Biostats Reading #4

The purpose of a t test

To test for differences between two groups

T/F: t test is the most common test in stats

True

Application of a one sample t test

Comparing one group mean to a fixed constant value

Two sample (Independent) t test application

comparing means of two separate independent populations

Paired t test application

Comparing two dependent measurements (ex. before and after) on the same person

What does the t test help define?

If an observed difference in means is due to a treatment effect or random sampling

The t test formula

t = difference in sample means / standard error of difference of sample means

What does a small t value mean?

The data is compatible with the null hypothesis and the samples came from the same population

Large t value

The samples likely came from the different populations and the treatment produced an effect

As sample size increases…

Standard of error decreases

3 certain conditions for validity

1. Normality, data needs to be normally distributed

2. Large sample Rule, larger than 30

3. Independence, two groups must be independent of one another

Null hypothesis

The assertion that there is no difference between the groups (they are drawn from the same population).

p value < 0.5

This means if the treatment had no effect.

Two - tailed

Looks for any difference (higher or lower).

One-tailed

Only looks for a difference in one specific direction.

Degrees of Freedom (v or df)

A value based on sample size used to look up "critical values" in a t table. For a two-sample test with equal groups, v = 2 (n-1).

The F = t² Rule

When comparing exactly two groups, the t test and Analysis of Variance (ANOVA) are mathematically identical

The Multi-Group Error

You cannot use multiple t tests to compare three or more groups

Why can’t you use multiple t tests?

Each test has a 5% error rate. If you do three tests, your total chance of a "false positive" rises to about 15% (3 × 5%)

How to solve multi-group error?

Use ANOVA first to see if any difference exists

What do you use if the data is not normally distributed?

• Wilcoxon signed-rank test: Alternative for the one-sample or paired t test

• Mann-Whitney (Wilcoxon) test: Alternative for the two-sample t test