# Understanding Statistics in TESOL, Part 1 (Descriptive Statistics)

“Statistics” is a term that can create a feeling of near-frights in the mind of some language educators. Isn’t this a term for mathematicians, economists, and scientists working in labs? Yes, of course, but knowledge of statistics is also vital for the educational researcher and any teacher designing their own tests and seeking to analyze the results. It is also a much-needed tool in the TESOL professional’s knowledge suitcase for reading journal articles, attending conferences and workshops, and, if the opportunity arises, conducting one’s own research.

Much of the fear related to statistics is based on the lack of understanding on the part of TESOL professionals of two key facts: first, statistical analyses used in the social sciences are quite different from those in the hard sciences; second, descriptive statistics, with which most teachers already have familiarity through their study of arithmetic in school, are less complex and much more commonly used in small-scale studies than are inferential statistics.

For this particular article, I will focus on descriptive statistics. Descriptive statistics you can expect to encounter in research articles include the following

1. mean: this represents the average score among results for a single test. It may also refer to the average rating among respondents to a Likert-style questionnaire, where each response (Disagree = 1, Slightly disagree = 2, . . . Agree = 4) is assigned a value to allow for statistical analysis.

2. median: this represents the score which is in the middle rank between the highest and lowest score among results for a single test. For example, in a set of nine scores, the median would be the fifth highest (or fifth lowest). In a set of ten scores, the median would be the value midway between the fifth and sixth highest scores. It is much less commonly reported than the mean, as the latter is has much more frequent use in more complex statistical formulas.

3. standard deviation: this is a measure of the degree of difference among a set of test scores. The larger the value of the standard deviation, the greater the overall spread there is among the scores. Variance, which is also included in statistical results, is simply the square of the standard deviation.

4. frequency: this refers to the number of responses for each choice in a Likert-style question, for example, or the number of students who selected each answer in a multiple-choice or fill-in-the-blank type question on a test.

5. proportion: In large-scale studies, the proportion represents the frequency of responses expressed in relative percentages. This information becomes valuable when actual frequencies become so large that comparisons become difficult.

6. percentile: this value represents the ranked score on a test in which the number of test-takers is in the hundreds or thousands. A percentile score of 95 means that a particular test-taker received a higher score on that test than all but 5% of those who took the test.