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# Questions tagged [z-statistic]

The statistic used in z-test, namely the ratio of a parameter estimate and its estimated standard error.

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### Eta-squared from Kruskal-Wallis in R

Is it possible to calculate Eta-squared from Kruskal-Wallis test results? I know how to do it by hand for the ANOVA or Mann-Whitney using the Z-statistics, but i must use the KW test for my current ...
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### Why does the pivotal quantity $g(X,θ)$ have to be a monotonic function of $θ$ for a fixed $X$?

I'm learning about pivotal quantities, which are functions $g(X,θ)$ of the data $X$ and the parameter $θ$. One property they must satisfy is that $g(X,θ)$ is a monotonic function of $θ$ for a fixed $X$...
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### Standard deviation Vs ٍٍStandard error

I'm little bit confused, when I want to standardize a normal distribution, when to use standard error and when to use standard deviation ?. In statistics we often use samples so, is it always we use ...
53 views

### Using the $Z$-test instead of the binomial test for small $n$ - effect on power and Type I error

Setup Let $M \sim \text{Bin}(p,n)$. Let us then state the following two hypotheses: \begin{align} H_0: p = 0.5 \text{ vs } H_1: p > 0.5 \end{align} To test these hypotheses, I could use the ...
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### how can the probabilities of sampling subset proportions be tested?

Assume we have 10 different jigsaw puzzles. Each puzzle has a different number of pieces, e.g., ...
191 views

### Using z-standardization to account for covariate

I would like to know whether z-standardization is an appropriate way to account for a covariate. Please consider the following dummy example (I am not interested in the interpretation of the result ...