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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Is this alternative hypothesis possible?

Could anyone check that the alternative hypothesis is valid? I wanted to prove that the "Mahalanobis distance ($\mathbf{T_i} = \mathbf{(x_i - \bar{x})^T \Sigma^{-1}(x_i - \bar{x})}$)" is a Log ...
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26 views

The role of validation in estimation and hypothesis testing

Validation, with or without statistical/machine learning procedures, is used often, if not universally, in prediction. In estimation or hypothesis testing that does not seem to be the case, yet I ...
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31 views

What are the ''desirable'' statistical properties of the likelihood ratio test?

I am reading an article whose method is fully based on the likelihood ratio test. The author says that the LR test against one sided alternatives is UMP. He proceeds by claiming that "...even when ...
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2answers
57 views

Should I divide p into 2 for a one-tailed test in lsmeans?

I have used LMM with this formula: f1 <- lmer (dprime_f ~ language_f + (1+language_f|listener_f), data = data1.frame, REML = TRUE) Then I used lsmeans to run ...
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17 views

Correct Method: Scale emprical CDF or best fit CDF

I have some data, with max value $M$. I assume it is sampled from some distribution with infinite support. A best-fit CDF is calculated $F(y)$ and so is an empirical CDF $F_{N}(y)$. My issue is that ...
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1answer
63 views

How to test for a statistically significant difference between 3 percentages?

I have samples of stories from three newspapers, all testing for the same proportion of stories with a certain characteristic. The data I have is: np1=16.34%, np2=14.00%, np3=18.29%. I want to ...
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43 views

Hypothesis testing – abusing notation or am I missing something?

In a number of statistics books and references you can find formulas such as: $P\,(result~|~H_0)$ (Bortz, p. 114) $P\,(reject~H_0\;|\;H_0~valid)$ (Wikipedia - Statistical hypothesis testing) and ...
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1answer
33 views

Method for a hypothesis testing non normal distribution number of retweets

I am a stats-beginner, Using pandas I am analysing a small dataset. There are 60 data-points, 22 of which are from Group A and 38 are from Group B. The dataset is made up of the number of retweets ...
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1answer
22 views

Hypothesis test calculation [on hold]

The annual profit for your organisation last year was £1203, per employee. The average for the sector was £1228 per employee. You need to know if there is evidence that your organisation is not as ...
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9 views

Comparing accuracy of two non-parametric predictors

I have a quantity x_i that I have n measurements for. I also have for every point two separate non-parametric and non-symmetric distributions A_i and B_i that are supposed to predict the quantity ...
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1answer
29 views

Difference between modelling and testing association

I have data set with binary outcome, with 5 continuous covariates and 4 discrete covariates. I am little confused as to how I test for association, for the discrete covariates, I used a chi sq test, ...
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4 views

Compare samples when each “object” of the sample is a success rate [0,1]

(I don't have a STATS background) I have two samples of different sizes (around 100) A = {0.1, 0.2, 0.21, 0.42, 0.56, 0.32, 0, 0,...} B = {0.943, 1, 0.56, 1, 0.86 ... } each element/object of A and ...
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1answer
23 views

Confused about hypothesis testing, tails, and confidence intervals

$Y_1, \ldots, Y_{10}$ are $N(\mu, \sigma)$ random variables. We observe $\overline{Y} = 20$ and a standard deviation of $1.265$. We are asked for a $95$% confidence interval. Use the t-table, we find ...
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2answers
353 views

Is rejecting the hypothesis using p-value equivalent to hypothesis not belonging to the confidence interval?

While formally deriving the confidence interval of an estimate, I ended up with a formula that resembles very closely the way $p$-value is computed. Thus the question: are they formally equivalent? ...
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12 views

Significance test for difference between subset mean and population mean

I have customer usage data - number of products purchased by each customer during a specified time period & customer attributes (gender, location etc.) I want to make statements like male ...
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10 views

Significance test for subset variation from population

I have customer churn data: independent features like customer gender, location, age etc. outcome feature representing whether he/she has churned or not My population churn rate is around 30% ...
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2answers
44 views

How to interpret the means of different sample sizes

I have three sets of data I am working with. The N of each are all vastly different and the means are also very different. I obviously don't want to interpret it so black and white because I know the ...
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1answer
99 views

Goodness-of-fit test in Logistic regression; which 'fit' do we want to test?

