When TESOL professionals worry about their ability to comprehend statistics, it is likely inferential statistics that they are concerned about. While descriptive statistics are used simply to describe numerical frequencies, means, and variability, for example, inferential statistics, briefly put, are used to ascertain whether one or more effects or relationships exists among variables.
What follows is a short introduction to the types of inferential statistical analyses most often used by educational researchers and which are encountered in TESOL-related journal articles. To understand these analyses, it is important to know what is meant by the term “variable”. According to Creswell (2012), a variable “is a characteristic or attribute of an individual or an organization that (a) can be measured or observed by the researcher and that (b) varies among individuals or organizations studied.”¹ Such attributes as first language, native country, and proficiency level, (beginner, intermediate, …), as well as academic achievement or proficiency in a particular language skill, are very frequently studied by researchers. For the purposes of statistical analysis, variables are labeled as “independent” and “dependent” in order to test the particular effect or relationship one is interested in. An example analysis would be to measure the effect of first language, an independent variable, on oral ability, a dependent variable, whose statistical value is potentially influenced by first language. The performance of learners from two or more first language groups would be statistically compared on, say, a course-final oral presentation, with the scores on the presentation being used in the analysis.
With that information in hand, here are a few of the inferential statistical analyses that you are likely to encounter in TESOL journal articles:
1. correlation: Is there a significant statistical relationship between two variables? (Example: comparing proficiency on the ibt TOEFL and an in-house test using test scores)
2. t-test: Does a single independent variable have a statistically significant effect on a single dependent variable? (Example: Using a pre-test post-test research design to test the effect of a particular teaching technique on listening ability).
3. ANOVA²: Does one (or more) independent variable(s) have one or more statistically significant effect(s) on one (or more) dependent variable(s)? (Example: Measuring the potential separate and combined effects of proficiency level and instructor on reading proficiency using final grades in an EAP reading course with multiple class sections).
4. Multiple regression: How much statistical variance in a particular dependent variable is due to the effect of each independent variable? / Which independent variable(s) significantly affect(s) the dependent variable? (Example: How much is performance on a course-final reading comprehension test affected by vocabulary knowledge, topic familiarity, hours of study, and rate of attendance?)
5. Factor analysis: What underlying construct(s) (i.e. independent variables) are reflected in the data? (Example: What factors affect students’ responses to an end-of-program questionnaire on student satisfaction administered to international students completing an English program in preparation for entrance to an English-speaking university.)
The statistical analyses used in TESOL-related research studies is far broader than what is presented here. Many of the more complex analyses are not common and have a very limited target audience and are thus not included in this article.
¹Creswell, J. W. (2012). Educational Research: Planning, Conducting, and Evaluating Quantitative and Qualitative Research. Fourth Edition. Pearson Education, Inc.
²ANOVA is a “family” of statistical analyses with a number of variants: one-way ANOVA, factorial ANOVA, ANCOVA, MANOVA, MANCOVA. A full list and description of each variant is beyond the scope of this article.