confidence interval insight.
how did you deduce from the ci that the level of magnesium is higher?
The key is to look at how we calculate the difference.
First, take a look at the difference column, it calculates the difference between before and after with formula:
difference = after - before.
Think about it, what if the difference is positive? what if it's negative? what does it mean?
It means if the difference is positive or we can say "after > before" -> level of magnesium after is higher than level of magnesium before.
Then, we want to know, on average, level of magnesium is higher or lower?
we calculate the mean -> on the video, it's 0.33,right? what does it mean?
It means the level of magnesium after is higher than level of magnesium before with the increase of level of magnesium, on average, 0.33.
But, our sample is too small isn't it?
So, we need to have something more reliable, which is, as this course suggested, confidence intervals.
Then, we calculate the confidence intervals.
We want to know, On average, where the difference will likely to fall into?
Apparently, with 95% of confidence, we can state that the level of magnesium change (differ from "before") around 0,01 - 0.65.
We also can flip it around.
if we flip the formula of difference to be:
difference = before - after.
If the difference is positive, then we can say the level of magnesium before is higher than after.
If the confidence intervals fall between positive numbers in this case, then it means our pill isn't effective and caused the opposite effect because the level of magnesium before is higher than after consumption.