Analyzing the Results of Demonstration Studies - Evaluation Methods in Biomedical Informatics - page 241

3. Consider an alternative, hypothetical outcome of the information
retrieval study as shown below. Make a plot of these results analogous to
that in Figure 8.2. What would you conclude with regard to a possible sta-
tistical interaction?

Mean SD, by assigned

problem set

±

Access mode A B

Boolean 19.3 ± 5.0 12.4 ± 4.9

( n = 11) ( n = 11)

Hypertext 15.7 ± 5.7 21.8 ± 5.1

( n = 10) ( n = 10)

Analyzing Studies with Independent and
Dependent Variables that are Continuous

Studies with One Independent Variable
Recall from Chapter 7 that in simple correlational studies, the investigator
makes at least two measurements, the dependent or outcome measure and
at least one independent variable. Often both of these variables are con-
tinuous in nature, such as age and usage rate for an information resource.
Many readers will be familiar with the use of simple regression analysis to
analyze such data. Here, the continuous dependent variable is plotted
against a single continuous independent variable on an x - y graph and a
regression line is fitted to the data points, typically using a least squares
algorithm—see Figure 8.3 for an example. Here, the number of times each
of a set of 11 users logged on to an information resource per week is plotted
against the age of that user. A regression line, or line of best fit, has been
added by the spreadsheet package. In addition, the package has calculated
the equation of the line, showing that the predicted usage rate per week ( y )
is approximately 35 - 0.4 times the user age ( x ). However, it is clear from
the graph that there is a lot of scatter in the data, so that although the
general trend is for lower log-on rates with older users, some older users
(e.g., one of 47 years) actually show higher usage rates than some younger
users (e.g., one of 23 years).
In this two-variable example, the slope of the regression line is propor-
tional to the statistical correlation coefficient ( r ) between the two variables.
The square of this correlation, seen as R 2 in Figure 8.3, is the proportion of
the variation in the dependent variable (here, log-on rate) that is explained
by the independent variable (here, age). In this example, the R 2 is 0.31,
meaning that 31% of the variance in usage rate is accounted for by the age
of the user, and the other 69% is not accounted for.