Data Analysis - Biomedical Informatics in Translational Research - page 181

hypothesis . The null hypothesis is the prediction that there is no difference. For our
particular example, then, the null hypothesis is that there is no difference in BMI for
individuals with diabetes as compared to the rest of the population.
The result of a statistical hypothesis test is a statistic that can be used to calcu-
late the probability or P value of the null hypothesis versus the alternative hypothe-
sis. For example, a P value of .05 says that there is a 5% chance of the null
hypothesis. In a hypothesis test, we define a threshold for significance (such as .05
or .01). If the resulting P value is less than our threshold, then we reject the null
hypothesis in favor of our alternative; otherwise, the null hypothesis stands.
A number of different statistical hypothesis tests are available, each often
with its own variants, so it is critical that we select a test that is appropriate for our
data set. Table 9.1 lists some of the factors to consider in selecting the right tool, and
the following subsections discuss the most frequently used statistical hypothesis
tests.

9.2.2.1 Pearson's Chi-Square Test
Pearson's chi-square test tests whether the observed event frequency is different
from the expected frequency. The test examines a 2 2 contingency table of observed

and expected frequencies of events and derives a P value from the

×

2

χ distribution.

9.2.2.2 Student's t -Test
Two sample test with variants that can be used for paired or unpaired data, with
known or unknown variance. Student's t -test assumes a normal distribution.

9.2.2.3 ANOVA
ANOVA is used for testing two or more groups and assumes a normal population
with equal variance.

9.2.2.4 Wilcoxon Signed-Rank Test
This text is similar to a paired two-sample t -test, with the exception that the distri-
bution need not be normal.

Table 9.1 Factors to Consider When Selecting a Hypothesis Test

Factor Description

Number of groups being tested Many hypothesis tests can only be applied when there

are just two groups being tested.

Paired versus unpaired data In an unpaired test the variables are assumed to be inde-

pendent. If our variables are dependent (for example,
testing the same group twice), we must use a paired test.

Equal or unequal variance Variance is a measure of the spread of values for a given

variable. Some tests require an equal or similar variance.

Population distribution Many tests assume a normal distribution (also called a

Gaussian distribution or bell curve).