Comparing 2 population means

Question 1

Comparing 2 independent samples

Answer 1

Parametric test (for normal data): t-test

Non-parametric equivalent: Mann-Whitney U-test

Question 1

Comparing 2 non-independent = paired samples

Answer 1

Parametric test (for normal data): Paired t-test (= test for 2 “non-independent” samples)

Non-parametric equivalent : Wilcoxon test for paired samples

Question 2

Why do we do this? What is the aim of the t-test?

Answer 2

AIM: Detect a difference between 2 groups of the same variable:

1.Differences between means.
2. Variances for each group – if all values for each group lie close to the mean (small variance), then we might still detect a difference even if the means of the 2 groups don’t differ that much.

Question 3

Working with probabilities

Answer 3

p = the probability that value from one sample (group) will fall within the central 95% of the other group

The probability that the two groups are the same increases if the means are close to one another

*When the means are far apart: p tends to be small.
*…when the means are closer together, probability of overlap between the two samples increases.
*…the probability that they are the same is LOWER when the SDs are smaller (i.e., less variation within each sample).

see slide 10 lec 10

Question 4

What does p mean for our hypothesis?

Answer 4

So: if p < 0.05 (5%):

Null hypothesis H0:
no difference or relationship
5% chance that there is no difference .

Alternative hypothesis HA: there is a difference or relationship
…95% chance that there is a difference

We say there is a significant difference
when p is less than or = 0.05 (p ≤ 0.05)
So the smaller the p, the more significant the effect

We relate the probabilities to the Null Hypothesis

To determine the probability of a sample from one population falling within the 5% of the other population, we need to compare a calculated t-statistic with the critical value of the t statistic for a distribution of given sample size and degrees of freedom.

https://www.youtube.com/watch?v=-6vDjGR41YM

Question 5

How many tails?

Answer 5

ONe tailed test:
H0 = there is no difference between two groups
HA = the mean of one group is larger or smaller than the mean of the other group (i.e. you predict the direction of the difference between groups)

Two tailed test:
H0 = there is no difference between two groups
HA = the mean of one group is different to the other group (either larger or smaller; but there no previous expectation about one group’s mean being larger or smaller than the other)