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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Hypothesis testing- lognormal distribution

I have a conditional mean and standard error for a parameter log-normally distributed. I want to test whether the mean of the distribution is significantly different from an alternate estimate of ...
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1answer
12 views

Analysing data from summary table on R (interactions)

If I want to test whether data[,1]:setB is equal to 0 or not, do I just use the given t value and p value or do I need to add it with the data[,1] values? looking at the p value of data[,1]:setB, I ...
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9 views

Extending log-likelihood beyond a pair of hypotheses

I use log-likelihood ratio to show likelihood of co-occurrence of features in samples (out of a set ~100k possible features, where I have millions of samples, each with 10-100 feature occurrences) - ...
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1answer
46 views

KS-test - how is the p-value calculated?

How is the p-value calculated in Kolmogorov-Smirnov test? What's the formula for it? I suspect it's derived based on the definition of p-value. The value of test statistic is the largest differnece ...
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45 views

Statistical significance level - hypothesis testing

Why is significance level called the probability of rejecting the null hypothesis given that the null hypothesis is true? This is my understanding of hypothesis testing, correct me if I'm wrong. For ...
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10 views

test fitting different sinusoidal models

I have some time series data and would like to see whether it can be better described by fitting (1) one sinusoidal function or (2) two sinusoidal functions combined, both with different frequencies. ...
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4 views

Distribution testing in presence of variable noise

I have a number of integer data points $x_1, ..., x_n \in \{0, 1, \dots\}$ and would like to test whether they belong to a certain distribution discrete distribution. For this purpose, it seems that ...
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1answer
19 views

Transformation of any normal distribution into a standardized t-distribution

What will be the transformed Mean and transformed standard deviation if any normal distribution is transformed into a standardized t-distribution? Does t force ...
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2answers
49 views

What will be the t-value if my sample size increases to an infinity compare to z value?

I do not know where to check this. Any reference/help is much appreciated. If the sample size, n increases to an infinity then will the t-value be larger/smaller ...
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1answer
11 views

Proportion test with null hypothesis p1=x*p2

I'd like to compare the proportion of two sets of binomial data where the null hypothesis is not p1=p2, or p1-p2=x, but \begin{equation} H0: p1=x*p2 \end{equation} I've been computing a z test as ...
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8 views

Binary variance? Comparing two sacks of uneven coins or two heterogenous groups of people

I have two sacks of coins. In one sack, the coins are all uniform, each giving a fairly constant 0.5 chance of heads (based on tossing a few of them and also visual inspection). I then estimate the ...
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9 views

What are Bayes Factors and how can they be used to demonstrate a null finding of “no difference” between two groups?

A prominent journal in my field recently updated its advice to authors to state: Null findings: Authors should only report ‘no difference’ between conditions or lack of associations if they can ...
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10 views

Is there a statistical basis to adjust an observation based on prior observations [on hold]

I have an observation for a parameter, X1, on the basis of that observation a process adjustment is made for batch Y1. Is it justifiable to adjust observation Xn by some weighted average of Xn-1 to ...
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57 views

Is this good statistics?

I have the mean of 2 samples, as well as the standard deviation. I wanted to see if I could run a t-test on this data, and using the standard deviation and my knowledge of the 68–95–99.7 - I did the ...
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1answer
15 views

Test two 1-10 ranking processes on same data and test for statistical significance in the two processes

I have one set of data. I have two procedures for making 1-10 ranking of the data (one was used previously and one is a new procedure). I want to do a hypothesis test to see if the ranking is the ...
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38 views

How does left truncation affect the calculation of the logrank statistic for comparing two survival curves?

I'm currently doing survival analysis in R with left truncated data and am having trouble understanding how truncation affects the shape of a survival curve, and the results of a logrank test which ...
2
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1answer
34 views

Are there test statistics for which a larger sample size does not tend to produce a smaller p-value?

