Students’ misconceptions of statistical inference: A review of the empirical evidence from research on statistics education

Abstract

A solid understanding of inferential statistics is of major importance for designing and interpreting empirical results in any scientific discipline. However, students are prone to many misconceptions regarding this topic. This article structurally summarizes and describes these misconceptions by presenting a systematic review of publications that provide empirical evidence of them. This group of publications was found to be dispersed over a wide range of specialized journals and proceedings, and the methodology used in the empirical studies was very diverse. Three research needs rise from this review: (1) further empirical studies that identify the sources and possible solutions for misconceptions in order to complement the abundant theoretical and statistical discussion about them; (2) new insights into effective research designs and methodologies to perform this type of research; and (3) structured and systematic summaries of findings like the one presented here, concerning misconceptions in other areas of statistics, that might be of interest both for educational researchers and teachers of statistics.

When null hypothesis significance testing is unsuitable for research: a reassessment

“…Better Training and Better Use of More Statistical Methods: from Believers to Thinkers A core problem seems to be that the statistical subject knowledge of many researchers in biomedical and social science has been shown to be poor (Oakes, 1986;Gliner et al, 2002;Castro Sotos et al, 2007Wilkerson and Olson, 2010;Hoekstra et al, 2014). NHST perfectly fits with poor understanding because of the perceived simplicity of interpreting its outcome: is p ≤ 0.05 (Cohen, 1994)?…”

“…That is, researchers are interested in the post-experimental probability of H 0 and H 1 . Most probably, for the reason that researchers do not get what they really want to see (Murdoch et al, 2008 and the only parameter NHST computes is the p-value it is welldocumented (Oakes, 1986;Gliner et al, 2002;Castro Sotos et al, 2007Wilkerson and Olson, 2010;Hoekstra et al, 2014) that many, if not most researchers confuse FRP with the p-value or α and they also confuse the complement of p-value (1-p) or α (1-α) with TRP (Pollard and Richardson, 1987;Cohen, 1994). These confusions are of major portend because the difference between these completely different parameters is not minor, they can differ by orders of magnitude, the long-run FRP being much larger than the p-value under realistic conditions (Sellke et al, 2001;Ioannidis, 2005).…”

Investigación en educación matemática : [actas del XXI Simposio de la Sociedad Española de Investigación en Educación Matemática : Zaragoza, 6-9 de septiembre de 2017]

“…La reseña de investigaciones sobre concepciones erróneas de la Inferencia Estadística de Castro-Sotos et al (2007) tiene un apartado dedicado al contraste de hipótesis. Los autores organizan su exposición sobre las dificultades y concepciones erróneas acerca del contraste de hipótesis en 5 componentes, lo que ilustra la dificultad del tema.…”

Un estudio comparado de los contenidos de muestreo en la Educación Secundaria Obligatoria en Chile <br> A comparative study of sampling contents in the Chilean curriculum for compulsory secondary education

“…A pesar de la importancia del tema resaltada en los apartados anteriores, la investigación didáctica sobre el muestreo es escasa, y se centra principalmente en la evaluación de la comprensión del tema por los estudiantes (ver, por ejemplo, los resúmenes de estas investigaciones en CASTRO-SOTOS et al, 2007;o HARRADINE;BATANERO;ROSSMAN, 2011). Para completar dichas investigaciones, la finalidad de nuestro trabajo es analizar la forma en que introduce y se va ampliando el muestreo en las directrices curriculares chilenas, con niveles progresivos de complejidad.…”