# Tag Info

5

A chi-square statistic gets bigger the further from expected the entries are. The p-value gets smaller. Very small p-values are saying "If the null hypothesis of equal probabilities were true, something really unlikely just happened" (the usual conclusion is then usually that something less remarkable happened under the alternative that they're not equally ...

4

Actually, when $x_o$ is Poisson, the estimate of (or sometimes the population value of) $\text{Var}(x_o)$ is $x_e$. But that second formula can occur in a variety of contexts. The sum of the squares of $k$ independent standard normal random variables is distributed as $\chi^2_k$. So if you have $x_o$'s that are approximately normal, and $x_e$ is the ...

3

If your interest is in comparing the proportion of requests that attract offers for the two vehicle types, then it's a two sample proportions test. That could indeed be done as a chi-square test. However, it sounds like your alternative is one tailed (you're interested in telling if there's a bias in a particular direction). If that direction of ...

2

When performing hypothesis tests, the p-value is the probability (under the null) of a result as, or more extreme than the test statistic you observed. Here 'more extreme' means 'more consistent with the alternative'. So which parts of the null-distribution of the test statistic you're interested in depends on your alternative. In particular (for an ...

2

Hints: (a) Sometimes the population distribution is of interest in itself - the data-generating mechanism gives insight into the phenomenon behind the data. The gamma distribution is a nice example - read up on it, paying attention to its relation with the exponential distribution. (b) When you're modelling, carrying out hypothesis tests, or whatever, ...

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It's not the observed numbers that need to be anything. It's the expecteds that need to be 'not too small' in order for the chi-square approximation to be reasonable for the usual Pearson chi-square statistic. In any case the rule is very old (over 5 decades) and numerous studies since have argued that it's too conservative. However, in your case, that ...

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