Tagged Questions

Hypothesis testing assesses whether data support a given hypothesis rather than being an effect of random fluctuations or some other process described by an alternative hypothesis.

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Filter insignificant proportions statistically

I have a set of proportions: $(1/10,4/6,1/1,1/1,13/18,3/3,55/57,2/20,416/441,23/29,4/4,...)$. The numerator stands for number of links to some finite group $\{A,B,...\}$, the denominator stands for ...
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Age Interactions in mixed models

We are using a mixed model to describe trends as subjects age. We have multiple measurements per subject of a continuous outcome. We also adjust for the age at entry into the study. It is of ...
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When designing experiments why is it necessary to have multiple groups run in parallel?

Let's say I wish to test the effectiveness of a new technique of teaching as opposed to an old one. Why is it recommended to have a control group running the experiment in parallel with the group ...
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z-test vs t-test under assumptions

A traditional t-test to compare two means assumes independent random variables, $X_1,...,X_n \sim n(\mu_1,\sigma_1 ^2)$ and $Y_1, ...,Y_m \sim n(\mu_2,\sigma_2 ^2)$. One usually assumes normal ...
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How to compare the mean of two samples whose data fits exponential distributions

I have two samples of data, a baseline sample, and a treatment sample. The hypothesis is that the treatment sample has a higher mean than the baseline sample. Both samples are exponential in shape. ...
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When n increases the t-value increases in a hypothesis test, but the t-table is just the opposite. Why?

The formula for $t$ in a hypothesis test is given by: $$t=\frac{\bar{X}-\mu}{\hat \sigma/\sqrt{n}}.$$ When $n$ increases, the $t$-value increases according to the above formula. But why does ...
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Using $\chi^2$ or Fisher's exact test with low expected counts

Let's say I have 7 urns filled with random numbers of colourful marbles. An example dataset is as below: ...
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How to address and acknowledge a significant interaction that has little practical meaning

I am building a model with a highly significant interaction. This interaction was one of our main hypotheses. It is clear, however, that the form that the interaction takes does not represent a ...
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Combining p-values from different statistical tests applied on the same data

Although the title of the question appears trivial, I would like to explain that it is not that trivial in the sense that it's different from the question of applying the same statistical test in ...
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Diagnosis of normality assumption and fitting linear regression in R

I am using the data veteran from R package survival. How can I diagnose the normality ...
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observation and hypothesis testing

Can observation be used to collect data for hypothesis testing? Can we be confident with the power of the test in those cases? We know power of the test can be applied with hypothesis testing for data ...
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Interpretation of hypothesis testing

I have the following sample. Now I have to test: $$H_0\!:\mu=60,\!000 \quad \text{Vs.}\quad H_a\!:\mu>60,\!000$$ I have computed it in R Software But I do not ...
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I have a set of data which i need to explain and compare with ADF-GLS test and ADF test in eview. I don't understand the principle of ADF-GLS test with trend and intercept or only intercept. However ...
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What is the intuition behind exchangeable samples under the null hypothesis?

Permutation tests (also called a randomization test, re-randomization test, or an exact test) are very useful and come in handy when the assumption of normal distribution required by for instance, ...
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Difference between 'ovtest' and ovtest,rhs'

After running an OLS regression, I ran the Ramsey RESET test using the stata command 'ovtest' and 'ovtest,rhs'. Two tests gave the opposite results. With the first one, I could not reject the Null, ...
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Get probability of no positive results in a population?

I have a population of say 100,000 records that can be either Positive or Negative (true probability of Positive is very small, but unknown - may even be zero). I want to take a sample and estimate ...
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Is there such a thing as a matched-pairs t-test between two lists of proportions?

I am aware that there is a matched-pairs t-test between two lists of counts. However, I cannot find any matched-pairs t-test of proportions. For example, list a may be [1/2, 24/30, 5/8] and list b may ...
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How to test the randomness of a sequence of real m-tuples?

1) Let $\{a_i\}_{i = 1, ...,n}$ be a real sequence generated by a pseudorandom number generator. How can I check the randomness of such real numbers using, for instance, Runs test? 2) Assume three ...
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To what extent is survey research the most effective data collection method for hypothesis testing?

I want to know whether survey research the most effective data collection method for hypothesis testing. In order to answer first of all i will try to mention about the significance of survey, ...
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How to check if the results of two methodologies are the same?

I have two models that essentially are supposed to produce the same results. Given that the first model is correct, what tests are available that I can use to check the validity of the second model ...
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Mixed Model t Test (Toothaker’s t-Test)

I'm trying to do a follow up test for a mixed model ANOVA, and I figured that I need do a Mixed Model t test also known as Toothaker's test. I just don't know how do it. I was wondering if anyone has ...
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Implications of current debate on statistical significance

In the past few years, various scholars have raised a detrimental problem of scientific hypothesis testing, dubbed "researcher degree of freedom," meaning that scientists have numerous choices to make ...
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Multiple regression and hypothesis test $H_0$:$\beta_2=0$

Multiple regression model $H_0$:$\beta_2=0$, $H_1$:$\beta_2 \neq 0$ where $\beta_2$ is the vector of elements ($\beta_2, \beta_3, \dots, \beta_k$) and $\beta$ is slope of regression line. Why it is ...
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Bayesian and frequentist interpretations vs approaches

I have been reading about the frequentist vs bayesian issue (this article has helped a lot, specially with the example; also this one), and I haven't come to terms with it. At the moment it seems like ...
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Writing null hypothesis and deciding on rejection criteria

The number of faults in one metre of a thread is Poisson distributed.It is claimed that the average number of faults is 0.02 per metre.A random sample of 100 one metre lengths of the thread reveals a ...
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Is this test answer good enough to show Granger Causality?

I used an inbuilt Matlab function to check for Granger Causality between two time series P and T that have a correlation coefficient of 0.6. The function is : ...
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hypothesis testing using poisson distribution

At a nuclear plant great care is taken to measure the employees health.These are the number of visits made by each of the 10 employees to the doctor during a calender year. 3,6,5,7,4,2,3,5,1,4 ...
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Hypothesis testing with exponential family

I'm interested in running hypothesis tests for a variety of members of the exponential family with continuous support, for different values of the parameter/s, for a sample of n i.i.d random variables ...
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Significant differences between dependent samples beta-weights test

I am testing a model in which I have 2 independent variables (IVs) and 2 dependent variables (DVs). I am hypothesizing that both IVs will predict both DVs; however that the relationship between IV1 ...
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How to test for randomness in bins with small N?

I observe a series of crime incidents linked by modus operandi or some other peculiar characteristic of the crime (e.g. cutting catalytic converters from underneath vehicles). I would like to know if ...
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Challenging Likelihood Ratio Test

Derive Likelihood Ratio Test of size $\alpha$. H$_0$: $\theta=\theta_0$ H$_1$:$\theta \neq \theta_0$ $${f}(x,\theta , c) = \theta(x-c)^{\theta-1} \ {c<x<c+1}$$ I ...
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What is the best way to analyze data if your experimental design changes while running the experiment?

I imagine this is a somewhat common situation in practice. I am thinking mainly in terms of preclinical drug trials. 1) During the course of the study a new technique is learned or some time/money is ...
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How do I test that two continuous variables are independent?

Suppose I have a sample $(X_n,Y_n), n=1..N$ from the joint distribution of $X$ and $Y$. How do I test the hypothesis that $X$ and $Y$ are independent? No assumption is made on the joint or marginal ...