I am referring to this question and its answers: How to compare (probability) predictive ability of models developed from logistic regression? by @Clark Chong and answers/comments by @Frank Harrell. ...
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1answer
51 views

how to calculate type II error $\beta$?

My question is how to calculate type II error $\beta$? Suppose I want to test $H_0: \mu=0$ vs $H_1: \mu=1$ (I need to calculate type II error $\beta$, so I need to fix a $\mu$, say 1, in $H_1$). ...
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13 views

Calculating power of sampling 10 marbles from 1000 [closed]

Suppose I would like to know what's the power of sampling 10 red marbles from 1000 marbles at the 0.05 level. The probability of red marbles is 1%. Which statistical test would I use?
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1answer
19 views

Seeming Unrelated Regression (SUR) for logistic regression

I would like to perform linear hypothesis testing on whether $\beta_{11}=\beta_{21}$ in the logistic regressions \begin{align*} \text{logit}[P(Y_1=1|X)]=(\beta_{10}+\beta_{11}X)\\ ...
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15 views

how to test if 5 data are homogeneous or not significantlly different

I am currently analysis data of radionuclide content in soil profiles. I have different profiles and data every five cm depth. Each profile contains 5 values of a certain radionuclide. I can represent ...
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2answers
52 views

Why applying the same test to several hypotheses reduces its rejection power?

Reading "Kernel Methods for Pattern Analysis", by John Shawe-Taylor, I've got stuck into this sentence: [...] if we applied the same test for $n$ hypotheses $P_1, \dots, P_n$, and found that for ...
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1answer
32 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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1answer
20 views

Two-step Engle and Granger's procedure

If I want to check if there is cointegration between $X_t$ and $Y_t$ in the following model, is it enough to check p-value of Breusch-Godfrey test? The maintained hypothesis in this test is no ...
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1answer
106 views

What exactly is the critique in this regression?

Warning: I might be forgetting basic statistics here. Please edit title if it can be improved. This paper, seemingly summarized in the fancy ZUI slideshow here, points out a possible "critique" in ...
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21 views

Specifying integration level of time series

How to specify the level of integration of $X_t$ in such case? I am familiar with testing integration in R, cointegration strategies, but which method to use in such case? In brackets there are ...
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1answer
45 views

How can correlation be 0 in % terms but 0.5 when measured in dollars?

I am trying to see if there is a causal relationship between Marketing Spend and Revenue on a monthly basis for the Jan to July 2015 period. I calculated the percentage change in Spend and the % ...
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10 views

comparing two frequency distributions and finding which is better to use [closed]

I am starting to learn some statistical tests to use in my work - I have a query Say I have two frequency distribution tables - ...
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12 views

What is the correct test to use for a categorial dependent variable and an ordinal independent variable?

I am trying to figure out if there exists a relation between the region someone lives in and their ranking of a website. The region variable is categorical, dependent, and spans 11 levels such as the ...
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26 views

How to compare percentages?

I have percentages for a variable that has two levels X and Y. The percentages are calculated using the Actual number of observations divided by the Expected number of observations (which are ...
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10 views

Is a test set sampled after training examples have been removed by an active learning algorithm valid?

In this case desire is to optionally label a final test set after training. The training is to be done using an active learning approach which can be biased towards different characteristics ...
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17 views

SAS Proc ARIMA: How to interpret ADF test with several lags

I've been trying to examine the stationarity of variables in a model and from my research have seen a lot of people recommending the approach of ADF testing with several lags. However I am not ...
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11 views

On a problem with the implementation of the test of Dielbold and Mariano for equal predictive accuracy

To recall how the test of Dielbold and Mariano is set up I utilize the parsimonious words of Dielbold himself: Now, I have been trying to perform this test on the respective vector of errors of ...
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64 views

Using Jensen's Inequality to identify blackbox function as convex?

