The Number of Pairs (N) Excluding the Plus N Control Is 10

APPENDIX 18

COMPUTING THE COEFFICIENT OF CORRELATION (r) TO SHOW THE RELATIONSHIP BETWEEN SHOOT AND NODULE WEIGHTS IN A RHIZOBIUM STRAIN SELECTION EXPERIMENT

The data in Table A.15 presents the dry weights (g) of the plant tops and nodules from a rhizobial strain selection experiment for cowpea (Vigna unguiculata). The experiment was a Randomized Complete Block Design with three blocks and 11 treatments (nine inoculated and two controls). Each treatment was replicated once within each block. Each treatment-plot was a Leonard jar with two cowpea plants. The plants were harvested at 30 days and the tops and nodules oven-dried at 70C for 2 days. The plus-N control will be omitted from the correlation analysis. Construct a new table containing the following data sets of plant tops (x) and nodules (y), as in Table A.16.

The number of pairs (n) excluding the plus N control is 10. Calculations:

Calculate the Mean of x = Mx

Mx = ∑x = 14.21 = 1.421 n 10

2 2 Calculate Mx = (1.421) = 2.019 Table A.15. Dry weights of tops and nodules from a rhizobial strain selection experiment.

Dry weight(s) Host of Isolation Rhizobia plant tops nodules

TAL 173 Vigna unguiculata 2.29 0.21 TAL 651 Calopogonium mucunoides 2.08 0.23 TAL 209 Vigna unguiculata 1.71 0.29 TAL 309 Macrotyloma africanum 1.67 0.26 TAL 1147 Desmodium intortum 1.67 0.22 TAL 22 Phaseolus lunatus 1.63 0.18 TAL 310 Dolichos biflorus 1.30 0.19 TAL 647 Pueraria phaseoloides 0.97 0.15 TAL 379 Glycine max 0.75 0.13

Control -- 0.14 0.00 (uninoculated) Control -- 4.03 0.00 (+ 70 ppm N)

Compute the Standard Deviation (SD) for x:

2 Similarly compute the SDy after determining My and My : Table A.16. Data sets for use in the computational formula for r.

x x 2 y y 2 xy 2.29 5.244 0.21 0.044 0.4809 2.08 4.326 0.23 0.053 0.4784 1.71 2.924 0.29 0.084 0.4959 1.67 2.788 0.26 0.068 0.4342 1.67 2.788 0.22 0.048 0.3674 1.63 2.657 0.18 0.032 0.2934 1.30 1.690 0.19 0.036 0.2470 0.97 0.941 0.15 0.023 0.1455 0.75 0.563 0.14 0.017 0.0975 0.14 0.019 0.00 0.000 0.0000 Σx = 14.21 Σx2 = 23.94 Σy = 1.86 Σy2 = 0.4054 Σxy = 3.0402

The correlation coefficient:

From the table: Therefore:

** Denotes significance of r at 1%.

To test the significance of r at the 5% (p = 0.05) and 1% (p = 0.01) significance levels consult a table giving the values of the correlation coefficient. The significant value of r depends on the degrees of freedom (df) as with the F-test. Since the data used in the correlation is paired, the df = n-2.

Whenever r is equal to or greater then the appropriate significant value, regardless of whether r is positive or negative, we can conclude that r is significant at the level of probability being used.

From the table of correlation coefficients, for df n=8, r is 0.632 at p = 0.05 and 0.765 at p = 0.01. Since r calculated from the data (r = 0.84) is greater than the tabulated value at both levels of significance, we conclude that r is highly significant. From the viewpoint of the top and nodule dry weights, the highly significant value of r indicates that there is a linear relationship between the dry weight of the plant tops and the nodule dry weight under the growth conditions of the experiment.

Once a relationship between the dry weights of tops and nodules has been established, the data can be represented graphically. The best straight line (the regression line) can then be drawn through the points after obtaining the regression equation describing the line. This line is easily transferred to the graph by drawing a line through any pair of points on it, preferably chosen as far apart as possible.

The equation for the regression line for a predicted value of y is given by:

Since r = 0.84; SDy = 0.077; SDx = 0.616; Mx = 1.421 and My = 0.186;

By substituting into the regression equation, when x = 2, then y

= 0.246 and when x = 0.5 then y = 0.089. These two points determine the regression line shown in Figure A.18. Figure A.18. Relationship between dry weights of nodules and plant tops in cowpea (Vigna unguiculata)