How to Display Data- P12

How to Display Data- P12:The best method to convey a message from a piece of research in health isvia a fi gure. The best advice that a statistician can give a researcher is to fi rstplot the data. Despite this, conventional statistics textbooks give only briefdetails on how to draw fi gures and display data.
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How to Display Data- P12 Relationship between two continuous variables 471 year.3 Measurements recorded include maternal age (in years), birthweight(kilograms) and the gestational age (weeks) of the baby. The correlations between all possible pairs of variables can be done by meansof a correlation matrix as in Table 5.1. In this, the correlation coefficients areshown in a triangular display similar to the charts in road atlases showing thedistances between pairs of towns. The graphical equivalent, in Figure 5.4 isTable 5.1 Correlation matrix for gestation, maternal age and birthweight for98 pre-term babies3 Gestation (weeks) Maternal age (years) Birthweight (kg)Gestation (weeks) 1.00Maternal age (years) 0.01 1.00Birthweight (kg) 0.81 0.02 1.00 Birthweight (kg) Gestation (weeks) Maternal age (years)Figure 5.4 Scatter diagram matrix showing each of the two-way relationship betweenmaternal age, birthweight and gestation in 98 premature babies.348 How to Display Dataeven better. Here it is clear that there is a strong correlation between birth-weight and gestation age, and no relation between either birthweight andmaternal age, or gestational age and maternal age.5.3 RegressionWhen it is plausible that the values of one variable exert an influence on thevalues of the other variable a technique known as regression can be used.In this chapter we shall only consider the simple case of a single continu-ous explanatory (independent) variable and a single continuous outcome(dependent) variable. Further methods of displaying the results of a regres-sion analysis with more than one explanatory variable are given in Chapter 7.Often it is of interest to quantify the relationship between the two variables,and given a particular value of the explanatory variable for an individual, topredict the value of the outcome variable. As with correlation, these data shouldbe plotted using a scatter diagram. However, unlike correlation it is essentialthat the explanatory variable (the one exerting the influence) is plottedon the X-axis and the outcome variable (the one being influenced) is plottedon the Y-axis. Figure 5.5 shows the birthweight and gestational age of 98 pre-termbabies in the Simpson study. As birthweight, to some extent, is influencedby gestational age it is important to plot gestational age on the X-axis andbirthweight on the Y-axis. Using regression, birthweight can be predictedfrom gestational age. The response variable is always plotted on the vertical,or Y, axis and the predictor variable on the horizontal, or X, axis as illus-trated in Figure 5.5. When displaying the scatter diagram for a regression analysis the regres-sion line should be plotted. The regression equation can also be included.The regression equation is given by the formula y a bx. Briefly theintercept, a, is the point at which the line crosses the Y-axis (i.e. when thevalue of the x variable is zero) and the slope, b, gives the average changein the y variable for a single unit change in the x variable. The slope coef-ficient for gestational age is 0.135 kg and this suggests that for every unitor one week increase in gestation, then birthweight increases by 0.135 kg.The intercept coefficient is 2.66. In most medical applications the valueof the intercept will have no practical meaning, as the x variable cannot beanywhere near zero. The value of r2 or R2 is often quoted in published art-icles and indicates the proportion (sometimes expressed as a percentage) ofthe total variability of the outcome variable that is explained by the regres-sion model fitted. In this case 66% of the total variability in birthweight isexplained by gestation. Relationship between two continuous variables 49 2.4 2.1 1.8Birthweight (kg) 1.5 1.2 0.9 0.6 Slope (b) Intercept (a) Birthweight 2.66 0.135*Gestation R-squared 0.66 22 25 28 30 32 Gestation (weeks)Figure 5.5 Relationship between gestation and birthweight in 98 pre-term babies.3 Note that the regression model should not be used to predict outside ofthe range of observations. In addition, it should not be assumed that justbecause an equation has been produced it means that x causes y. In thepresent exa ...