** Edits: In light of the comments I received: I'll appreciate any elaboration on the questions I present. If you can provide examples of what I would need (assumptions, test cases, etc), ...
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36 views

Testing the Validity of a Test Statistic (incorrectly)

In this post @Wolfgang shares a few lines of code to test in a simulation the ability of a particular test statistic to perform as expected, measured by the percentage of type I errors. He shows by ...
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1answer
27 views

Multivariate Hypothesis Testing - How do you choose best combination of factors without explicitly testing every combination (2^n)?

Let's say I have 10 variables that I want to vary (each can be 0/1) on a page in order to determine what leads to the best conversion. How can I choose the best combination of factors without having ...
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16 views

comparison of N groups of independent individuals curves: summary-variables or nonlinear mixed effect model?

I want to assess wether there is a significant difference among two groups, based on a sample of independent individual curves in each group. The logical next step is to try to understand what ...
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1answer
35 views

Which test should I use for hypothesis testing with a small sample size?

I've run a test with one control and one experiment group, and am questioning myself on whether or not I've used the right test (or if significance can even be calculated on the following sample ...
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1answer
26 views

simple vs composite hypothesis doubt

So if we have $H_0 :\theta=\theta_0$ vs $H_1 :\theta=\theta_1$ It is easy to see that this is a case of simple vs simple hypothesis (assuming that $\theta$ is the only unknown parameter of our ...
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Test hypothesis of rare event with real life data using a Bayesian Model

Since I found out what Bayesian Theory I got really interested in using it in my everyday life to find a numerous of things, but I wasn't able to get any result due to my lack of understanding of ...
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21 views

Relationship between Matthews correlation coefficient (MCC) and the Pearson's Chi-square

I would like to find a reference showing that the MCC follows a Chi-square distribution. This is suggested in this wiki: https://en.wikipedia.org/wiki/Matthews_correlation_coefficient, as they claim ...
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22 views

Statistical test for changes in ranks

I am investigating changes in rankings of schools. For example, in year t school X may have been in the 17th percentile (poor performer) but in year t+1 it may have improved to be in the 94th ...
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1answer
26 views

Types or Methods of Testing Correlation

Suppose I have two variables, which have over 500 data points per variable (though they are not continuous on timeline). what other kind of methods or test in can use in R to test the correlation? ...
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54 views

Test for difference in proportions with small probabilities

I want to perform a test for differences between 2 binomial populations. The probabilities are small (usually less than 10 %). I can define the successes as "rare events". I think that the z-test ...
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Hypothesis Testing with limited resolution

Assume two univariate, normal distributions e.g. A~N(x,0,1) and B~N(x,1,1). Assume that we receive a value e.g. t=0.2 (e.g. via measurements) We want to perform hypothesis testing and decide if t ...
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How to determine proper significance level in forming hypothesis?

I am conducting a Two-Way ANOVA test on a set of data, with replication; there are two variables, each with 3 different categories (thus, 9 different groups). Each group has 4 data points, bringing ...
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The best model to analyse this data set: Comparing bacteria communities within calves

The design is like this: I have 18 calves in the experiment, and all these calves were divided into 3 groups with 6 calves in each group. The 6 calves in group 1 were euthanized at the end of the ...
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Probability standard deviation random fluctuation in data

Let's say we have n vectors with k elements: $v^1$ = [$e^1_1 ,e^1_2,...e^1_k$] $v^2$ = [$e^2_1 ,e^2_2,...e^2_k$] and so on till $v^n$. Now let's suppose i have an algorithm that selects an element ...
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Testing whether two samples come from the same population without assuming independence?

I'm doing some analysis of frequency data coming from the Sun. I want to test the null hypothesis of two different signals coming from the Sun having the same frequency. I measured both of these ...