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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1answer
94 views

Chi Square Goodness of Fit vs. Igloo

I am very new to Chi square goodness of fit tests but have done a fair bit of research. Basically, I have the following 12 data points: 7392, 7656, 7241, 6164, 4984, 4664, 15262, 17053, ...
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1answer
168 views

Unit testing sampling methods

I'm writing a bit of code that makes pretty heavy use of sampling (eg, MCMC, Particle Filters, etc), and I would really like to test it to make sure that it's doing what I think it is before claiming ...
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1answer
45 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. ...
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31 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 ...
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1answer
68 views

Failing to obtain $\chi^2(1)$ asymptotic distribution under $H_0$ in a likelihood ratio test: example 1

I have a large sample (a vector) $\mathbf{x}$ from a random variable $X\sim N(\mu,\sigma^2)$. The variance $\sigma^2$ is known, but the expectation $\mu$ is unknown. I would like to test the null ...
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17 views

Testing the ratio of SLR coefficients

Consider applying simple linear regression (SLR) to the data $\{(X_{i},Y_{i})\}_{i=1}^{n}$. Furthermore, let's assume that the errors are conditionally normal, i.e $$Y_{i} = \beta_{0} + \beta_{1}X+e_{...
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39 views

What statistical test should be used for testing the association between ordinal data and 2 categorical variables?

I am trying to find the association between grades and most and least preferred subjects, wherein it is hypothesized that subject preference is the independent variable to the dependent variable ...
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1answer
31 views

How to test the relationship between variance of functional trait value (dependent variable) and elevation range of occurrence?

I have a data set consisting of functional trait values for trees across an elevation gradient. Hence each functional trait value (dependent variable) has a corresponding elevation value (independent ...
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1answer
43 views

Can I test this hypothesis with a one-tailed test?

A student wants to investigate whether people from northern USA are more severely affected by winter depression ("seasonal affective disorder") than people from southern USA, using a ...
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1answer
28 views

Performing hypothesis test with two categorical variables, where one variable has four ordered categories

I'm working with two categorical variables and need to test whether they're related. This isn't the exact problem I'm solving but the example should help illustrate the nature of the problem I'm ...
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1answer
55 views

Seeing if (and *how*) two categorical variables are related

Consider the variables sex (male or female) and political party affiliation (Democrat or Republican). In this case, the null hypothesis and alternative hypothesis would be: H0: Sex is independent ...
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1answer
3k views

How to detect intermittent time series?

I need to automatically identify if a time series is intermittent or not. Depending on the result I'll use one or another method for forecasting it. Is there any test to detect intermittent time ...
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2answers
87 views

Asymptotic null distribution of the LR statistic with point null and point alternative

I have a large sample (a vector) $\mathbf{x}$ from a random variable $X\sim N(\mu,\sigma^2)$. The variance $\sigma^2$ is known, but the expectation $\mu$ is unknown. I would like to test the null ...
2
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1answer
50 views

Why is a t statistic used for standardized regression coefficients?

I understand the sampling distribution of unstandardized linear regression coefficients is normal, and therefore a t distribution can be used to determine p values for given coefficient and standard ...
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4answers
238 views

Testing Hypothesis with different alternatives

I want to test whether $\mu=\mu_0$ where $\mu_0$ is some fixed number. Consider the following two different testings. Hypothesis Testing 1: $H_0:\mu=\mu_0,H_1:\mu<\mu_0$ Hypothesis Testing 2: $H_0:\...
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19 views

Which to Use: Likelihood Ratio Test or Uniformly Most Powerful Test?

I've recently been learning about MPTs (most powerful tests), UMPTs (uniformly most powerful tests) and LRTs (likelihood ratio tests), and do not totally understand in which context the different ...
2
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1answer
231 views

Adjust ROC analysis for multiple testing?

we did an exploratory prospective study in medicine in order to find parameters which are able to predict a specific post-surgical event (0/1) before the actual surgery. We have about 10 parameters ...
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28 views

How to test the difference between dependent partial correlations in the presence of autocorrelation?

Background and what I am trying to do: I have a single dependent variable $Y$, and $K$ independent variables of interest ($X_1, X_2... X_k$). I also have a single independent variable of non-interest, ...
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1answer
363 views

How to run Friedman test correctly across three sets of questionnaire data divided into sub-groups?

I am trying to evaluate the usability of three prototypes of an application and want to see if there is a significant difference in terms of usability. For this I have collected responses from users ...
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7 views

Why we use the number of params as degree of freedoom in the F test for regression?

In a linear regression, we can assume that $\frac{(SSD_y - SSR)/p-1}{SSR/(n-p-1)}$ have a $F$ distribution if the null hypothesis $Ho$ is true, with $SSR$ being the sum of residues of the regression ...
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2answers
31 views

Choosing a test for questionnaire analysis

I want to analyse the data from the following experiment setup: Participants were divided into three groups, each group read a story and had to anwser a question by choosing option A or B. The age, ...
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9 views

spatial correlation between two hexa/density maps

I was working on a report and was faced with a question regarding maps and spatial analysis. I want to compare some maps and find the similarities/differences among them. The maps represent the sum of ...
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1answer
54 views

What does it mean that the p-value is a function of the sample size?

I have heard the phrase the "p-value a function of the sample size" but am not sure if I really understand what it is saying. I normally refer to thinking about a t-test where the t-...
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22 views

Proper Test for Type of Data

Warning: I have not done any statistical analysis since 2012. Problem: I have a list of lists of lists: Each of the $289$ ($17\times 17$) element is $\{\phi_{j,1},\phi_{j,2},f(\phi_{j,1},\phi_{j,2}),\{...
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10 views

How to select variables for Little´s Test?

