All Questions
Tagged with hypothesis-testing inference
453 questions
8
votes
3
answers
2k
views
Why does $\mu > 0$ (or even $\mu > \epsilon$) "seem easier” to substantiate than $\mu \neq 0$?
Consider a random variable $X$ following a normal distribution $N(\mu,\sigma^2)$. Suppose that we have drawn iid samples of $X$, obtaining a data set with a sample mean $\bar{x}>0$.
We want to test ...
- 138
1
vote
0
answers
32
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Game design urn problem
I am designing a tabletop game and trying to conceptualise the probabilities involved. These can be expressed as an urn problem:
Our urn contains seven counters, either green or red. We draw five and ...
- 11
0
votes
1
answer
133
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Which SD to use in z-test for proportion in population
Background:
I am testing the prediction ability of games in a league season and as a naive approach would like to check if the proportion of correctly predicted games is > 0.5 and statistically ...
- 103
0
votes
1
answer
76
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Use regression model results to estimate change in dependent variable
A dataset consists of sales of a product in different regions alongside advertising budget in three different media: Radio, Instagram, Facebook. A model is developed to predict sales on the basis of ...
- 1
0
votes
1
answer
61
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Test hypothesis of a given problem
Hi guys I found this problem in an old book but can't seem to find a solution to it. To be honest I don't really have much of an idea how to go about it. I am trying to study statistics on my own. Can ...
0
votes
1
answer
149
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Should a Test Statistic Consist of a Consistent Estimator for the Parameter of Interest?
Suppose that we want to test the following hypothesis:
$$H_0: \theta \in \Theta_0\quad vs \quad H_1: \theta\in \Theta_0^c.$$
Suppose that our test statistic is $T_n$.
Then, should the test statistic $...
- 945
2
votes
1
answer
8k
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How to check if a sample is representative of a population if I know the population’s parameters in advance
I have a dataset with the real height of an entire generation of high school students. Since I have the height of literally every student in the generation, I know the population’s mean, $\mu$, as ...
- 569
0
votes
1
answer
168
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What statistical parameters change when I exchange the null and alternate hypothesis?
I have the following data from a weight loss survey from a diet program.
I calculated the following things from the data and formulated my null hypothesis and alternate hypothesis as follows.
My ...
1
vote
1
answer
452
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How to state null and alternative hypotheses for one and two-sided tests
website link
Here are some of the hypothesis statements, I don't know why do cases (i),(j) null hypothesis would not be another way around, and they also contradict to the case (b),(f)
Any ideas on ...
- 331
0
votes
1
answer
837
views
Correct implementation of wilcoxon test for time series data in R
Am I testing the right thing or rather, am I testing what I think I am testing?
As the answer of this question points out, a wilcoxon test is suitable to make statements about the inference of the ...
- 3
1
vote
1
answer
909
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How to do correlation between likert and binary variables [duplicate]
I want to look at whether socioeconomic status influences students’ self-efficacy in science subjects.
My socioeconomic questions are yes/no questions or choice out of a list of parental occupation
...
- 11
3
votes
2
answers
41
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Can statistical models be used for this kind of problem?
Sorry for the long post:
Here is the situation (it's a silly example just to illustrate the point):
A computer repair company is primarily focused on repairing computers. However, the company has ...
3
votes
1
answer
779
views
Simpson's Paradox
I need some help figuring out whether the phenomenon of Simpson's paradox has occurred.
Here is a plot of the first dataset (correlation between probability of contracting a disease vs. hours slept ...
- 43
0
votes
0
answers
26
views
What statistical test to perform ? How do I compare the feature for two categories?
I have a data set of 200 observations and 24 nominal features , 100 of those observations are for product A and remaining is for product B .
I want to check how differently those features attributes ...
1
vote
1
answer
618
views
Find Critical region for exponential distribution
The lifetime in hours of each bulb manufactured by a particular company follows an independent exponential distribution with mean $ \theta $ . To test the hypothesis $ \ H_0 :
2000 $ versus $ \ ...
- 387
1
vote
1
answer
83
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Disagreement on choice of null in popular hypothesis testing
My question is about hypothesis testing. In hypothesis testing we want to put the hypothesis we want to prove in the alternative hypothesis since we fix the typeI error but cannot make any statements ...
- 11
0
votes
1
answer
92
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How do you calculate the 95% confidence interval between 2 percentages, without knowing n?
I am trying to figure out a statistics homework question, and I am unsure where to start ...
I am pretty sure that I need to identify a confidence interval, and then note if the country is outside ...
