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> Finally, I used LibreOffice to tabulate and graph the data, and perform t-tests. T-tests are simple statistical tests used to determine the probability that a
by gwern 9y ago
> Finally, I used LibreOffice to tabulate and graph the data, and perform t-tests. T-tests are simple statistical tests used to determine the probability that a null hypothesis (H0) is correct. If it is less than 5% probable that the null hypothesis is correct given our data, we will reject the null hypothesis and consider our alternate hypothesis (HA) to be correct.
Obligatory stats nerd: that's not what a p-value means, that reverses it.
- xapata 9y agoReverse isn't the right word here, either. Better to restate the definition: the p-value is the probability of observing the data (as represented by its aggregate statistics), under the condition of the null hypothesis.
- gwern 9y agoI say 'reverse' because that's what it is formally: confusing P(data|null) with P(null|data). It reverses the conditional probability.
- xapata 9y agoReversing the arguments of the conditional probability, yes, but just saying "it's the reverse" is a bit ambiguous. > If it is less than 5% probable that the null hypothesis is correct given our data, we will reject the null hypothesis and consider our alternate hypothesis (HA) to be correct. You could be reversing the 5% to 95%, could be reversing null hypothesis to alternate hypothesis, could be reversing reject to accept, etc. Too many moving parts. P-values are so often misinterpreted, it's best to err on the side of specificity.
- btilly 9y agoMy biased opinion is that the only reason why p-values are popular is that it is a concrete question whose answer can be confused with the impossible question that we really want an answer to. If you object to the confusion, you've just taken away the main reason why it is popular.