some minor typos and suggestions

I hope this is helpful!

Under 1.7.1.: „Both WHAT EXACTLY? remain possible, and we do not quantify the probability of either possible reality” -> from an old comment? (I think it is understandable what “both” refers to.)

Under 1.8.2. Q3: “In the plot, the red areas visualize Type 1 errors. The blue area visualizes the Type 2 error rate (which we will discuss below)…”  may come from copy paste from an earlier section?

First code Code in section 2.4


par(bg = backgroundcolor) PROBLEM AS BEFORE
 ```{r}
   backgroundcolor not specified. Maybe drop altogether?

Under 3. “In the Neyman-Pearson approach, likelihoods play an important role through the Neyman-Pearson lemma, which shows that the likelihood ratio test **it** -> **is** the most powerful test of H0 against H1, and is useful in determining the critical value that is used to reject a hypothesis”

Under 3. “The binomial probability of observing x successes in n studies is…” -> wouldn’t it be “k successes”?

Under 3: “The grey curve, exactly underneath the 12 out of 20 heads curve, is calculated by multiplying the likelihood curves: L(p_combined) = L(p = 0.8) * L(p = 0.4).”
Last part might be within $$ $$  or L(p_{combined})?

Under 3: “We can subjectively interpret this likelihood ratio, which tells us an unfair coin that our observed data is 6.87 times more likely under the hypothesis that this coin will turn up heads 80% of the time, than under the hypothesis that this is a fair coin”.
Maybe:
We can subjectively interpret this likelihood ratio, which tells us that our observed data is 6.87 times more likely under the hypothesis that this coin is unfair and will turn up heads 80% of the time, than under the hypothesis that this is a fair coin.

Under 4.1 “ In Bayesian statistics, the probability of data under a specified model (D|P(H_0) is a number that expressed what is sometimes referred to as the absolute evidence, and more formally referred to as a marginal likelihood.” -> P(D|H_0) ?

Thank you for the great content! As a fresh PhD student, this book is pure gold!

Lakens / statistical_inferences

some minor typos and suggestions #59