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9.4.1.Example 2
Unit 9 - Correlation and regression
9.4.1 Example 2
The correlation between length and weight ‘or a particular fish species is observed to be 0.7 from a sample of 18 specimens.ls it significant?
Answer: Let denote the population correlation coefficient between length and weight of fish.
(i) Hypothesis
H0 : = 0 ; H1 : ≠ 0
(ii) Test statistic
=3.92
Table values of t are t16 (5%) = 2.12, t16 (1%) = 2.92(iii) Statistical decision :
Since the calculated value of t is greater than the table value oft at 5% and 1% level of significance, reject H0. Hence, the correlation coefficient is significant.
Note: It is however, not necessary to carry out the‘t’ test described above for testing the significance of the correlation coefficient as readymade table of critical values of r for different degrees of freedom at 5% and 1% levels of significance is available (Fisher and Yates 1963). Compare the calculated value of r with the critical value of r from the table. If the calculated value of r is higher than the critical value, then correlation is significant.
Last modified: Friday, 16 September 2011, 5:29 AM