Exam II Marks
Feb 23, 2016
Exam II Marks
Chapter 20.1 Correlation
Correlation
β’ Correlation is used when we wish to know whether two randomly distributed variables are associated with each other
β’ Exampleβ Total length Y1 of aphid stem
mothers and mean thorax length Y2 of their parthenogenetic offspring.
No causal ordering
Contrast to regression
π=βπ½1,2β π½2,1
π=cos (π)
ππ π=0π , hπ‘ ππ π=1ππ π=90π , hπ‘ ππ π=0ππ π=180π , hπ‘ πππ=β1
β1β€ πβ€1
Formal model
Regressionβ’ randomly distributed
response variable ~ fixed explanatory variable
Correlationβ’ two random response
variablesβ’ No causal ordering, thus no
explanatory variable
[π 1 ,π 2 ]=ππΆ β Ξ»+π
Estimate
οΏ½ΜοΏ½=π= 1πβ1 β
β (π 1βπ 1 ) β (π2βπ 2 )π 1βπ 2
Compute t
State HA/Ho pair
HA: Ho:
Crunch the numbers
οΏ½ΜοΏ½=π= 115β1
ββ ([8.7 ,8.5 ,β¦ ]β9 ) β ([5.95 ,5.65 ,β¦ ]β5.73 )1.88 β0.59
π=10.0715.49=0.650
More number crunching> cor.test(dat$th.length,dat$tot.length)
Pearson's product-moment correlation
data: dat$th.length and dat$tot.length t = 3.0867, df = 13, p-value = 0.008666alternative hypothesis: true correlation is not equal to 0 95 percent confidence interval: 0.2070464 0.8720726 sample estimates: cor 0.6503335
Conclusions
β’ r = 0.650, n = 15, p = 0.0086β’ Thorax length of offspring is positively related
to stem mother total length. β’ The relation of offspring thorax length to size
of aphid stem mothers is monotonic but not necessarily linear.