- 3
1
vote
1
answer
561
views
Posterior calculation on binomial distribution using quadratic loss function
Que
Let x be a binomial variate with parameters n and p (0<p<1). using a quadratic error loss function and a priori distribution of p as $ \pi(p) $ = 1, obtain the bayes' estimate for p.
Hey ...
- 387
1
vote
3
answers
225
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Unbaised estimator of $\ e^{- 2 \lambda } $ is t(x) = $ \ (-1)^x $
Prove that
Unbaised estimator of $\ e^{- 2 \lambda } $ is t(x) = $ \ (-1)^x $ ,
when x follows poisson distribution with parameter $\lambda $
Sorry to ask the direct question but I need a starting ...
- 387
1
vote
1
answer
1k
views
Why do you need oversampling/undersampling?
My understanding of oversampling/undersampling is merely manipulate the data to increase the proportion of rare group in your target. Isn’t this manipulating data? How could you expect a reliable ...
- 61
2
votes
1
answer
7k
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alpha value for one tail test and two tail test in t-test
I am using t-test with confidence interval of 95%
so my significance level is p = 0.05
Now if I am using ...
- 23
2
votes
0
answers
106
views
Multiple hypothesis testing: lower bound for sample complexity of finding the different one
We have $m$ distributions $D_1,\dots,D_m$. We know that $m-1$ of them are $\mathcal{N}(\epsilon,\sigma^2)$ ($\epsilon>0$) and one of them is $\mathcal{N}(0,\sigma^2)$, but we don't know which one ...
- 297
1
vote
1
answer
333
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Can you include between-subject control variables in random effect structure of mixed models if they are not fixed effects?
I tried finding similar cases and questions but failed and got even more confused because the answers seem to depend on when the questions were asked due to changes in the lme4 package. So I'm sorry ...
- 11
0
votes
1
answer
615
views
Joint hypothesis testing: How to set up restricted model for equality of more than 2 coefficients?
Say I am running the following regression:
$Y=\beta_0 + \beta_1X + \beta_2Z +\beta_3W + othercontrols + error$
I want to test the null hypothesis that the first three coefficients are equal, or:
$H_o =...
- 711
2
votes
0
answers
192
views
Measuring "uniqueness of fit" or "unique goodness of fit" of a model to some data
Given some parametric model, we can determine the best-fit parameters to some data set. Once we have quantified goodness of fit for each parameter set, we can easily generalize from this to measure ...
- 475
2
votes
1
answer
51
views
Test on a parameter in which $H_1$ is not complementary to $H_0$. Is this possible?
I have the following problem and I don't know how to solve it.
We have a population of $N=20$ enterprises. Each enterprise has a probability $p$ to reduce his customers independently from the others.
...
- 121
1
vote
1
answer
587
views
How to statistically test data points that are coming from two groups of distributions?
Suppose we have two groups of data points, i,e, A and B, and we want to know if they are coming from two different distributions or just one? The candidate solutions are standard t-test or Kolmogorov ...
- 65
0
votes
0
answers
76
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What follows after a Mann-Whitney U Test?
I have a statistically significant result for the Mann-Whitney U Test. The groups used are slightly overlapping so what i am interested in now is finding out the best splitting point between two ...
- 101
1
vote
0
answers
52
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T distribution for other functions than the mean [closed]
If there are $X_1,\cdots,X_n \sim N(\mu,\sigma^2)$ independent random variables, then their mean $n \cdot \overline X = X_1 + \cdots + X_n $ has the property that it is independent of $(n-1)S = \sum_{...
- 831
1
vote
3
answers
153
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How to perform Hypothesis Testing (2 samples) when one sample is normal and the other is non-normal? [duplicate]
Recently, I was helping a colleague to perform hypothesis testing for 2 independent samples, but the data one sample followed a normal distribution and the other followed a non-normal distribution.
...
- 13
4
votes
2
answers
207
views
How do I know whats my null hypothesis?
I was reading about t-tests and began wondering why the null hypothesis is chosen such that it states there is no difference between the means.
The deeper question I have here is how do I state my ...
- 1,097
2
votes
1
answer
91
views
CLT so we have enough burgers!
An event has 32 people. Caterers need to make burgers for these people. They expect that a person at this event might need 0, 1 or 2 burgers with probabilities 0.2, 0.55, and 0.25 respectively. We ...
- 49
1
vote
0
answers
20
views
Testing with multinomial covariates
I have a question about how to perform analysis and testing in this setup.
I have two groups of people, one group with healthy individuals and one group with infected individuals.
A questionnaire has ...
- 332
1
vote
0
answers
27
views
How many frequencies to display? [closed]
Recently, a friend asked me an interesting question. Although it is not the first time I have been asked the same question. Well, she did some research and presented me with the graph below asking me ...