I'm assuming that there is a genuine population effect. By test statistics I mean test statistics that are in accepted use, and not a hypothetical test statistic that a reader might simply make up. ...
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23 views

Testing a proportion in an online setting

I work in an online security setting. My goal is to detect if the number of locked accounts per time unit is stable or not. I've tried several approaches, detailed below, but I am not satisfied yet. ...
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2answers
35 views

Non-parametric tests in big data scenario

Suppose I have two populations A and B , with sizes $n_1$ and $n_2$ respectively, where both $n_1$ and $n_2$ are large (say, above 500). I want to test that the values $x_1, \dots, x_{n_1}$ of A ...
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1answer
36 views

Aren't normality tests backwards?

Currently hypothesis tests for normality are setup so that the null hypothesis is that the data is normally distributed and the alternative hypothesis is that the data is not. This seems to have ...
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5 views

Factorial Design with Completely randomized Design [closed]

A researcher conducted an experiment to determine the effects of 4 different pesticides on the yield of three varieties of citrus. Eight trees from each zariety were randomly selected from an orchard. ...
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10 views

How to tell in Panel Data how the independent variables affect the dependent for specific countries instead of the whole sample in total?

I am working on my Master Thesis on how some specific independent variables (like inflation) can affect a specific index which is the dependent variable. I am taking 25 annual values for 12 countries. ...
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15 views

consistency of two multiple hypothesis tests

For a multiple hypothesis test $H_{10}, H_{20},...,H_{n0}$ (e.g. tests of difference of gene expressions; assume to be independent to simplify the question), there are two independent test statistics ...
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3answers
50 views

Why does Type I error always occur in a NHST? Or, is NHST too weak to tell the truth?

Recently I have noticed that Type I error of a test is too much persistent. Even if all the values are almost equal (variance is extremely low) and tested to that value (true mean), still there is ...
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8 views

In a simple hypothesis vs composite hypothesis test, are the p-values the same?

In a simple hypothesis test, we have something like $H_0 = 5$ and $H_A = 10$ while in a composite hypothesis test we have something like $H_0 = 5$ and $H_A >5$. Since the p-value is defined to be ...
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1answer
40 views

Results of 2-sample t-test does not seem intuitive; wrong procedure?

I have data shown below, with a response variable tabulated by hour (x-axis) as well as numerous other factors: larger chart available here I want to see if the colored points (red, light and dark ...
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18 views

Why is likelihood ratio test for two hypotheses defined like this?

Likelihood ratio for rejecting some null hypothesis is defined as $$\Lambda(x)=\frac{\sup\{\,L(\theta\mid x):\theta\in\Theta_0\,\}}{\sup\{\,L(\theta\mid x):\theta\in\Theta\,\}}.$$ This makes sense, ...
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1answer
26 views

Comparing distributions of categorical data

Suppose that there are four categories: 1,2,3 and 4. The data sets look like this: Data 1: 1,2,4,3,4,1,2,3,4 Data 2: 3,3,4,1,2,3,4,3,2,1,2,3,4 What ...
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1answer
28 views

Testing Hypothesis

I have a sample of 40 data, that shows the average of time a person waits in a gas station line. Descriptive statistics of this sample are as follow: N= 40, mean= 115sec, std.dev.=11sec, min=90sec, ...
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1answer
28 views

how to simulate type I error and type II error

Suppose $H_0: F_0$ and $H_1: F_1$, I want to simulate (lower bound of) the sum of type I($\alpha$) and type II($\beta$) error based on n observations. (Q:Am I posing the problem in the well-defined ...
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18 views

Restrictions implied by the null hypothesis

Suppose, we are testing $H_0:\theta\in\Theta_0$ against $H_a:\theta\in\Theta_1$, $\Theta_0\cap\Theta_1=\emptyset$ and $\Theta_0\cup\Theta_1=\Theta$, the whole parameter space. I have seen two ...
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58 views

t-statistic vs two-sample t-tests

When and in which context is the t-statistic used? $ t = \frac{\hat{\beta} - \beta_0}{se(\hat{\beta})} $ where $\beta_0$ is a non-random, known constant, which defines the null-hypothesis in the ...
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2answers
68 views

Constructing alternate hypothesis: How to determine if Ha > H0 or Ha < H0

In Chapter 8, Test of Hypotheses based on a Single Sample, in Devore's Probability & Statistics for Engineering and Sciences, he states that the null hypothesis, $H_{0}$, is the a priori claim ...
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1answer
24 views

How to estimate relative risk for a small group which has 0 members with the outcome?

