1. How does the Unpaired t-Test work?
(measurements in each treatment are independent of each other)
Signal
Signal
Noise
Ratio
Noise
The Standard Error for the t-Test (SE) comes from the Variance within the two data sets.

2. Noise
Signal

3. When measurements in each Treatment are not Independent:
Signal
When measurements in each Treatment are not Independent:
Noise
(SE)
Paired t-Test Formula

4. Tell a neighbor:
What is the null statistical hypothesis (H0) for the t-Test?
H0: u1 = u2
In other words, the means of the populations from which the samples were taken are equal.
But, can we infer from the sample that the population means are not equal?

5. H0: u1 = u2 Our ultimate statistical question is:
What is the probability of generating, by accident, an observed t statistic (and a signal to noise ratio) as large as or larger than our tobs if the Null Statistical Hypothesis is true?

6. Signal
Noise
Ratio

7. Critical t-values Table Df = (n-1) + (n-1) = 18
Statistics Guide, p.19
Critical t-values Table
Df = (n-1) + (n-1) = 18
tobs (3.04) > tcrit (2.10)
The probability (p) of generating a tobs of 3.04 or greater if H0 is true is < 0.05.
The Iron Cay mean relative hindlimb length is significantly larger than the Experiment Island mean.
We can therefore infer that the populations from which the samples were taken are different.

8. Critical t-values Table Df = (n-1) + (n-1) = 18
Statistics Guide, p.19
Critical t-values Table
Df = (n-1) + (n-1) = 18
tobs (3.04) > tcrit (2.10)
Sample means with 95% confidence intervals.
The probability (p) of generating a tobs of 3.04 or greater if H0 is true is < 0.05.
The Iron Cay mean relative hindlimb length is significantly larger than the Experiment Island mean.
We can therefore infer that the populations from which the samples were taken are different.