CHAPTER 2 Overcoming Mathophobia: Reading and Understanding Mathematical Expressions 25

In doing so, it also provides the “cookbook” instructions for calculating the result,

which in this case is the SEM for any values of SD and N.

The book also contains another type of equation that appears in algebra, asserting

that the terms on the left side of the equation are equal to the terms on the right.

For example, the equation x

x

2

3 asserts that x is a number that, when added

to 2, produces a number that’s 3 times as large as the original x. Algebra teaches

you how to solve this expression for x, and it turns out that the answer is x

1.

Counting on Collections of Numbers

A variable can refer to one value or to a collection of values called arrays. Arrays

can come with one or more dimensions.

One-dimensional arrays

A one-dimensional array can be thought of as a list of values. For instance, you

may record a list of fasting glucose values (in milligrams per deciliter, mg/dL)

from five study participants as 86, 110, 95, 125, and 64. You could use the variable

name Gluc to refer to this array containing five numbers, or elements. Using the

term Gluc in a formula refers to the entire five-element array.

You can refer to one particular element of this array (meaning one glucose mea-

surement) in several ways. You can use the index of the array, which is the number

that indicates the position of the element to which you are referring in the array.»

» ^{In a typeset formula, indices are typically indicated using subscripts. For}

example, Gluc3 refers to the third element in the array (which would be 95 in

our example).»

» ^{In a plain text formula, indices are typically indicated using brackets (such as}

Gluc[3]).

The index can be a variable like I, so Gluc[i] would refer to the ith element of the

array. The term ith means the variable would be allowed to take on any value

between 1 and the maximum number of elements in the array (which in this case

would be 5).

In some programming languages and statistical books and articles, the indices

start at 0 for the first element, 1 for the second element, and so on, which can be

confusing. In this book, all arrays are indexed starting at 1.