Answer and guidance to the Paulo Question

Rank 1 Rank 2 D D2
1 3 -2 4
2.5 5 -2.5 6.25
2.5 1 1.5 2.25
4 4 0 0
5 7 -2 4
6 2 4 16
7.5 6 1.5 2.25
7.5 10 -2.5 6.25
9 8 1 1
10 9 1 1

Once you had completed the D² column , you needed to use the formula from the front of the booklet to work out the rest of the calculation as follows:

∑D²= 43  (here the ∑ means sum total, you just had to add up the D² column on your calculator).

6×43=258     N=10    102=100    100-1= 99   99×10=990



In terms of working out whether Paulo should reject the null, the answer is YES!

The extract mentions that Paulo thought he would get a positive correlation and this means he will do a one tailed test

  • as he has stated the direction he expect the results to go in, his hypothesis would be directional
  • as one goes up the other also goes up
  • he could have said there “will be a correlation” but not stated whether it would be positive or negative
    • this would result in a two tailed hypothesis
    • leading to a two tailed test (thus a different critical value).

You needed to find the correct column in the critical values table by finding the 0.05 column for a one tailed test and then look at the row for n=10 (where n=number of participants) and found that the critical value was 0.442.

If you read the bottom of the critical values table it tells you the observed value (calculated must be equal to or exceed the tabled value (critical value); Paulo’s observed value of 0.739 is much bigger and he must reject the null, as he will be accepting the alternative hypothesis.

Next you could also check whether his results are significant at the 0.01 level as this would tell us whether the probability that his results were due to chance is less than (<) 1 in 100.