yr2 chap 1 regression, correlation + hypothesis testing

• to carry out a one-tailed test for zero correlation:

  • write out the null hypothesis rho = 0 and alternative hypothesis rho > 0 or rho < 0
  • write down the critical value, found using the table
  • compare r and the critical value
  • if r is in the critical region, r < critical value, accept the null hypothesis as there is no evidence of correlation
  • if r is not in the critical region, r > critical value, reject the null hypothesis as there is evidence of correlation
• the product moment correlation coefficient describes the correlation between two variables, it is represented by $\rho$
• the pmcc can take any value between -1 and +1
• if pmcc = +1, the correlation is perfectly positive
• if pmcc = -1, the correlation is perfectly negative
• the closer pmcc is to +1 or -1, the stronger the correlation
• if pmcc = 0, there is no linear correlation
• to calculate the pmcc from a table of data:

  • enter both rows into the first two columns of stats mode
  • select CALC then REG then X then AX+B
  • pmcc is the number labelled as r
• to carry out a two-tailed test for zero correlation:

  • write out the null hypothesis p = 0 and alternative hypothesis p != 0
  • remember to halve the significance level
  • write down the critical value, found using the table
  • compare r and the critical value
  • if r < critical value, the result is significant, there is evidence of correlation
  • if r > critical value, the result is not significant, there is no evidence of correlation