22 PART 1 Getting Started with Biostatistics

There can be logarithms to any base, but three bases occur frequently enough to

have their own nicknames:»

» ^{Base-10 logarithms are called common logarithms.»}

» ^{Base-e logarithms are called natural logarithms.»}

» ^{Base-2 logarithms are called binary logarithms.}

The logarithmic function naming is inconsistent among different authors, pub-

lishers, and software writers. Sometimes Log means natural logarithm, and some-

times it means common logarithm. Often Ln is used for natural logarithm, and Log

is used for common logarithm. Names like Log10 and Log2 may also be used to

identify the base.

The most common kind of logarithm used in this book is the natural logarithm, so

in this book we always use Log to indicate natural (base-e) logarithms. When we

want to refer to common logarithms, we use Log10, and when referring to binary

logarithms, we use Log2.

An antilogarithm (usually shortened to antilog) is the inverse of a logarithm. As an

example of an antilog, if y is the log of x, then x is the antilog of y. For another

example, the base-10 logarithm of 1,000 is 3, so the base-10 antilog of 3 is 1,000.

Calculating an antilog is exactly the same as raising the base to the power of the

logarithm. That is, the base-10 antilog of 3 is the same as 10 raised to the power

of 3 (which is 10³, or 1,000). Similarly, the natural antilog of any number is e

(2.718) raised to the power of that number. As an example, the natural antilog of

5 is e⁵, or approximately 148.41.

Factorials and absolute values

So far we’ve covered mathematical operators that are written either between the

two numbers, which are the subject of the operation (such as the plus in 5 + 8), or

before the number it operates on if there is only one number (like the minus sign

used as a unary operator described earlier, as in –5°). Next we cover factorials and

absolute values, which are mathematical operators that have a unique format in

typeset expressions.

Factorials

Although a statistical formula may contain an exclamation point, that doesn’t

mean that you should sound excited when you read the formula aloud (although it

may be tempting to do so!). An exclamation mark (!) after a number is shorthand