The Normal Distribution - How does it keep going if the dist of scores stop at zero?

#1
Hi there,

I'm trying to figure out how the normal distribution works if a distribution of scores is normally distributed, but the scores don't go below zero?

For example, if we are looking at exam scores - even if the scores of the exam are normally distributed, nobody on an exam can get less than a zero on the exam.

The normal distribution is supposed to be asymptotic - it never touches the X-axis. But how can this be in the above case - once you get down to zero, wouldn't the curve just end?

Thanks to anyone who can help clarify this for me.

Thanks,
Frodo
 

rogojel

TS Contributor
#2
Re: The Normal Distribution - How does it keep going if the dist of scores stop at ze

hi,
you need to understand that the normal distribution is a mathematical abstraction never to be seen in real-life. E.g. we say that the heights of people are normally distributed yet no one seriously believes that there are 10 m high people somewhere, with a vanishingly small but non-zero probability as well as people with 10 cm height.

Same with scores: it is a matter of judgment to decide whether the normal model is applicable or not . If the scores are high enough and the spread low enough so that they are in general far enough from zero then the normal model could be acceptable. If the scores are close to zero another, more right skewed, distribution could be a better choice.

regards
 

hlsmith

Omega Contributor
#3
Re: The Normal Distribution - How does it keep going if the dist of scores stop at ze

Scores bound within 0-1, if they are all not centrally located, the beta distribution can be used. The same concept comes up with the binomial distribution landing on the bounds of 0-1, given a series of Bernoulli trials, and making sure the confidence intervals don't go into the unfeasible areas >1 or <0. There are special formulae to address this. But as rogojel stated, you are applying the ~N to your data generating process, where it may seem to be a good fit asymptotically, but may not be the right selection.
 

Dragan

Super Moderator
#4
Re: The Normal Distribution - How does it keep going if the dist of scores stop at ze

Yes, the normal (Gaussian) distribution is a mathematical abstraction - there is no real-world data set that will exactly follow any theoretical statistical distribution.. The interrogative is tantamount to; "Can the height of the Normal Distribution exceed the value of 1."

The answer is, yes, it can...It's when the value of Sigma lies between: 0 < Sigma < 1/(Sqrt[2*Pi]).
 
#6
Re: The Normal Distribution - How does it keep going if the dist of scores stop at ze

Thank you all very much for your help - I truly appreciate you taking the time.

I don't understand everything you have all said, but you have helped me understand that it isn't a literal application of the normal cruve, but that the the normal distribution is a theoretical tool/distribution that is appropriate in certain situations (when we can know or can assume a distribution of scores is relatively normal in shape).

Thanks,
Frodo