Confusion between σ² and s² and other queries

1.  Sometimes for standard deviation the sign used is "σ" while sometimes "s" is used instead. Similarly, for variance they use " σ² " while sometimes they would use " s² ". Is there any difference? If yes how would I know when to use which?

2. What is this chi-square thing, and when exactly do I use it? i am so confused.

3.  Why is it that in some cases, when I am solving via the random variable "Z", i have to append +/0.5 before consulting the probability tables?

Student X

[The above was posted by an engineering undergraduate from Nanyang Technological University (NTU) in a forum earlier. ]

1.  Ok I am not going to deny this slightly ambiguous representation of standard deviation in various notes and books:

σ refers to the population standard deviation; σ² refers to the population variance. This part should be fine.

Now for the confusing part.

These days, junior colleges typically use s² to denote unbiased estimate of population variance, which is slightly different from that of the sample variance. If sample variance is a certain value say A, then JC students are required to state that s² equals n/(n-1) times A, where n is the sample size. Yet back then, I was taught that σ (hat)² represented the unbiased estimate of the population variance, while s² denoted sample variance. (why did you think they call it s? Because s simply stood for sample.)

Since you are in university, I won't want to you to sweat the small details, so just treat s² as sample variance. End of story.

2.  Imagine you have to conduct a certain experiment. Beforehand you have a list of expected(theoretical) results. Then upon conclusion of the experiment you have a corresponding list of measured (actual) results. The Chi Square test is thus employed to investigate the goodness of fit between expected and actual result sets.

3. Are you referring to the usage of continuity correction? This must happen when you are approximating discrete distributions to continuous ones (eg from binomial to normal).

Hope this helps. Peace.

Best Regards,

Mr Koh