Not an elaborated answer since we have already one, but a bit more focus on this part of the question: Now I see that p1 is smaller than p2, is there anything I can say regarding which vaccine is ...

I am a bit surprised that this question did not get more traction ... So, I start the discussion and let's see if it moves further. It is clear that the small sample size of your experimental group ...

To answer the first part of your question, i.e. what you are doing wrong. In your example, you are testing the following hypotheses: $H_0: \mu_s \le \mu$ and $H_1: \mu_s > \mu$ where $\mu = 2.366$ ...

I feel it could bring some value to illustrate @Lewian's answer and @Henry's comment for people like me who are more "visual". I will take the example of the same t-test used in the question ...

If I got it right, I think you are struggling with rejecting or not the null hypothesis. I will take a simple example of people's height in cm for a fictious country for which we know the population ...

The sample size formula depends on the test that you want to carry out. The one you mention looks like a Questionnaire/Survey study type. In this formula, there are assumptions on whether the studied ...

I think the sequence of your story is incorrect (the high level picture). From a high level perspective, you start first with a (random) sample from which you would like to draw inferences about a ...

Notation If your notation refers to R, when using * for interaction terms, both the main effect and the interaction are included in the model. In this regards, model 2 and model 3 will be equivalent. ...

It would deserve more than a simple answer... but if you think about it, it actually makes sense! Intuitively, in your first model you try to explain your outcome variable with only one independent ...

Some additional information to help you to move forward with categorical variable... When dealing with categorical variable (which can be enforced using factor() to make sure that R does not treat it ...

Not really an answer since @BruceET provided already a detailed one, but more a comment on: we get the calculated 𝑛=8, which is absurd. As mentioned in @BruceET's answer in bullet (3), the effect ...

I propose to put some visuals/intuition to your question... using an empirical approach (bootstrapping) to make it more concrete, especially in reference to the following: Usually experiments can't ...

Another answer... from an intuitive perspective... The standard deviation is a measurement of the dispersion around the mean. Suppose you have two data sets distributed as below, set 1 is on the left ...

To complement the existing answer with a more visual/intuitive aspect of the sample size formula you mentioned. As you might have read from the Wikipedia page that these formulas actually origin from ...

Following @Nick Cox's answer (and comments - EDIT), some examples in R: tree <- data.frame(c(1,2,3,4,5,6), c(10,13,1,7,13,12), c(15,20,3,16,15,18)) names(tree)<-"TreeID" names(tree)...

I am sharing some notes (certainly too simplistic)... But I agree that some basic notions can, sometimes, be confusing. Random sample The random variables $X_1, ..., X_n$ are called a random sample of ...

Since you know the full population, you are (indeed) in a position where you do not need to make inference. So, you « simply » need to analyse the figures. Using "side-to-side" boxplots can ...

Actually you got it right in the first place: écart-type is standard deviation while variance is the same word in French. Bonne lecture !

If this is the case, then I encourage you to determine the confidence interval of the mean difference (the narrower, the better) which will make your demonstration even stronger. First, I would ...

You are dealing with very small proportions, so detecting an effect requires relevant sample size. For the last age group (80+), the test significant is if $\alpha = 0.05$ but not if $\alpha = 0.01$. ...

Why doesn't the effect of old variables remain the same when including a new variable? Reading your question again, I believe that you are referring to the previous point "the effect of X on Y ...

As you pointed out (and assuming that your random sample comes from a normal distribution), an estimator of the standard error $SE$ is $\sqrt{\frac{S^2}{n}}$. In the same way you see the $\bar{X}$ as ...

To complement the existing answer and since I saw your follow up question in the comments, I believe that it is important to stress that the confidence interval formula you mentioned \$CI = \bar Y \pm ...

Forgive me if it seems too trivial sometimes but I feel there are some confusions... Sample size formula First, it starts with a question that you want to answer: you may want to compare the ...

Your loop covers the different possibilities indeed. However, bootstrapping allows you to do more since it imitates how samples are drawn from the population. For instance, it can simulate the “with ...

In general, when you don't get an answer on this site, it is mainly because people are struggling to understand the question... while you might have a valid point, which, I think, is the case here. ...

There are possibly some challenges with the wording here. Two-sample test and independent samples test actually refer to the same type of tests: they are used to determine whether the difference ...

Based on the information you provided, it seems that you want to compare the means of two populations (continuous data, sample size n=24) and determine whether they differ. Therefore, your hypothesis ...