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It can mean multiple things.

X is a normal distribution N(mean, variance)

X has probability N(10, 5) means X is normal distribution with mean = 10

and variance = 5 and standard deviation = sqrt(5)

also, N can mean the number of samples

except in cases where both “n” and “N” are used

Then:

in cases where both small “n” and capital “N” are used

n means the number of samples and

N means the size of the populations

this is used in the Standard error for a proportion equation with a

sample size correction

as follows

SE for a proportion = sqrt[ p ( 1 – p ) / n ] sqrt[ ( N – n ) / ( N – 1 ) ]

where p = proportion (average proportion, often)

n = number of samples

N = number of values in the whole population

A lowercase n denotes the number of people in a sample. An uppercase N represents the number of people in a given population.

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I’m assuming you mean “n”, not “N”.

- n = sample size, number of data points. Also, this can mean the number of trials in a probability experiment

Assuming you referring sample size. Sample size helps to maximize the chance of detecting the statistical difference of a parameter( I.e mean difference) when it actually exists. Optimal sample size is a crucial step in statistics and it must be chosen before study.

Hope this helps.

See other answer for some common examples, but generally any symbol can mean anything you define it to mean. A properly written report/article/book/lecture note set etc will define a symbol at the time of its use (or make it clear from the context what it is being used for as in, for example, shorthand for the normal distribution), and then use that symbol definition consistently for the remainder of the work.

It is important to note that although it may appear that some symbols have set, unique definitions in Statistics (eg using the Greek symbol mu to represent a population mean), this is not actually the case and is more just a matter of people conforming to common useages. You can use any symbol to represent anything, as long as it is clearly defined so the reader understands.

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In sampling theory the letter ‘n’ denotes the sample size.

When it comes to probability ‘n’ is the total number of outcomes in the sample space.

“n” represents your usable sample size – that is number of subjects (or scores or whatever) that were considered for the statistic that follows. You can usually determine the n by adding 1 to the degrees of freedom in an equation.

It means factorial of 3. ! This symbol is factorial function.

3! = 3 x 2 x 1 = 6

n! = n(n-1)(n-2)…..3,2,1

Where n is a positive integer.

2!= 1×2 = 2

3! = 3 x 2 x1= 6

Uppercase N represents the population size and lowercase n is for samples.

Don’t read the rest of this, unless you are curious about how sample size is important in a variety of ways to researchers. . . It isn’t necessary information, but it may give some context. Here goes!

Note that for inference, when calculating say, variance we use n-1 as such statistics have been shown to best be calculated in this manner, in order to result in a non-biased estimate (when the sample is small) of the statistic (variance, for example).

The sample size is very important as it influences the power of being able to estimate various statistics quite well or quite badly (depending on the size of the effect such as difference between means). If the sample size is bigger, then (keeping in mind the principle of diminishing returns) it estimates population statistics better than otherwise.

A small sample size coupled with a small effect size (the REAL difference between means is tiny, say) can actually make it so you cannot detect the difference using statistical inference. This is one reason for doing a meta-analysis, in which you look back at previous research and try to get an idea as to the size of the effect (say the difference between means or a correlation size) and use this with your sample size to indicate the power, or probability that your study could detect the effect size. Sometimes your budget is such that you can’t have a sufficiently large sample to undertake the study you want to do!

So sample size is super important! Great question!

Homocedasticity means residuals (difference between model value and sample case) with Normal Distribution and no change along the range (Upper limit value – Lower limit value).

Pictures explain the difference between homocedasticity and heterocedasticiy (2 examples). You can see clearly the tendency of residuals.

Case 1: standard deviation no change but mean along independent variable change: Right side you can see the residual values negatives at ends and positive in the middle.

Case 2: residuals mean no change, standard deviation change along independent variable change.

Means residuals are due to chance, random. It’s called homocedasticity.

Otherwise, if there’s a tendency, it’s called heterocedasticity.

Example, consider lifetime of car tires (dependent variable) versus pressure (independent variable).

As over pressure reduce contact to road concentrating wear in the middle of the band and underpressures in the borders, The regression isn’t linear.

Heterocedasticity or non-random error: Residuals are positive or negative depending the value of independent variable.

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