What does \rho represent?

The product moment correlation coefficient of the whole population.

What does \rhos represent?

The Spearman rank correlation coefficient of the whole population.

Give the alternative hypotheses for a test for positive or negative correlation.

H1:\rho0 or H1:\rho<0 (one-tailed).

What should you do if r is in the critical region?

Reject H0 and state in context that there is evidence of correlation.

Can failing to reject H0 prove there is no correlation?

No. It means there is insufficient evidence of correlation.

What does the product moment test require of the data?

A bivariate normal population (roughly elliptical scatter diagram).

Why might a Spearman test be preferred?

It needs only a monotonic relationship, so it suits ranked data and small samples.

Testing for zero correlationEdexcel A-Level Further Maths: Flashcards

Card 1 of 120 of 12 known

Question

What is the null hypothesis for a test of correlation?

Tap or press Space to reveal

Tap card or press Space to flip

See all 12 cards

What is the null hypothesis for a test of correlation?: $H_0:\rho=0$ (or $H_0:\rho_s=0$ ): no correlation in the population.
What does $\rho$ represent?: The product moment correlation coefficient of the whole population.
What does $\rho_s$ represent?: The Spearman rank correlation coefficient of the whole population.
Give the alternative hypothesis for a test for any correlation.: $H_1:\rho\ne0$ (two-tailed).
Give the alternative hypotheses for a test for positive or negative correlation.: $H_1:\rho>0$ or $H_1:\rho<0$ (one-tailed).
Which table column is used for a two-tailed 5% test?: The one-tailed 2.5% column.
What is the critical region for $H_1:\rho>0$ ?: $r\ge$ the critical value.
What is the critical region for $H_1:\rho<0$ ?: $r\le-$ the critical value.
What should you do if $r$ is in the critical region?: Reject $H_0$ and state in context that there is evidence of correlation.
Can failing to reject $H_0$ prove there is no correlation?: No. It means there is insufficient evidence of correlation.
What does the product moment test require of the data?: A bivariate normal population (roughly elliptical scatter diagram).
Why might a Spearman test be preferred?: It needs only a monotonic relationship, so it suits ranked data and small samples.

Exam questions on Testing for zero correlation

For a random sample of 10 adults, the product moment correlation coefficient between weekly hours of exercise and resting heart rate is $r=-0.60$ . A test is to be carried out, at the 5% significance level, to see whether there is any correlation between the two variables in the population.
The researcher now only wants to test for negative correlation, using $H_0:\rho=0$ and $H_1:\rho<0$ at the 5% significance level. Using the critical value $-0.5494$ , carry out the test and state your conclusion in context.2 marks
A teacher ranks 8 students by their coursework mark and by their end-of-year examination mark. Spearman's rank correlation coefficient between the two sets of ranks is $r_s=0.69$ . The teacher tests, at the 5% significance level, whether there is positive correlation between coursework and examination performance.
Using the critical value $0.6429$ , complete the test and state your conclusion in context.2 marks
A farmer applies different masses of fertiliser to 12 randomly chosen plots of land. The product moment correlation coefficient between the mass of fertiliser and the crop yield is $r=0.65$ .
Test, at the 5% significance level, whether there is positive correlation between the mass of fertiliser and the crop yield. Use the critical value $0.4973$ and state the hypotheses clearly.3 marks

See the full worksheet

Written by the Exaim team, led by Shaun Daswani (Head of Upper Secondary, Improve ME Institute; MSc Financial Mathematics, Imperial College London; BSc, UCL) and Jason Daswani (operational lead, Improve ME Institute; LSE).