A brief guide to some commonly used statistical symbols:

Symbols for the mean:

(an upper case X with a line above it) or (lower case x with a line above it) denote "the mean of the X scores". Thus if the X scores are 2, 3 and 4, then X = (2+3+4)/3 = 3.0. If you have two sets of scores, one lot would be the X scores and the others would be the Y scores. The formula for the mean is the same, whether it is the population mean, the sample mean, or the sample mean used as an estimate of the population mean.

m (the greek letter "mu") is used to denote the population mean. The population mean is worked out in exactly the same way as the sample mean: add all of the scores together, and divide the result by the total number of scores.

In journal articles, the mean is usually represented by M, and the median by Mdn.

Standard deviation symbols:

s (the greek lower-case letter,"sigma") is usually used for the population standard deviation.

s is used to denote the standard deviation of a sample of scores.

The formula for the standard deviation differs slightly, depending on whether it is the population s.d., the sample s.d., or the sample mean used as an estimate of the population s.d..

On Casio calculators, the "sⁿ " button gives you the version of the standard deviation that you would use if you merely wanted to describe your sample OR if you were actually able to get a score from every single individual within a population (which you are almost never able to do in psychology). The "s^n-1" button gives you the version of the standard deviation that you would use if you wanted to use your sample's characteristics as an estimate of those of the entire population (which you often want to do in psychology, as we're normallly interested in trying to extrapolate from our sample to the entire population from which that sample came).

The "s" version of the standard deviation usually gives a larger value for the standard deviation than the "s^n-1" version, because the standard deviation of a sample tends to underestimate the standard deviation of the population from which the sample originated.

In journal articles, "s" or "s.d." are often used as abbreviations for the standard deviation; unfortunately, it's not always clear which version of the formula the authors used. Fortunately, in practice it generally doesn't make a huge difference to the value of the s.d.

Quantity symbols:

X: used to represent the raw scores in a group. Thus if you have five scores, NX = 5, and åX means ("add together all the X scores").

N or n means the number of scores or individuals in a group. Thus if you have 6 scores, n = 6 and n-1 = 5. "NX" means "the number of scores in group X".

< "less than": when used between two things, it means that the one on the left is smaller than the one on the right. NOT to be confused with ">", meaning "more than".

Thus "X < 10" means that whatever X is, it's smaller than 10.

> "more than": when used between two things, it means that the one on the left is bigger than the one on the right. NOT to be confused with ">", meaning "more than".

Thus "X > 10" means that whatever X is, it's bigger than 10.

å (the greek upper-case letter, "sigma") means "sum of". Add up everything which immediately follows this symbol.

Thus "åX" means "add together all of the X values". If the X values are 2, 3 and 4 then åX = 9.

NB: åX-1 is NOT the same as å(X-1). åX-1 means "find the sum of the X scores, and then subtract 1 from that total". å(X-1) means "take each X score; subtract 1 from it; and then add up all of these scores".

Thus if X = 2, 3 and 4, then åX-1 = 9-1 = 8 but å(X-1) = 6.

The order in which you perform arithmetic:

BODMAS is a handy mnemonic to help you to remember the order in which you perform mathematical operations. Do things in Brackets first; then Divisions; then Multiplications; then Additions; and finally, Subtractions.

Thus the order in which you work out the following equation is as follows:

(1+2)/3-6*2

(a) Brackets first - so add together 1+2 to get 3. Replace the bracketed bit with 3.

(b) 3/3-6*2

Division next - so 3/3 = 1.

(c) 1-6*2

Multiplication next - so 6*2 = 12.

(d) 1-12

Finally, do the subtraction that remains. The answer is -11.

Negative and positive numbers:

A positive number multiplied by a positive number is always positive.

2 * 2 = 4.

A negative number multiplied by a negative number is always positive.

-2 * -2 = 4.

A negative number multiplied by a positive number is always negative.

-2 * 2 = -4.

Decimal places:

Normally with statistics in psychology, 2 decimal places is sufficient for the answer to a calculation: e.g. round up 2.35555 to 2.36, round down 2.3114 to 2.31.

However, to avoid rounding errors having a cumulative effect during the process of performing calculations, while you are carrying them out it's best not to round up or down too much: either leave the numbers as accurate as the calculator displays them, or round them to three or four significant digits (e.g. 2.311 or 2.3114).

Multiplication symbols:

* is used for multiplication rather than x, because x would get confused with X (meaning a raw score). Sometimes, just to confuse you further, the multiplication symbol is omitted altogether, as in "åXY", which means "first multiply each X score by its corresponding Y score; then add together the results of all of these multiplications". Thus if X = 1, 2 and 3, and Y = 2, 3 and 4, you would calculate each value for XY : 1*2 , 2*3 and 3*4. Then you would add the results of these calculations together: 2+6+12 = 20. Thus "åXY" = 20 in this case.