Worked example: T-test

Solution

• Null hypothesis: There is no significant difference between the ear lengths of the rabbits in populations A and B
• Sample sizes:
  • Population A: n₁ = 15
  • Population B: n₂ = 15
• Step 1: Calculate the mean for each data set:

• Step 2: Calculate the standard deviation (s) for each set of data:

Worked example t-test table 1

• Divide the sum of each square by n – 1 for each data set, and take the square root of each value:

Worked example t-test table 2

• Step 3 to 5: Sub all known values into the t-test equation by:
  • Step 3: Square the standard deviation and divide by n (the number of observations) in each sample, for both samples:
  • Step 4: Add the values from step 3 together and find the square root
  • Step 5: Divide the difference between the two means by the value from step 4

Worked example t-test table 3

• Step 6: Calculate the degrees of freedom (v) for all the data:
  • v = (n₁ – 1) + (n₂ – 1) = 14 + 14 = 28
• Step 7: Look at a table that relates t values to the probability that the differences between data sets is due to chance to find where the t value of 1.91 for 28 degrees of freedom (v) calculated lies

T value worked example table

• Step 8: Draw a conclusion about the statistical relevance of the data:
  • A t value of 1.91 represents a probability between 0.05 and 0.1 which is greater than the critical value of 0.05.
  • This means the null hypothesis should be accepted, as there are no significant differences between the two sets of results (any differences between the means of the ear length of rabbits in the two populations are due to chance)