How do you assess the statistical significance of an insight?

How do you assess the statistical significance of an insight?



Statistical significance can be accessed using hypothesis testing:
- Stating a null hypothesis which is usually the opposite of what we wish to test (classifiers A and B perform equivalently, Treatment A is equal of treatment B)
- Then, we choose a suitable statistical test and statistics used to reject the null hypothesis
- Also, we choose a critical region for the statistics to lie in that is extreme enough for the null hypothesis to be rejected (p-value)
- We calculate the observed test statistics from the data and check whether it lies in the critical region

Common tests:
- One sample Z test
- Two-sample Z test
- One sample t-test
- paired t-test
- Two sample pooled equal variances t-test
- Two sample unpooled unequal variances t-test and unequal sample sizes (Welch's t-test)
- Chi-squared test for variances
- Chi-squared test for goodness of fit
- Anova (for instance: are the two regression models equals? F-test)
- Regression F-test (i.e: is at least one of the predictor useful in predicting the response?)

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