Ordinal Frequency

Ordinal Frequencey

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Looking at the mean of ordinal data is not all that helpful. Let us illustrate that. Consider the Student Opinion Questionaire for two sections. Recall, that SOQ values are 1=Strongly Disagree. 2=Disagree, 3=Neutral, 4=Agree, and 5=Strongly Agree. These are classic ordinal values. Assume that an SOQ question is "My instructor is professional in class." The results for two sections are given in Table 1.

Table 1
Section 01		Section 02
# of 1's	0	# of 1's	5
# of 2's	0	# of 2's	0
# of 3's	0	# of 3's	0
# of 4's	20	# of 4's	0
# of 5's	10	# of 5's	25
Section mean	4.3333	Section mean	4.3333

The R statements to demonstrate this are:

#look at some ordinal data
section_01 <- c(rep(4,20),rep(5,10))
section_02 <- c(rep(1,5),rep(5,25))
section_01
section_02
mean( section_01)
mean( section_02)

and the Console display from running those statements is shown in Figure 1.

Figure 1

The two sections have identical means. If you were to evaluate the two sections based upon their mean values you would have no indication that the sections are vastly different. In fact, at WCC, a mean score of 4.33, although below the average for all instructors, is still way above the 3.75 that is used to raise concerns about the section. Neither section would be reviewed based upon the mean scores.

However, the frequency distribution for the two sections tells another story. Whereas section 01 students view the instructor's professionalism in a fairly unified way, the section 02 students fall into two very different groups. One small group has the most negative view of the instructor's professionalism while the other group has the most positive view of the same thing. As an evaluator I would be quite concerned about the situation in section 02; it has a minority of students who are really upset. The frequency distribution indicates that this section deserves a much closer examination! For example, are there some students who have been insulted, demeaned, embarrased, harassed, or slighted in such a way as to create this gap? An all too common instance of this kind of problem is where a class that is "traditionally" taken by one gender has an instructor who "plays" to that predominant gender with sexist comments abut the minority gender. Such problems may be completely hidden when we look at mean values as an indicator of disfunction.