T-tests

Question 1

How to choose

Answer 1

Comparing means

One sample with an expected value -> One sample t-test
Compare means of 2 independent groups -> Independent sample t-test
Is there a difference between 2 paired groups i.e. mean difference ≠ 0 -> Paired sample t-test

Question 2

Independent samples t-test

Answer 2

Estimate signal/noise ratio, t.

The difference between the means is the signal that we are interested in.
The variation in each group is the noise.

The t-test does NOT require variances to be approximately equal. Last presentation, see how to present results

Question 3

One sample t-test

Answer 3

Comparing an experimental mean to a known standard or population mean.
Large t, more confidence in difference between groups
TCritical in table, normal distribution.

If t > tcritical then there is ≤ 5% probability that the sample mean and the expected value are the same
i.e. we reject H0 and accept H1 as we have evidence that there is a difference
between the sample mean and the expected value

If t < tcritical then there is > 5% probability that the sample mean and the expected value are the same
i.e. we accept H0 and reject H1 as we have no evidence that there is a difference between the sample mean and the expected value

Question 4

Paired sample

Answer 4

When we can’t use independent t test. Hypothesis, test statistic, probability of H0 or H1 according to significance level: 5%, confident limits, presenting result in a table.