Correlation 3rd
Download as PPT, PDF0 likes319 views
This document discusses correlation and the Pearson correlation coefficient (r). It investigates the linear association between body weight and plasma volume in 8 subjects. The correlation coefficient (r) between weight and plasma volume is calculated to be 0.76, indicating a strong positive correlation. A t-test shows this correlation is statistically significant. Values of r range from -1 to 1, where higher positive or negative values indicate stronger linear relationships.
Correlation 3rd
- 2. CorrelationCorrelation The aim is to investigate the linearThe aim is to investigate the linear association between two continuousassociation between two continuous variables.variables. Correlation:Correlation: Measures the closeness of theMeasures the closeness of the association.association.
- 3. CorrelationCorrelation SubjectSubject Body wt. KgBody wt. Kg (X)(X) XX22 Plasma volumePlasma volume liter (Y)liter (Y) YY22 (XY)(XY) 11 5858 2.752.75 22 7070 2.862.86 33 7474 3.373.37 44 6363 2.762.76 55 6262 2.622.62 66 70.570.5 3.493.49 77 7171 3.053.05 88 6666 3.123.12 ∑∑ XX ∑∑XX22 ∑∑YY ∑∑YY22 ∑∑XYXY
- 4. Correlation, cont.Correlation, cont. In general, high plasma volume tend to beIn general, high plasma volume tend to be associated with high weight. This association isassociated with high weight. This association is measured by Pearson correlation coefficient (r)measured by Pearson correlation coefficient (r)
- 5. Correlation coefficient (r)Correlation coefficient (r) r =r = ∑ ∑∑∑ ∑ ∑ ∑ −− − n y y n x x n yx xy 2 2 2 2 )( )( )( ( ))((
- 6. Scatter diagramof plasma volume and bodyweight showing linear regression line y = 0.0434x + 0.0998 R2 = 0.5818 0 1 2 3 4 45 55 65 75 85 Body weight (Kg) Plasmavolume(liter)
- 7. ResultsResults N = 8N = 8 ∑∑x = 535 Mean x = 66.875x = 535 Mean x = 66.875 ∑∑xx22 ==35983.535983.5 ∑∑y = 24.02 Mean y = 3.0025y = 24.02 Mean y = 3.0025 ∑∑yy22 = 72.798= 72.798 ∑∑xy = 1615.295xy = 1615.295 r =r = 76.0 )6780.0)(38.205( 96.8 =
- 8. Significance testSignificance test A t test is used to testA t test is used to test whether (r) iswhether (r) is significantly differsignificantly differ from zero ie whetherfrom zero ie whether the observedthe observed correlation couldcorrelation could simply due to chance.simply due to chance. t =t = 2 1 2 r n r − −
- 9. Significance test, cont.Significance test, cont. d.f. = n-2d.f. = n-2 t =t = d.f. = 6d.f. = 6 P < 0.05P < 0.05 86.2 )76.0(1 6 76.0 2 = −
- 10. Significance test, cont.Significance test, cont. Note: A significance level is a function ofNote: A significance level is a function of both the size of the correlation coefficientboth the size of the correlation coefficient and number of observations.and number of observations. A weak correlation may therefore beA weak correlation may therefore be statistically significant if based on a largestatistically significant if based on a large number of observations, while a strongnumber of observations, while a strong correlation may fail to achieve significancecorrelation may fail to achieve significance if there are only a few observations.if there are only a few observations.
- 11. Interpretation of rInterpretation of r r is always a No. between minus 1 andr is always a No. between minus 1 and plus 1.plus 1. r is positive if x and y tend to be high orr is positive if x and y tend to be high or low together, and the larger its value, thelow together, and the larger its value, the closer the association.closer the association. r is negative if high value of y tend to gor is negative if high value of y tend to go with low values of x and vice versa.with low values of x and vice versa.
- 12. r valuer value InterpretationInterpretation ZeroZero No correlationNo correlation 0<r<10<r<1 Imperfect (direct) positiveImperfect (direct) positive correlationcorrelation 11 Perfect (direct) positivePerfect (direct) positive correlationcorrelation -1 < r < 0-1 < r < 0 Imperfect negativeImperfect negative (inverse) correlation(inverse) correlation r = -1r = -1 Perfect negative (inverse)Perfect negative (inverse) correlationcorrelation
- 13. Guideline values for interpretationGuideline values for interpretation the value of (r)the value of (r) rr Degree ofDegree of associationassociation ± 1± 1 PerfectPerfect ± 0.7 - ± 1± 0.7 - ± 1 StrongStrong ± 0.4 - ± 0.7± 0.4 - ± 0.7 ModerateModerate < 0.4< 0.4 WeakWeak 0.00.0 No associationNo association
- 14. NotesNotes r measures only linear relationship.r measures only linear relationship. When there is a strong non-linearWhen there is a strong non-linear relationship, r = zero.relationship, r = zero. So we have to draw a scatter diagram firstSo we have to draw a scatter diagram first to identify non-linear relationship.to identify non-linear relationship. If you calculate r without examining theIf you calculate r without examining the data, then you will miss a strong but nondata, then you will miss a strong but non linear relationship.linear relationship.
- 15. The coefficient of determination (rThe coefficient of determination (r22 )) When r = 0.58, then r2 = 0.34.When r = 0.58, then r2 = 0.34. This means that 34% of the variation in theThis means that 34% of the variation in the values of (y) may be accounted for byvalues of (y) may be accounted for by knowing values of (X) or vice versa.knowing values of (X) or vice versa.