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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How to analyze an inflection point in univariate time series?

I have a univariate time series with 36 data points (monthly data for 3 years). The general trend of this time series is relatively steep decline, but for the most recent one year, it is almost flat ...
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29 views

Resources to understand why dependence is a problem [duplicate]

For many statistical procedures, it seems the observations must be independent. For example the observations within each group in a two-sample t-test must be independent for the standard error/P-value ...
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Concept learning

Assume you are considering an instance space of 6 binary and 1 nominal (with 3 possible values, like Rainy/Sunny/Snowy) attributes. What is the total size of this instance space X with these 7 ...
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15 views

How many hypotheses are needed when researching one category with multiple likert-scale question

I am currently researching two groups on their willingness with 5 questions on a 7-point Likert-scale. My hypotheses are: $H_0$: There is no difference in willingness between the two groups. $H_1$: ...
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74 views

Does the birth date of professional boxers matter? Prove/disprove what an astrologer might predict

As a followup to my question about the birth month of boxers, I am posing the fundamental question along with my hypothesis (testing if there is any truth to a conclusion an astrologer might make): ...
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42 views

Has the free kick spray in soccer an effect? Binomial Testing

In Germany a referee supported the use of the free kick spray introduced on the World Cup 2014. He reported some statistics. His data supported the assumption using the spray leads to more goals after ...
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1answer
27 views

A reference for Pearson's chi-squared testing

I am wondering if there is a reference for the Pearson's chi-squared test suitable for technically-sophisticated audience that simply presents when the test (in its various forms) is appropriate and ...
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2answers
121 views

Statistical significance of birth month of professional boxers

I looked at the birth dates of the top 100 ranked professional boxers of all time (67 of them to be exact). 40% of them were born during certain 3 month-long time periods. If birth date of boxers ...
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7 views

How to test composite hypothesis for the linear regression model

I want to test $H_0:\beta_1>0,\beta_2=\beta_3=0$ in the model $Y = \beta_1x_1 +\beta_2x_2 + \beta_3x_3+\epsilon$. How can I do this?
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what are the assumptions of permutation test?

It's often stated that permutation tests have no assumptions, however this is certainly not true. For example if my samples are somehow correlated, I can imagine that permuting their labels would not ...
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22 views

Using sample standard deviation to estimate the standard error

In single-sample hypothesis testing, we can collect a sample and test whether the mean of this sample might have been drawn from the same population as some hypothesised mean. We use the standard ...
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20 views

Using the Hotelling package in R

I have two samples of data in $\mathbb{R}^2$, assumed drawn from a gaussian distribution, and I would like to test whether the two samples have the same mean. I know that the right test to do this is ...
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14 views

Is there a non-parametric repeated measures test for replicated block data?

Following on from an earlier question, I've got another question about comparing machine learning classifiers on various datasets. From the response to that question, and also to this paper I ...
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How can I calculate the significance of an acquisition test campaign on Facebook by using chi-squared test?

Should I use number of installs and spending or should I use impression and install numbers in Chi-Squared Test (Evan's Awesome A/B Tools)? Here is the link of the ...
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1answer
12 views

Verify accuracy of asymptotic variance of estimator

The asymptotic variance of a maximum likelihood estimator can be obtained from the inverse of the Hessian of the log-likelihood function at the MLE, and the variance of derived quantities can be ...
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1answer
31 views

Hypothesis testing of two standard mortality ratios

Probably this is an easy question, but I don’t seem to find an answer. The standard mortality ratio (SMR) is defined as “the ratio of actual number of deaths in the group under study to the expected ...
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26 views

Denominator term in Chi-Square-Test for association in a contingency table

The general formula for the Chi Square Test for association in a contingency table with $I$ rows and $J$ columns, and cell counts $n_{ij}$ is $$ \chi^2 = \sum_{i=1}^I \sum_{j=1}^J \frac{(n_{ij} - ...
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39 views

Paired samples or independent sample hypothesis test for two time periods

I want to know if employees in an organization are surveyed in 2013 and again in 2014 if the samples from the two time periods are considered related and dependent or independent if they are asked the ...
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0answers
30 views

How can MANOVA report a significant difference when none of the univariate ANOVAs reaches significance?