- 572
1
vote
2
answers
573
views
Estimating minimal sample size for two sample test (comparing means)
If I want to perform a hypothesis test to compare the means of 2 equally big samples from normal distributions with equal variances, how would I compute the minimum required sample size for each ...
- 49
1
vote
0
answers
16
views
Test to see if differences between measurements are different across groups
Here's a simplified version of my problem. I asked two people to guess the height of people walking by. The guesses were very different. I learned that sometimes estimators would sit and sometimes ...
- 147
0
votes
1
answer
283
views
How do I determine the efficacy of a ranking metric?
I have a dataset where I am attempting to perform a classification task. At present only 15% of the data is a positive class. I believe with some feature engineering I've been able to generate a ...
0
votes
0
answers
34
views
Confusion in hypothesis testing
I'm working at a project in a distribution company. Let's say that in the beggining of this year some major change was made in the sale's area, and my job is to evaluate if this change actually ...
- 67
0
votes
0
answers
26
views
How to test whether each sample is generated from bivariate gaussian distribution?
I have dataset that each samples has its frequency along x and y axis. A sample can be visaulized as above. Each sample can be thought as an image which has only one channel.
Each image has central ...
- 33
2
votes
1
answer
33
views
How do I chose the right distribution for this specific circumstance?
Posted this on stack overflow and people said its probably more suited for this forum.
I am currently generating a panel dataset with random numbers. I simulate a questionnaire where "people"...
- 31
3
votes
2
answers
194
views
Two ways of writing the critical region for Hypothesis Testing
I have one confusion in writing critical region. Let us suppose that we have a test condition that rejects the the null hypothesis if $T(X) > \chi_{2n,\alpha}$. Can we also write this same test as ...
- 1,048
3
votes
3
answers
750
views
Having a problem getting the Intuition behind t-tests and z-tests
Say we have a population of $n$ rodents and that the mean of the population is $\mu$ with standard deviation $\sigma$, the standard error of means in this population would be $\frac{\sigma}{\sqrt n}$ ....
- 132
2
votes
2
answers
415
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Testing the Difference between Two Time Series ~ Similar to paired t-test
I hope everyone is doing well. I have two time series data sets (Time Series 1) and (Time Series 2). These two series are produced monthly (from 1-2020 to 12-2020) 12 data points. Thus, I took the ...
- 33
0
votes
1
answer
529
views
Negative binomial one-sided confidence interval?
Suppose someone was flipping a coin, and want to test the hypotheses:
$$
H_0: p=0.5 \\
H_a: p>0.5
$$
First, assume they decided to run 20 trials. They observed 14 heads and 6 tails. We can create a ...
- 294
0
votes
0
answers
250
views
Event study: test for cumulative abnormal returns
I am performing an event study, across different firms, using the market model theory.
$$\
{R_{it}=α_i+β_{i}R_{mt}+ε_{it}}$$
With Abnormal Returns (AR):`
$$AR_{it}=R_{it}−α_{i}−β_{i}R_{m
t}$$
How can ...
- 11
4
votes
1
answer
96
views
Does one need to test independence of variables first?
Suppose one is given the following data set $X$.
"8 5 12 4 11 6 8 7 7 12 7 3 11 14 11 9 6 6 5 6 10 14 4 5 5" Let $n$ be number of data points.
One wants to obtain 95% ...
- 1,465
2
votes
1
answer
109
views
Confusion in Confidence Interval and Hypothesis Testing
Consider a normal distribution $N(\mu, \sigma^{2})$ where $\sigma^2 = 9$ and we draw 100 samples from this distribution. Now, we set up a hypothesis testing problem: $H_{0}:\mu = 0$ against $H_{a}:\mu ...
- 1,048
0
votes
1
answer
37
views
Which statistical analysis/design to use on clinical hospital data with varying amounts of available data for each patient?
We are currently working in our local hospital on a paper about the influence of the nephrologist on patients with kidney failure.
We are aiming to look at a couple of clinical (laboratory) outcomes ...
- 3
0
votes
1
answer
21
views
What test can i use for this hypothesis? It has a continous variable and a categorical variable
I have two variables
Financial literacy- It's a continuous variable with high and low scores
Default(It means to Not pay their loan)- Yes or no (I can code this as 0 and 1)
What test can I use to test ...
- 101
1
vote
0
answers
48
views
Statistical test to tell whether multiple samples come from the same distribution type
I have many samples $S_1,S_2,\dots ,S_n$. Each sample consists from different number of observations $O_1,O_2,\dots,O_n$. Now I want to conclude that all samples come from the same distribution type (...
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