I have a contingency table that looks like this: ...
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4 views

How to asses significant differences in between participant pretest posttest design?

So, the groups would be control group and experiment group. The scale used is ratio. Both will be given pretest and posttest. So, how should I assess the differences between control group and ...
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2answers
29 views

How to show that the condition of one hand predicts the condition of the other hand

I have this kind of data: subject hand condition s01 left 1 s01 right 0 s02 left 2 s02 right 2 .. .. .. ...
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1answer
12 views

Help - what is the correct test? [closed]

im a novice at this and really need some help. I am trying to compare a before and after set of data on 4 different subjects scores. For example: Car scores (3 different scores) pre-work: Car 1: 36, ...
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8 views

Two-way ANOVA, not quite right

All my data in independent and a random sample from a population. I have collected data and have one dependent variable and 2 different independent variables: Dependent = Length Independent = ...
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42 views

How to check if a sample is representative or not biased?

We are studying the difference in behavior between genders on an online community. We are only interested on those users who participate in the site and whose gender could be easily inferred by other ...
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3answers
53 views

Highly significant Pearson's chi-squared test (goodness of fit) when observed & expected are very close

I have two arrays that I would like to do a Pearson's chi-squared test (goodness of fit). I want to test whether or not there is a significant difference between the expected and observed results. ...
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92 views

One-sided significance test for correlation

Let's say you have data from two random variables $X$ and $Y$, and the two random variables are highly correlated (ex: $r=.97$). The p-value, which is testing the null hypothesis that there is no ...
3
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1answer
19 views

What is a paired observation or paired variable?

The question kind of asks itself, can anyone explain what a paired observation or paired variable is in basic terms? My data consist of the number of words learnt in a week for 19 different ...
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42 views

How I can interpret mean, and standard deviation

have a sample of 30 data for daily energy consuming of a person. I found the "Mean" and "Std.Dev." of my samples as follow' Mean = 150 Std. Dev.= 30 I want to prove that he/she has a stable energy ...
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0answers
26 views

Testing significant difference of correlation matrices

I'm interested in exploring whether responses to a series of attitudinal questions differ across various countries. I could check significant difference in mean scores but am more interested in the ...
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1answer
21 views

Does rejection of null hypothesis ($p < \alpha$) for one representative sample imply rejection in a different sample?

I am new to hypothesis testing so forgive me if this has already been asked. Suppose that I've already decided on a null hypothesis with a significance level $\alpha = 0.05$, then obtained my ...
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3answers
105 views

Testing for autocorrelation: Ljung-Box versus Breusch-Godfrey

I am used to seeing Ljung-Box test used quite frequently for testing autocorrelation in raw data or in model residuals. I had nearly forgotten that there is another test for autocorrelation, namely, ...
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8 views

Which hypothesis test to use to test significance of trend line on time series whose points are computed as average measures?

I would like to test the significance of a trendline visible in my data set, which consist in 17 successive points (i.e. my data set is a time series of length 17, considering 17 years). However, each ...
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13 views

What exactly is a proportionality test?

I have heard and read informally about proportionality tests in the context of NHST, but I still don't understand what they are and what they measure. I couldn't find examples or a definition on ...
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21 views

Eliminating a nuisance parameter in likelihood ratio test

I am having an argument with a co-author about how to eliminate a nuisance parameter in a simple likelihood ratio test and am hoping that the community helps us settle it. Our data $\mathbf{x}$ can ...
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28 views

Comparing two algorithms by time series analysis

I have two algorithms. There is one vector of accuracy measurements for each algorithm. Each accuracy result in a vector corresponds to a moving average over a sliding time window and the vectors are ...