I would just like to ask if it is normal for the values from my multivariate tests to be significant but for the values from my univariate tests of between-subjects effects table to be insignificant. ...
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50 views

How to calculate p-value using an algorithm on R assuming that distribution is unknown

For a given sample x, where x is distributed with a normal distribution mean known but variance unknown. I am testing the hypothesis that variance is equal to one or greater than 1. The question is to ...
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30 views

Appropriate Statistical test for Analysis [duplicate]

I have built and tested a computer application, which involved two participant groups (Group-A with existing knowledge of databases and Group-B without knowledge of databases). I was required to ...
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2answers
99 views

Test predictions of football scores against a null model of “no predictive skill”

So, I am trying to prove that I can predict football scores better than randomly assigning win,draw or loss. I have predicted 140 scores, I have succeeded at 67. My null hypothesis is that ...
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37 views

Can confidence interval from hypothesis test inversion ever contain observed difference if that difference is significant?

My question concerns the method for constructing a confidence interval for a difference in means based on a randomization test (that can be found here , check under 'Confidence interval based on the ...
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40 views

If I have to run 500 statistical tests, should I consider each case separately or find the “fittest” one technique?

Suppose I have to run 500 tests. For example, compare two groups with respect to 500 variables. If for a given variable the two samples are normally distributed, I could do a Student's independent two ...
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31 views

Suppose a random sample of size n=2 is generated from a $N(\mu, \sigma^2)$ population. Test the following hypothesis

This is a homework problem that I figured having someone explain and solve would be helpful. Null hypothesis $H_0:\mu =4$, $H_1:\mu \neq 4$. The sample is drawn from ${[x_1, x_2]}={[5,11]}$. Can $H_0$ ...
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How to test difference between standardized difference between means

On a data set I inherited, I calculated the standardized difference between the means of 2 groups, d, for each of 5 variables. All the data was collected from same set of about 175 people, with 35 in ...
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Determining statistical significance in difference between two CRF models

I have trained two Conditional Random Field (CRF) models Ma and Mb in CRF++, the first using a simple set of features, the ...
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69 views

How do I know if my data is meaningful?

I am a 17 year old conducting a very scientific experiment into the best method for pulling Christmas crackers in order to get the highest chance of winning the prize. I have 1000 crackers and a team ...
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105 views

Paired t-test when each data point was repeatedly measured different number of times?

I have an existing data set that comes from the same group of people before and after they received a treatment. The data set comes from when participants tested their blood sugar values over a 30 ...
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8 views

rejection region for correlated bivariate normal

Suppose $ \left( \begin{array}{ccc} \ Z_1 \\ Z_2 \end{array} \right)$ follows a Bivariate standard normal with covariance $ \rho $ I am trying to solve for c as a function of $\alpha$ such that: $ ...
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28 views

How can I write the t-statistic in cases where I have three populations and linear relationship between the three?

I sample height measurements from people from three populations, which I call P1, P2, and P3. My null hypothesis that the average height in group P1 equals 2/3 times the group P2 average plus 1/3 ...
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14 views

Jackknife for Hypothesis Testing

I have a question concerning the Jackknife resampling technique. I read that the Jackknife give better critical value than the bootstrap technique. However, it is not much used for nonparametric ...
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Test equality of binomial variances across four groups

I have four 100x1 vectors of binary outcomes of a particular experiment. I want to test for equality in variance across all of the four different treatment groups. At the moment I have used the ...
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70 views

Determine distribution of test statistic

I have a set of normally distributed parameters, $\hat{b}_{i}$, with different but known variances $\sigma_{i}^2$, that is $\hat{b}_{i}\sim N(b_{i},\sigma_i^2)$ where the $\hat{}$ indicates a ...
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Test whether effect in one model is significantly higher than effect in other model

