The Logic of scientific inquiry

All scientific inquiry involves logic or reasoning. In research, logic is used in analyzing data: we compare results in terms of relative sizes (how large is one average in relation to another) or we make a judgment about how strongly one variable is related to another (like schooling and fertility). Logic is also used in drawing conclusions from our findings.

Specifically, two systems of logic, called inductive and deductive logic, are used in research. Inductive logic is used in reasoning from many particulars, such as many bits of data, to a more general level. Drawing a conclusion from various bits of data is an example of inductive logic. Deductive logic works in the opposite direction. It involves formulating a statement from some broader basis. Deriving a hypothesis, as a specific statement, from a theoretical framework, illustrates deductive logic. Several examples should help you see how each form of logic is used.

Inductive logic

First, let's look at how inductive logic is used. To illustrate this process we will use two now familiar sets of data from the Sudan Fertility Survey — years of schooling among women and their fertility. With these data we would have two observations, one for schooling and one for fertility, for each woman in the sample.

These observations are the particulars, the bits of raw data, which we will use to illustrate the inductive process. Our intent is to find out what relationship exists between these two variables.   One way to do this is to display the observations in graphic form as shown in Figure 3.1(A).

Each women is represented Figure 3.1(A) by a dot or point corresponding to her years of schooling, shown on the horizontal line of the figure (the X axis), and her fertility, shown on the vertical (Y) axis. Assume that the first woman in the sample had 6 years of schooling and had given birth to 5 babies. In the figure, she is represented by the dot above the 6 on the X-axis and across from the 5 on the Y-axis. Another woman, with 11 years of schooling and with 3 children, is represented by the dot above the 11 on the X-axis and opposite the 3 on the Y-axis. Continuing this process, observations for fertility and schooling for all women would be plotted. With over 3,000 women we would have a dense mass of points - one for each woman. For the purposes of this illustration we have simplified the graph by showing only a small number of points

After showing the data in this way, we would look for the pattern running through the mass of points.   Looking at the points, it seems there is a pattern. To show the pattern, we draw a line through the middle of the mass of points. When we did this, as indicated in Figure 3.1(B), we find a line sloping downward from left to right. This line indicates a negative relationship between the variables: that is, as schooling increases, fertility tends to decrease.   This line summarizes the relationship between schooling of women and fertility.

Figure 3.1(C) shows the outcome of this inductive process. The particulars, the original bits of data represented by the many dots, are now replaced by a single line that represents the finding of the study. We have gone from analysis of particulars to the expression of a conclusion - namely, that there is a negative relationship between the schooling of women and their fertility. In actual research, a statistical measure called the coefficient of correlation would be used to express the relationship between the two variables (see Chapter 19).