Statistical Analysis for Education and Psychology Researchers

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Appendix A2 Statistical Notation

Statistics makes use of algebraic notation to express mathematical operations.

1 Notation for variables and values
Generally a variable is denoted with a particular upper case Latin letter, for
example, X. An individual value of that variable is represented by a lower case
letter and a subscript, such as xi. Here i is the subscript which denotes the ith
value for the variable X.
For example, look at this set of 5 anxiety scores:

5 4 7 9 8

If you wish to refer to a single score from this set without specifying which one,
you could can refer to xi, where i can take on any value between 1 and 5. The first
score (5) would be referred to as x 1 , the second x 2 , and so on. A general form of
notation for this example would be (xi; I=1, 2,...n). This means in the set of n
values of the variable X, a single value xi may extend over a range of values from
1 to n.
2 Summation
In statistics we are often required to sum a set of values. The upper case Greek
letter sigma (Σ), means add up or sum what follows. So, Σxi is read sum over all
xi. To be perfectly correct, the notation for summing all n values of xi (from
i=1,2,...n) is:

Appendix 348