Confidence notes

Log e as natural logarithm: e = 2.718 - The natural log is the inverse of e (e means opposite). The Latin name is logarithmus naturali, hence, ln. In brief e is the constant proportional to the growth rate of the curve.



Confidence Interval: Importantly, there is a trade-off between precision (interval length) and reliability (coverage).

Source: Dept. of Continuing Education: Statistics for Health Researchers Course, Oxford Univ.



Null Hypothesis

The p-value is effectively the likelihood of making a type I error and we typically accept the null hypothesis if the p-value is above the threshold of 0.05, which corresponds to a test with a significance level of 5%.

Statistics course, Oxford Univ.

Sample quantiles

In general the kth centile is the point below which k% of the values lie. In other words, we are looking for a subset of the values.

Think of the dividing point as the 'neutral zone', above which and below which the subest of interest lie. that is why you don't find an 'equal' anywhere.

Let's try something pictorial, considering deciles (division into 10 equal groups):

See the 10 dots below. They enclose only 9 spaces, 'space' being the quantity of interest here.

. . . . . . . . . .

So to have 10 spaces you need 11 dots. So now you have 10 spaces in 10 equally marked divisions. The star-dot represnts the boundary (I used star as I couldn't use another colour), above and below which you have, in this case, 50% of the spaces (and in fact 50% of the dots if you exclude the boundary).

. . . . . * . . . . .


I hope this helps to make it a little clearer why there isn't an 'equal'.

Marialena