## Solved – Test if two samples of binomial distributions comply with the same p

Suppose, I have done: \$n_1\$ independent trials with an unknown success rate \$p_1\$ and observed \$k_1\$ successes. \$n_2\$ independent trials with an unknown success rate \$p_2\$ and observed \$k_2\$ successes. If, now \$p_1 = p_2 =: p\$ but still unknown, the probability \$p(k_2)\$ to observe \$k_2\$ for a given \$k_1\$ (or vice versa) is proportional … Read more

## Solved – Aside from Durbin-Watson, what hypothesis tests can produce inconclusive results

The Durbin-Watson test statistic can lie in an inconclusive region, where it is not possible either to reject or fail to reject the null hypothesis (in this case, of zero autocorrelation). What other statistical tests can produce "inconclusive" results? Is there a general explanation (hand-waving is fine) for why this set of tests are unable … Read more

## Solved – Aside from Durbin-Watson, what hypothesis tests can produce inconclusive results

The Durbin-Watson test statistic can lie in an inconclusive region, where it is not possible either to reject or fail to reject the null hypothesis (in this case, of zero autocorrelation). What other statistical tests can produce "inconclusive" results? Is there a general explanation (hand-waving is fine) for why this set of tests are unable … Read more

## Solved – Why is it wrong to stop an A/B test before optimal sample size is reached

I am in charge of presenting the results of A/B tests (run on website variations) at my company. We run the test for a month and then check the p-values at regular intervals until we reach significance (or abandon if significance is not reached after running the test for a long time), something I am … Read more

## Solved – Why is it wrong to stop an A/B test before optimal sample size is reached

I am in charge of presenting the results of A/B tests (run on website variations) at my company. We run the test for a month and then check the p-values at regular intervals until we reach significance (or abandon if significance is not reached after running the test for a long time), something I am … Read more

## Solved – Asymptotic power

I have found the term "asymptotic power of a statistical test" only related to the Kolmogorov-Smirnov test (to be precise: asyptotic power = 1). What does this term acctually mean? In my opinion it should be someting like this: "if the alternative hypothesis is true, than for every significance level alpha there exists a sample … Read more

## Solved – Mahalanobis distance on non-normal data

Mahalanobis distance, when used for classification purposes, typically assumes a multivariate normal distribution, and the distances from the centroid should then follow a \$chi^2\$ distribution (with \$d\$ degrees of freedom equal to the number of dimensions/features). We can calculate the probability that a new data point belongs to the set using its Mahalanobis distance. I … Read more

## Solved – Why does the research findings contradict the hypothesis result

From my research findings/results it was clear that lecturers and students use different web 2.0 applications. But my null hypothesis result is contradicting this one of my null hypotheses is 'there is no significant difference between the web 2.0 application commonly used by students and those used by lecturers'. Please help, I am confused Best … Read more

## Solved – test/technique/method for comparing principal components decompositions between samples

Is there any methodical way to compare the directions, magnitudes, etc of PCA results for different samples drawn from the same population? I'm leaving the nature of the test deliberately vague because I'd like to hear all the various possibilities… e.g. there might be (and I'm speculating here) a test comparing the sizes of the … Read more

## Solved – test/technique/method for comparing principal components decompositions between samples

Is there any methodical way to compare the directions, magnitudes, etc of PCA results for different samples drawn from the same population? I'm leaving the nature of the test deliberately vague because I'd like to hear all the various possibilities… e.g. there might be (and I'm speculating here) a test comparing the sizes of the … Read more