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Meaning of the sample correlation coefficient (r)

Meaning of the sample correlation coefficient (r). A measure of the closeness of linear relationship between two variables. r= Σx 1 x 2 / [(Σx 1 2 )(Σx 2 2 )] 1/2 Properties of r A pure number without units r between -1 and +1

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Meaning of the sample correlation coefficient (r)

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  1. Meaning of the sample correlation coefficient (r) • A measure of the closeness of linear relationship between two variables. • r= Σx1x2 / [(Σx12)(Σx22)]1/2 • Properties of r • A pure number without units • r between -1 and +1 • +1: a complete positive correlation, two variables increase or decrease together • -1: a complete negative correlation

  2. r = Σxy / [(Σx2)(Σy2)]1/2 = 120/ (60 x 240) ½=1

  3. Two group comparison • ANOVA • Methods to increase power • Paired concept • Adjusting for initial values • Method to examine the power of the data • Sample size calculation

  4. covariance(X1,X2) Variance in the analysis of independent samples vs. paired samples

  5. Sample 1 57 53 39 39 36 34 33 29 24 12 M1 =35.6 V1 = 152.8 Sample 2 53 44 32 31 30 30 24 19 19 11 M2 = 29.3 V2 = 136.4 Different 4 9 7 8 6 4 9 10 5 1 MD= 6.3VD = 7.2 Independent samples Paired samples Variance in the analysis of independent samples vs. paired samples < 1.96 > 1.96

  6. Interaction • One-way testing • (X2-X1) • Two-way testing • (X11 - X12)–(X21-X22)

  7. Sample size required to compare two means • n = 2δ2（Z α/2＋Zβ）2 / d2 • Two groups’ energy intake levels differ 840 kJ • δ2 = 2205 • For 90% power at 5 percent significance level, （Z α/2＋Zβ）= 10.5 • n = 2 x 2205 2x 10.5 /840 = 145

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