Charles Spearman(1863-1945)British Psychologist and pioneer of IQ theory

What can this test tell you?

Whether there is a statistically significant correlation between two measurements from the same sample when you have 5-30 pairs of data.

If the correlation is negative or positive

Spearmans Rank Correlation Coefficient

What is the correlation coefficient r ?

Does being good at maths make you better at biology?Is there a statistically significant correlation between these two sets of results?

StudentMaths exam scoreBiology exam scoreAnand5783Bernard4537Charlotte7241Demi7885Eustace5356Ferdinand6385Gemma8677Hector9887Ivor5970Jasmine7159

Spearmans Rank Correlation Coefficient: rsWhere:

N = the number of individuals in the sample

D = difference in the rank of the two measurements made on an individualrs will be a number between 1 and +1

This number can be compared with those in a table of critical values

H0 = there is no statistically significant correlation between Maths scores and Biology scoresHA = there is a statistically significant correlation between Maths scores and Biology scoresA negative value for rs implies a negative correlationA positive value for rs implies a positive correlationIf the value for rs exceeds the critical value, then you can reject the null hypothesis

Step 1: Rank each set of data31782591046(lowest to highest)Where two or more scores are tied each is assigned an average rank712839610548.58.5

StudentMaths exam scoreMaths rankBiology exam scoreBiology rankAlex5783Bernard4537Charlotte7241Demi7885Eustace5356Ferdinand6385Gemma8677Hector9887Ivor5970Jasmine7159

Step 2: Work out the differences in ranks(maths biology)- 405- 0.5- 1- 3.530- 12Step 3: Work out the square of the differencesStep 4: Work out the sum of the square of the differences160250.25112.25901468.5

StudentMaths exam scoreMaths rankBiology exam scoreBiology rankDD2

Alex573837Bernard451371Charlotte727412Demi788858.5Eustace532563Ferdinand635858.5Gemma869776Hector98108710Ivor594705Jasmine716594D2 =

Step 5: Work out the correlation coefficient, rsN = 10

D2 = 68.5= 1 0.415= 0.585Where:

Step 6: Compare your calculated value of rs with the relevant critical value in your stats tableFor N = 10 and P = 0.05, the critical value of rs is 0.65Our value of rs is 0.585Because this is below the critical value, we must accept H0There is no statistically significant correlation between Maths scores and Biology scores

rs critical values (P=0.05)No. of pairsCritical value80.7490.68100.65120.59140.54

Mad Geoffs Chaotic Firework Factory Do peoples stress levels increase the closer they live to Mad Geoffs Chaotic Firework Factory?Cortisol is a stress hormoneThe more stressed an individual is, the higher their blood cortisol levels will be

H0 = there is no significantly significant correlation between proximity to the fireworks factory and blood cortisol levels

ResidentAddressBlood cortisol level (g/ml)Karl (Caretaker)2 (Factory)13.4Lillie822.6Melanie1023.4Nigel1218.6Olga1217.4Peter1416.8Quentin1615.2Rajesh1610.2Susan189.8Toni1812.6Uri188.8Vanessa207.5

1234.54.567.57.510101012611121098743521-5-9-9-5.5-4.5-20.53.57581125818130.2520.2540.2512.25492564121513

ResidentAddressAddress rankBlood cortisol level (g/ml)CortisolrankDD2

Karl213.4Lillie822.6Melanie1023.4Nigel1218.6Olga1217.4Peter1416.8Quentin1615.2Rajesh1610.2Susan189.8Toni1812.6Uri188.8Vanessa207.5D2

N = 12

D2 = 513= 1 1.794= - 0.794Where:

When comparing rs to the critical value ignore the sign on rs For N = 12 and P = 0.05, the critical value of rs is 0.587Our value of rs is 0.794Because this is above the critical value, we can reject H0There is a statistically significant correlation between proximity to the fireworks factory and blood cortisol levelsrs is negative so there is a negative correlation... Therefore: the further one lives from the firework factory, the lower ones blood cortisol levels.

**************