Research Skills 10 : Student's t-test

Question 1

what are steps when studying the difference between two groups of observations?

Answer 1

• We first look at the effect size
• Then we compare the effect size to the variation
• Using raw data
• And s.e.m error bars
• To judge statistical confidence in the result

Question 2

What is a more exact way to judge statistical confidence/ uncertainty ?

Answer 2

• to calculate the 95% confidence interval (C.I.) for the difference between the two groups
• The p-value can sometimes also be useful

Question 3

How do w calculate these?

Answer 3

Open a statistics package on the computer
Type in the data
Request a t-test

Question 4

What is students’ t test?

Answer 4

Commonest test for comparing the mean of two groups of observations

Question 5

When do we use the t test?

Answer 5

Designed for cases where you have small numbers of observations

And you cannot tell the actual distribution of the data

Assumes normal distribution

But robust- gives a reasonable answer even when the data doesn’t exactly fit a normal distribution

Question 6

How does t test work?

Answer 6

It compares effect size with variation

Uses this to calculate a 95% C.I.

And to calculate an NHST p-value

Question 7

T test and Skewed data

What do t test assume?

Answer 7

The t-test mathematically assumes a normal distribution

But it is robust to variations from a normal distribution

And, with small numbers of observations, it is virtually impossible to be sure whether the data does or does not fit a normal distribution

Question 8

When is it safe to use t test

Answer 8

• For large numbers of observations, you are safe to use the t-test
• For small numbers of observations, the t-test may not be accurate
• Although, in most cases the p-value will be raised, you are more likely to get a Type 2 error than a Type 1 error

Question 9

Why is it not useful to use “non - paramric) test instead of the t test for skewed data?

Answer 9

1. Non-parametric tests don’t work well with small numbers of observations (they have low statistical power)
2. They do not provide a 95% C.I.

Question 10

What can you do instead for skewed data?

Answer 10

you can make your data closer to a normal distribution by a mathematical transformation

Question 11

paired data

Answer 11

eg. investigating a human population and a drug effect
each individual is different there fore looking at before and after results in a single individual ignores variation

study the effect and the variability of the effect itself

Question 12

Paired data can also arise in laboratory based experiments

Answer 12

One example
- We perform an experiment on a cell line on three different days

• The values for the controls differ on each day, because of slight differences in the growth state of our starting cells
• If we analyse the treated and control readings for each day as paired data, we can minimise the effect of day to day variation