CHAPTER 3 Getting Statistical: A Short Review of Basic Statistics 41

statistic is usually calculated as the ratio of a number that measures the size

of the effect (the signal) divided by a number that measures the size of the

random fluctuations (the noise).»

» ^{p value: The probability or likelihood that random fluctuations alone (in the}

absence of any true effect in the population) can produce the effect observed

in your sample (or, at least as large as the effect you observe in your sample).

The p value is the probability of random fluctuations making the test statistic

at least as large as what you calculate from your sample (or, more precisely,

at least as far away from H0 in the direction of HAlt).»

» ^{Type I error: Choosing that H}Alt ^{is correct when in fact, no true effect above}

random fluctuations is present.»

» ^{Alpha (α): The probability of making a Type I error.»}

» ^{Type II error: Choosing that H}0 ^{is correct when in fact there is indeed a true}

effect present that rises above random fluctuations.»

» ^{Beta (β): The probability of making a Type II error.»}

» ^{Power: The same as 1 – β, which is probability of choosing H}Alt ^{as correct}

when in fact there is a true effect above random fluctuations present.

Testing for significance

All the common statistical significance tests, including the Student t test, chi-

square, and ANOVA, work on the same general principle. They compare the size of

the effect seen in your sample against the size of the random fluctuations present

in your sample. We describe individual statistical significance tests in detail

throughout this book. Here, we describe the generic steps that underlie all the

common statistical tests of significance.

1.

Reduce your raw sample data down into a single number called a test

statistic.

Each test statistic has its own formula, but in general, the test statistic repre-

sents the magnitude of the effect you’re looking for relative to the magnitude of

the random noise in your data. For example, the test statistic for the unpaired

Student t test for comparing means between two groups is calculated as a

fraction:

Student t statistic = ^{Mean of Group}

Mean of Group

Standard Error of

1

2

the Difference

The numerator is a measure of the effect, which is the mean difference

between the two groups. And the denominator is a measure of the random