Lets assume there are 150 variables in a Dataset. For my analysis I only use around 50 of them. Of those 50 variables, there are 18 Variables which contain missing values. How should I perform the ...
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1answer
40 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 ...
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26 views

Correct test to verify that data stems from a (given) non-stationary categorical time-series

I have a categorical random variable that can take one of 3 values (red, blue, green). The variable is called Guess and - over the course of a time-continuous ...
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9 views

What does this ttest result mean?

[![stata ttest result][1]][1] What happen with this ttest result? What does it mean? Is it because of many dummy variable? Or is it because there is corellation among the variable? [1]: https://i....
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1answer
10k views

T-test for Bernoulli Distribution- Sample or Population data for SE calculation?

Am struggling to understand part of the answer to a question have done- Qu- In a given population, 11% of the likely voters are African American. A survey using a simple random sample of 600 landline ...
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14 views

What is the most appropriate statistical test to use to analyse Western blot results where the samples are grouped in pairs?

I am doing a Western blot data analysis. I am trying to identify whether there is a statistically significant difference in levels of a certain protein between wild-type and knockout mice brain lysate ...
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1answer
100 views

Runs test based on the median intuition

The following document http://www.ifp.illinois.edu/~ywang11/paper/ECE461Proj.pdf contains a very nice summary of some nonparametric tests for randomness. My question concerns the popular Runs test ...
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1answer
176 views

Contradictory Ljung Box results

We want to apply extreme value theory to the maximum yearly temperatures. Before we choose the model we want to test whether or not we can assume independence. First we made a plot of the ...
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2answers
49 views

Testing for equal proportions when sample sizes are very small

Suppose I observe binary data for two samples (hopefully the notation below is obvious) and I wish to test the hypotheses: $$H_0: p_1 = p_2$$ $$H_A: p_1 \neq p_2$$ I know there is a $z$-test for doing ...
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1answer
353 views

Why do some formulas for statistical power not take into account variance?

I just read this article on power analysis. I want to figure out the size of a sample needed to detect a 1% change in proportions for independent samples with a dichotomous outcome (see "Sample Sizes ...
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1answer
29 views

Normality test for circular data

I have some angles and I am wondering how can I test whether the distribution of my data is normal or not. In fact, I want something similar to KS test. Howver, I want to use it for circular data to ...
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1answer
24 views

Verbiage on rejecting null hypothesis, Sample Size, testing

I'm new to using statistics in psychology, and I'd like to seek some guidance from this forum. Context: I'm running an experiment involving 5,000 participants. Half of them (2500) will receive a ...
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1answer
24 views

Mutant analysis - should the t-test be paired or unpaired?

I have two bacterial strains - one is wild type and the other has one gene deleted. In my experiment, I calculate some observable characteristic (which is continuous) for both of these strains. I ...
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1answer
1k views

Tobit for corner solution models: normality and homoskedasticity tests

I would like to regress several explanatory variables (called X) on a dependent variable called Y where Y is strictly positive and continuous. It is left-censored at 0. Y represents how much a ...
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2answers
221 views

Hypothesis testing on subsamples and cross validation

When working on very large datasets, identifying effects rests more on quantification than significance and many questions/answers give insight on what to do regarding large samples like this (very ...
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1answer
36 views

Are there examples where errors in numerical analysis has caused wrong decisions in statistics?

I read from statistics books that numerical analysis is not in important role in statistics. Are there any examples in history where numerical approximation has been caused wrong decisions in ...
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31 views

Is an ANOVA appropriate?

I am trying to describe a data set measuring toxicity by group with and without a treatment. The data was collected in pairs, such that the researcher would take the difference in toxicity between a ...
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16 views

How to test/validate if a 1% week-on-week drop in a KPI(say Daily Active Users) is significant or due to random chance?

If seen that DAUs of a company are dropping for some time in the past 6 weeks by some small factor, nothing concerning to raise a red flag, just around 1% week-on-week. How can i know if this is ...
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1answer
22 views

Testing hypothesis for a fraction

Let's say I have a sample of $70$ people rating a book from $1$ to $5$: $n_1 = 5$ $n_2 = 8$ $n_3 = 20$ $n_4 = 31$ $n_5 = 6$ Where $n_i$ is a number of people who gave a rating $i$. I have to obtain a ...
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0answers
18 views

Carrying out a hypothesis test to check whether the marginal effect of education (on wage) is positively related with the level of experience

I used STATA to estimate regression of log of wage (monthly earnings) on education (in years), experience (in years), interaction between education and experience, tenure (years with current employer),...
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1answer
28 views

Hypothesis testing, type I and II error

A sample $X_1, X_2, X_3, X_4$ comes from a normal distribution $N(m, 2^2)$. To verify $H_0: m=4$ against $H_1: m = 1$ one uses a test with a critical region: $K = \{4X_1 − 2X_2 − 2X_3 + X_4 < −2\}$....
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22 views

What is a noise-resistant method for testing correlations of proportions

I have a friend who is trying to analyse a large Sanskrit corpus with many verbs in. Verbs can occur in the active or the passive, and they can occur in the past tense or the present tense. She wants ...
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0answers
18 views

What is a test function?

From what I understand, when we do hypothesis testing, we compare a test statistic, which represents some data, to a critical value that allows us to accept/reject our null hypothesis. However, I have ...
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1answer
31 views

Study association between continuous and categorical variables

I have independent continuous variables like Age, Price and outcome variable like purchased ...
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18 views

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 ...