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Questions tagged [hypothesis-testing]

Hypothesis testing assesses whether data are inconsistent with a given hypothesis rather than being an effect of random fluctuations.

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comparison of two independent data of same location using statistical test

I have elevation values of a geographical area with their lattitude and longitude, derived from two different satellites. How can I compare these data using some statiscal test?
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How to determine the sample size for a control group when conversion is low

I have to test a binary classification model, and I'm not sure how to define the control set. I have a 300k potential clients, and I have to choose the most probable 10k that will buy my product. The ...
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Binary coin toss statistics

I'm really new to statistics and I'm working on a project where I'm basically trying to rig a coin toss. I have three groups and $n = 50$ tosses for each group: Control (24/50 success) vs treatment 1 ...
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Identifiyng mutual trends between treatments

(WARNING: Not a statistician - do not get mad) We have two different treatments $A,B$, each was tested separately ($A$ treated group vs control, $B$ treated group vs control). In each comparison, the ...
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Hypothesis Testing: t or z distribution?

If we want to to do hypothesis testing when the sample size is small but the population standard deviation is known, do we use z or t distribution?
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Testing for difference in means with bimodally distributed data?

I have two bimodal distributions of data with two peaks (one around 0 and the other around 1). I have provided an example of one of the distributions. Although their means and variances are different,...
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Standardized differences between means in R?

There is data on a sample of 1,216 students that I'm missing, but I know the means and standard deviation of some key demographics on them. I have a subsample (120 students) with the means and ...
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How to test whether E[X]>E[Y] controlling for Z?

Question in mathematical terms. Assume an observation consists of three continuous variables $X$, $Y$ and $Z$. The sample comprises a sufficiently large number of observations. I would like to check ...
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Type-I and Type-II errors example explanation

In the following example, can someone help understand how the value for $k$ (highlighted in yellow) is derived below? How is $z_\alpha$ introduced in there?
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How can we check whether coefficeints of a multivariable regression models are zero(null hypothesis) without creating full and restricted model?

I want to test whether a variable Y has an influence over other variable Y. For this I have established a null hypothesis that the coefficients of Y in the regression model are zero. Can I test this ...
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Without testing: when are error terms possibly homoscedastic?

I am facing the following study: In the 1980's, Tennessee conducted an experiment in which kindergarten students were randomly assigned to regular and ...
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Find initial evidence that a treatment could be not enough to prevent a disease

I have just a basic understanding of statistics so please forgive me for the poor description I'm writing. I'm trying to design a small retrospective study to figure out if I can get some evidence ...
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Probit Hypothesis Test: $H_0: \beta_1 \geq 1$

Problem Given the output of a probit model and no knowledge of the sample data: ...
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$X_1,X_2,\dots,X_n \overset{\text{iid}}{\sim} N(\mu,\sigma^2)$. Derive a confidence interval for $\mu+\sigma$ and $\mu/\sigma$

I know how to find confidence interval for each of the parameters $\mu$ and $\sigma$ resectively but stuck in finding for the parametric functions above.
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Determine the effect of a binary variable?

Consider that a site A has ten thousand web pages. For each of the web pages, the server keeps the number of people visited each of those pages (plus some additional characteristics, such as ...
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What test should I use to compare two categorical distributions with replicate measurements?

So I have data from an experiment I did, and I'm at a loss for which test I should use to assess for significance. I took some cells in vitro and subjected them to either a treatment or a control. ...
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Problem of Critical Region and Significance Level (Statistics)

An investment adviser states that the risk (standard deviation) when investing in a certain instrument is greater than $3.$ To corroborate the validity of this statement, he plans to realize: $H_0: \...
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Stationarity tests

It is generally accepted that ADF is the most common test to check whether a time series has a trend or not. My question is: What if we just regressed the values of the dependend variable on their ...
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Power analysis for contingency table

Following a cardiac surgery a patient will be classified into one of four categories: Nothing, Mild, Moderate, Severe. There is a new test which, when performed after the surgery, claims to be able to ...
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When calculating sum of observation in Bayes Theorem, why do we remove one outcome?

relatively quick question regarding this course question: Hearing about your brilliant success in working with M&Ms, Mars Inc. transfers you over to the Skittles department. They recently have ...
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Degrees of freedom when manually doing (Welch) T-test?

I have two samples A and B and want to test if the (Pearson) auto-correlation of A is greater than that of B. So far I've computed the two autocorrelations, $r_a$ and $r_b$ and found their standard ...
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Would there any be a case when only one sided tests would be applicable. Could the collection of the data signal this?

Would there any be a case when only one sided tests would be applicable. Could the collection of the data signal this? Is there a way when I could tell from the collection of the data that I would ...
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A/B testing use case and test set up

Suppose I want to know whether a change to a website (such as changing the way the homepage looks) has no effect on a metric I care about, such as conversion. Can a frequentist (not Bayesian) A/B test ...
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Measuring causation

The tool I'm working on is used to process large number of documents. Recently, I've implemented small feature for this tool. The feature affects some % of all documents. After few days I received a ...
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Hypothesis test testing for monotonic group mean change

I wonder if there is a statistical hypothesis test testing whether group average monotonically increases across groups? For example, I have four treatment groups, A, B, C and D. I would like to test ...
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Is there any statistical test for the difference between two percentiles?

