SHOULD YOU USE THE ITEM MEAN OR MEDIAN? As mentioned previously, when the anchor distribution is negatively skewed, the mean will always be lower than the median, as it is for all three items displayed in the previous blog. The reason is that the mean is drawn toward the few extremely low ratings of SD. The mean is sensitive to extreme scores. (Statisticians’ Concern: For as long as statisticians can remember, the mean has always had an attraction for extreme scores. Granted, this affinity for outliers is not normal. However, statisticians have tolerated this abnormal relationship for years, but also felt compelled to create another index that is not so easily swayed: the median. You may now resume this paragraph already in progress.) Depending on the degree of skew, the bias in interpreting the mean can be significant or insignificant.
DIRECTION AND DEGREE OF ITEM MEAN BIAS: The problem is that the mean misrepresents the actual ratings in a negatively skewed distribution by portraying lower class ratings than actually occurred. This bias MAKES THE INSTRUCTOR APPEAR WORSE in teaching performance, on all of the items, than the students’ ratings indicate. This is not very desirable, especially if these results are used for summative decisions by your department chair or associate dean.
Although means are reported on most commercially published scales, it is strongly recommended that MEDIANS SHOULD BE REPORTED ALONG WITH THE MEANS. Although the median is less discriminating as an index, it is more accurate, more representative, and less biased than the mean for markedly skewed distributions. The lower the degree of skew, the more similar both measures will be. In a perfectly normal distribution, the mean and median are identical. However, keep in mind that ratings of faculty, administrators, courses, programs, and fast food are typically skewed. Therein lays the importance of picking the right index.
BOTTOM LINE RECOMMENDATION: Use both mean and median.
INTERPRETATION: PROFILE OF STRENGTHS AND WEAKNESSES: Since the item means/medians are based on the total N for the class, they can be compared. They display a profile of strengths and weaknesses related to the different teaching behaviors and course characteristics. On a 0−3 scale, means/medians above 1.5 indicate strengths; those below 1.5 denote weaknesses. The means/medians in conjunction with the anchor percentages provide meaningful diagnostic information on areas that might need attention. Again, this report is intended for the instructor's use primarily, although the results on course characteristics may have curricular implications.
Next, the meaning and uses of subscale and total scale scores will be discussed. They are basically summaries of the item scores. Hope you’re finding this stuff helpful. If not, let me know.
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