I have two models: one predicting the sales for a cheap product and another predicting the sales of a more expensive product (both of the same company). Let us say that both models look like this: ...
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1answer
34 views

Is this a right way to use paired t-test

Problem Description I want to enhance a photo and I have 3 software to do that, out of which 2 are my own. I show users 2 photos and ask them to choose a better one. Now, I compare software 1 vs. 2, ...
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Appropriate Test of Significance for Eye Tracking Data

Hello my clever friends, I conducted an eye-tracking study and now I'm in statistical hot water. Given the characteristics of the data, I am not sure which test of significance to apply to answer the ...
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16 views

Designing a hypothesis test

I'm trying to perform what I thought were relatively simple hypothesis tests but all I have managed to do so far is tie myself completely up in knots. So; I have two groups of data which I have ...
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27 views

Hypothesis testing for 2 proportions - for A/B testing

I was trying to understand the statistical tests to use during A/B testing and stumbled upon this documentation of the Amazon A/B testing SDK: ...
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35 views

Running sequential tests as data is collected - practical advice for researchers

I've observed that many experimental labs in my field don't do a power analysis before they start collecting data. In practice, it seems that many researchers collect data and periodically run ...
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38 views

Computing significance of a hypothesis test

I am constructing a hypothesis test on a distribution $Bin(10,p)$, $H_0:p=0.5$ vs $H_1:p=0.55$. I used R programming and I found the significance level when critical value is 8 to be 0.0546875. Why ...
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1answer
44 views

How can I calculate p-values in R?

I am trying to construct a hypothesis test for the variance of two populations. My test statistic is $F=$${\sigma_b^2}$/${\sigma_A^2}$. I want to implement this as a function in R so I computed: ...
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26 views

Application of Neyman Pearson Lemma for discrete cases

How should i use the Neyman Pearson Lemma in the discrete case: $f(x|\theta) = \theta \;\;\; if\; x=0$ $f(x|\theta) = 1-\theta \;\;\; if\; x=1$ Let the null hypothesis be $\theta = 0.1$ and the ...
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2answers
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Testing whether data follows T-Distribution

I am involved in a project where I need to check whether my data follows a T-distribution with N degrees of freedom for a given value of N. I know that Kolmogorov-Smirnoff can be used, but is there ...
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1answer
28 views

Is 0.40 Alpha score (KR-20) acceptable for a true-false test?

I have 10 true-false-Idont know test items. I codded correct responses as 1, incorrect ones and dont knows as 0. I got 0.40 alpha score (or KR-20). Do you think that this score is acceptable for such ...
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128 views

Why is P value interpreted under null hypothesis? [duplicate]

P value is explained very nicely in the link . But still i have not understood Why is P value interpreted under null hypothesis?
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Question for constructing hypothesis test

I am trying to construct a hypothesis test for the $p$ parameter of Bernoulli distribution. My null and alternative hypotheses are: $H_0=p=0.5$ and $H_1=p1=p>0.5$ After some work I obtained a ...
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Testing a claim that a coin is not biased

A coin is tossed 1,000 times, and 570 heads appear. At alpha=.05, test the claim that this is NOT a biased coin. Would the null hypothesis be Ho: p = .50 Ha: p does not = .50 P value would be ...
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Null hypothesis testing of population mean $\mu = \mu_0$ against $\mu < \mu_0$

Suppose that variable $X$ is normally distributed. With sample data done from $X$, we want to do null hypothesis testing $H_0: \mu = \mu_0$, where $\mu_0$ is some constant, and $H_1: \mu < \mu_0$. ...
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23 views

Power of hypoteses test

I am having some problems calculating the power in this exercise. http://snag.gy/LkulQ.jpg This is what i've tried. So since i know that $\alpha$ is 0.05. I thereby know that the upper boundary ...