Null Hypothesis Significance Testing I Class 17 , 18 . 05 Jeremy Orloff and Jonathan Bloom 1 Learning Goals

Null Hypothesis Significance Testing II Class 18 , 18 . 05 Jeremy Orloff and Jonathan Bloom

We continue our study of significance tests. In these notes we will introduce two new tests: one-sample t-tests and two-sample t-tests. You should pay careful attention to the fact that every test makes some assumptions about the data – often that is drawn from a normal distribution. You should also notice that all the tests follow the same pattern. It is just the computation of the test statis...

Null Hypothesis Significance Testing I Class 17 , 18 . 05

Frequentist statistics is often applied in the framework of null hypothesis significance testing (NHST). We will look at the Neyman-Pearson paradigm which focuses on one hypothesis called the null hypothesis: for example, that the tested treatment has no effect on the progress of the disease. There are other paradigms for hypothesis testing, but NeymanPearson is the most common. Stated simply, ...

1 Confidence Intervals : Three Views Class 23 , 18 . 05 Jeremy Orloff and Jonathan Bloom

1 2 Confidence intervals based on normal data Class 22 , 18 . 05 Jeremy Orloff and Jonathan Bloom

We will leave to later the explanation of exactly what the 95% confidence level means. For now, we’ll note that taken together the width of the interval and the confidence level provide a measure on the strength of the evidence supporting the hypothesis that the μ is close to our estimate x. You should think of the confidence level of an interval as analogous to the significance level of a NHST...

Confidence Intervals for the Mean of Non-normal Data Class 23, 18.05 Jeremy Orloff and Jonathan Bloom 1 Learning Goals

One common use of confidence intervals is for estimating the proportion θ in a Bernoulli(θ) distribution. For example, suppose we want to use a political poll to estimate the proportion of the population that supports candidate A, or equivalent the probability θ that a random person supports candidate A. In this case we have a simple rule-of-thumb that allows us to quickly compute a confidence ...