Unit 11: Hypothesis Tests

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Connections

Exploratory Data Analysis
  • Like confidence intervals, hypothesis tests help students use data to just answer that simple investigative question that they may have developed about a particular population. This should reference back to the first unit of the course.

  • In order to evaluate whether assumptions hold, need to look at shape, center, spread of sample distribution.
Inference
  • Like confidence intervals, hypothesis tests help us make inference about a population using just a single sample. Just as the previous units discussed, it is important to reiterate that we just need one sample to make inference.

  • Again like confidence intervals, hypothesis tests rely on sampling distributions and the Central Limit Theorem (if assumptions are met), so it is important to show students how these concepts all relate.

  • For assumptions to be met, we need to follow good data collection practices to obtain a random sample.

  • If the Central Limit Theorem applies, students will need to recall normal models and z-scores. Remember: their sample may not be normal, but the sampling distribution of their sample mean or proportion is normal under Central Limit Theorem.

  • It is very important to draw students back to informal inference done earlier using simulations; show them the same example using both methods so they can see that both achieve same goal; one is just a shortcut/approximation that might be faster to do.

  • If students can understand the intuition behind simulation-based inference, then formal hypothesis testing is just a shortcut we can use when assumptions are met that does the same thing with less work.

  • p-values are just how likely we are to get the observed statistic if we assume a certain model/hypothesis is true; this is the case whether we use the normal model (and look at a shaded region beyond the observed value) or use a model built from many simulations (and count the observations beyond the observed value).
Models
  • In this course, we assume sampling distribution follows a model with some hypothesized mean.

  • But no matter what, we assume some “chance” model that is plausible for our estimate.

  • It is plausible that our estimate comes from this model, but how plausible given the mean of that model? If it’s not very plausible, then we should look for a new model.
Probability
  • The p-value is just a conditional probability; given the null hypothesis, what is the probability of getting the observed statistic (or something more extreme)?