) \right\}$.
Where $n_i$ is the number ...
- 277
2
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1
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93
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Binomial hypothesis test - Coin flip
A coin was flipped 10 times and landed on head 9 times. We want to test $$H_0: p = \frac{1}{2} \ vs \ H_1: p > \frac{1}{2}, p = \mathbb{P}(head)$$ with a confidence level of $\alpha = 0.05$. The ...
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2
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1
answer
665
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How does Clopper and Pearson interval compute
Suppose we have $10$ observations and we run $20$ trials. A two-sided binomial test with $H_0:p=0.4$ from R I get is
...
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1
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2
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How many tests do I need to run?
My hypothesis is that the wording of a particular yes-no question affects whether people will answer "Yes" or "No", such that Wording 1 is more likely to be answered "Yes"...
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0
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51
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How to organize experimental data for A/B testing?
Context:
We have a fleet of aircraft in service, the manufacturer regularly produces upgrade recommendations (SB) to be implemented on aircraft in order to increase its reliability. Reliability is ...
- 181
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0
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51
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How can I improve the results of such a binomial test? Was it a good choice for this problem?
I have a dataset that looks like this:
initial
final
division
fsa
hrs_prev
fsa/hrs_prev
2020-01
2020-06
A
0
168
0
2020-01
2020-06
B
14,29
177,45
2020-02
2020-07
A
9,52
177,45
0,054
and so on
<...
- 15
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0
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35
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Binomial test for absenteeism
I have a dataset that looks like this:
Company
hrs_prev
fsa
fsa/hrs_prev
A
140
5
0,035
B
145
2
0,01379
C
140
60
0,4286
A
155
20
0,0129
A
180
25
0,1389
B
120
0
0
B
130
0
0
etc
etc
etc
etc
...
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1
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1
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63
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alternative to ANOVA or simplifying approximations for multi-factor,, batch design with binomial data (advanced beginner)
this is my first post. I did already read various didactic materials and related posts here, but still had trouble figuring this one out. Sorry this is so long but I am trying to be as specific as ...
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2
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0
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74
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How does the following term happen when using the Wald Test on two-sample binomials?
I'm having trouble understanding one of the steps of the Wald test used in two-sample binomial proportions.
More specifically, when $X_1, ..., X_{n_1}$ are iid Binomial$(1, p_1$), $Y_1, ..., Y_{n_2}$ ...
- 21
1
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1
answer
251
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Consecutive coin flips, what is the appropriate statistical test for this word problem? [closed]
I was listening to a podcast by NDGT (Neil deGrasse Tyson, a prominent scientist) and he posed a simple thought experiment to illustrate the susceptibilities to cognitive bias. What I've come here to ...
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2
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0
answers
49
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Testing sequence of ones and zeros for randomness
I am given a sequence of $40$ ones and zeros and I have to test the null hypothesis that ${40 \choose n_1}$ sequences are all equally probable ($n_1$ being the number of ones). To do so, I have to use ...
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1
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0
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20
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Lower confidence interval for quantile function [duplicate]
I have a real-valued, unknown distribution $\mu$ and would like to find the largest threshold $t \in \mathbb{R}$ such that
$\Pr_{X \sim \mu}\left[X \leq t\right] \leq q$
with high probability $1-\...
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1
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Central Limit Theorem for proportion - np >=10 or 5?
While trying to understand deeper about Central Limit Theorem for proportions, I learned CLT for proportions is based on the fact that binomial distributions can be approximated by normal ...
- 119
1
vote
1
answer
205
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Hypothesis testing: Should it be done on the transformed parameter or the non-transformed?
I want to compare two proportions, for example:
succN <- 2
d <- data.frame(pledge = c("yes", "no"),
s = c(succN, succN),n = c(100, 100))
...
3
votes
0
answers
293
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Power calculation for binomial test
I have been asked to do a particular power calculation: We assume that the true probability of an event is 93%. We will do a binomial trial of size N, observe the outcome, and construct a confidence ...
- 359
1
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1
answer
61
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Chess opening move selection [duplicate]
So I’m playing a chess game and using 365chess.com to help with my moves (this is totally legal btw as long as engine analysis is turned off) it says move A leads to a win with white* 36% of the time ...
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1
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1
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42
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Assessing the meaning of a metric in a binary design
I try to assess the meaning of a software metric lines of code on bug density with the help of statistical methods. I have information on bugs and other needed software measures for several years. ...
- 113
0
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0
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25
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Significance Testing for the Difference between Binomials [duplicate]
I have two algorithms, $A_1$ and $A_2$.
$A_1$ either accepts or rejects samples from dataset $P$
$A_2$ either accepts or rejects samples from dataset $Q$
Below is a 2x2 contingency table for the ...
- 160
0
votes
1
answer
181
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Independence Assumption Simulation?
I'm simulating what happens when you break the assumption of independence when you sample without replacement. The rule of thumb is that you shouldn't sample more that 10% of the population. Kahn ...
- 109
0
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1
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519
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Hypothesis testing two unfair coins to see if they have 'equal' bias [duplicate]
Consider tossing two unfair coins 100 times:
How can I know using the two sets of Heads or Tail results whether the two coins have an equal (or similar) bias with a 95% confidence?
I am currently ...
0
votes
0
answers
116
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Analytic expression for false-negative rate of binomial tests?
I wrote a previous question yesterday which was maybe too long and boring to read. So to try to get an answer, I've boiled down my question to something short and specific which is:
Is there an ...
- 496
3
votes
1
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283
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spicy binom_test gives the same answer for alternative greater or less
I'm seeing something very unexpected with the binomial test function in spicy (python).
...
- 2,630
0
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1
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623
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Interpreting binomial test results
I'm relatively new to stats and any help would be appreciated.
My experiment has two boxes one baited with food and the other non-baited. I am trying to test whether the probability of the animal ...
2
votes
4
answers
797
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How to derive the binomial test?
From what I understand from a pervious question I asked, the p-value for a particular binomial test (specifying a number of flips, and number of heads and tails, and a null-hypothesis to test against) ...
- 496
1
vote
1
answer
978
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If prop.test is an approximation to binom.test, why don't we use binom.test when computers can do it?
When computing by hand, it makes a lot of sense to approximate the binomial distribution with a normal distribution because otherwise it would be impossible to perform calculations.
However, when ...
- 6,603
1
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0
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75
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Statistical evaluation of a 'success rate'
A recent TV show concerned with phenomena "that science cannot explain" described the work of a researcher who examined the claim that some people had telepathic powers.
I did not note down ...
- 751
0
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0
answers
15
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Binomial Proportion Test on test and control populations [duplicate]
I am new to statistical tests and request your help with the following question:
A company wants to test the hypothesis that it's new ad will increase it's total number of subscribers (conversion rate)...
1
vote
0
answers
52
views
Binomial Zero Probability Test
Let's assume a histogram of $K$ cells and $N$ samples. In some bins, the counts are zero, $k(i)$ $i \in [1,K]$. How can I test the probability is really zero (Bayesian) or alternatively what is the p-...
- 461
3
votes
1
answer
86
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Can an inference be made about how an outcome might look with “more power”?
I have a binomial outcome that I have compared across two groups:
Control - 21/783 occurrences (2.68%, 1.71-4.14% 95% CI)
Experimental - 13/261 occurrences (4.98%, 2.79-8.57%, 95% CI)
The p value is ...
- 645