I know the R function t.test to perform the statistical test for the difference bewteen two means, is there any test for the difference between, say, the 95th ...
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The assumptions regarding the t-test

The t-test has an assumption that the sample provided has to be random in nature. Do we test our sample for randomness before carrying out the t-test ?
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Hypothesis Testing For Binomial Distribution

I have come across the following problem which confused me quite a lot and would be helpful to get your comments: Problem Suppose we are testing a newly programmed random number generator. We use ...
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How do I interpret my hypothesis in question given my data analysis results?

I have little statistics background and I am struggling to interpret these results in a data analysis. I wanted to test: 'Body image dissatisfaction is more likely to develop in female adolescents ...
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How do I interpret the p-value from a Shapiro-Francia Test?

I have a situation where I have more than 50 samples in a given set of inputs and I cannot use the Shapiro-Wilk test as I don't have the numbers for the pyramid for $n>50$. I was then asked to use ...
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P-value on statistical tests [duplicate]

If I have a p-value of 0.01 on a statistical test, does that mean the probability of my hypothesis being wrong is 1%? If not, why not?
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Two data sets from test with a 95% confidence limit of reproduceability and standard deviation of each data set

This may have been answered and I'm simply not using the correct search terms to find the answer/thread. If so i apologize, please point me in the right direction I have two data sets (3 ...
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cumulative effect of near significant differences?

My knowledge of statistics is pretty limited at this point, so you'll have to excuse my ignorance. We've performed prospective randomised study looking at the differences in detection rates of cancer ...
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Pairwise vs aggregate A/B/n hypothesis testing

I'm currently running a hypothesis test on multiple variants (say $n$ variants) of a webpage, trying to optimize conversion, and am unsure if I should run pairwise hypothesis tests of each variant ...
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Hypothesis Test of Hypothesis Tests

I am doing a linguistics project in which I am comparing the % of the time "um" follows a contraction vs. the % of time "um" follows what I call the full form (e.g. full form of don't is do not). I ...
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How to compensate for different statistical power in multiple comparisons? [closed]

Imagine we are performing 10 comparisons on a single variable of choice. The 10 respective experiments have different statistical powers. Now imagine that the least powerful and the most powerful ...
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Testing negation in the null hypothesis?

Is it valid to state a null hypothesis as the negation of an equality? Something like: $$H_0: \mu_1\neq \mu_2\,\,\,\,\,\,vs\,\,\,\,\,\, H_1:\mu_1=\mu_2.$$
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Mean Square of Regression Error for categorical variables while computing F statistic

Give the annova table in the image below: I need to calculate the F statistic for the null hypothesis: b2 = b3 = 0 . b2 is cofficient of cylinder and b3 is the coefficient of doors. The formula used ...
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Using difference-in-differences as data preprocessing

I am having difficulties with wrapping my head around an idea. Can difference-in-differences be used to remove bias from the data? I found a mention here: "Difference in differences is a well-accepted ...
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Type I and Type II errors in Hypothesis Testing

I am confused about the last highlighted sentence regarding finding a subset S, for which BOTH Type I and Type II error probabilities are 0. For $P_\theta S$, which is the probability with which we ...
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Generalization of one-sample t-test for multiple groups

If I have some data*, and want to test the hypothesis that it has a given mean $\mu_0$, I know of the possibility of using a one-sample t-test. Here, $\mu_0=0$ could be the null-hypothesis of a ...
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Which test should I use for numeric and counting variables

I have a variable "age" which is continuous variable, and the other variable is the "number of children" for example, 0, 1, 2, 3. I would like to test the relation between these two variables. If I ...
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Is this a matched pairs data set?

A review problem for one of my daughter's statistics classes: The arm span and height of 10 individuals is measured in order to test the hypothesis that arm-span equals height in humans. Perform an ...
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most powerful test between two density function

I need to derive the MP level α test: let $f(x)_0=(1/√2π)~~ exp(−x^2/2)~~ and~~ f(x)_1=(1/2)exp(−|x|)$ $H_0:f(x)=f(x)_0 ~~ vs~~~ f(x)=(1/2)f(x)_0+(1/2)f(x)_1$ below what I did, but I can not ...
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Do i reject or fail to reject the null in these instances?

I have got questions regarding Alternative and Null Hypotheses, but it confuses me, and well I just need help as I keep getting stuck on two questions, both about hypothesis but I'm only here to ask ...
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Pairwise non-parametric test?

I have 5 groups of patients (different sizes), for which I measured some property that is continuous but not normally distributed. I would like to compare every pair of groups in respect to this ...
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2answers
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Figuring out Which is Null and which is Alternative

After doing homework problems for stats, I am having a tough time for understanding which one is null hypothesis and which one is alternative hypothesis. Is there an intuitive explanation so that when ...
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1answer
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Causation vs Correlation( question about a specific case of faulty logic) [closed]

My question concerns the first two paragraphs of the text. Isn't the author falsly equating causation(austerity e.t.c leads to pathological lending patterns) with correlation( countries which display ...
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Comparing two discrete independent variables

I would like to perform something like two-sample Wilcoxon tests/T-test (paired = FALSE) to compare two method's expected scores. Here is the table of counts: ...
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How does Bayesianism deal with made up / post hoc explanations?

Consider the example of an object spontaneously going up in flames. Now one hypothesis may be that it was (A) some chemical reaction, but another could be (B) an invisible man with a lighter. This ...