Can There Be Too Much Interpretation?

Let’s face it, not all students and faculty are statisticians, nor do they want to be. However, students must still learn the ins and outs of statistical analyses. This means understanding terms and symbols and learning to conduct and interpret the output. SPSS offers a steep learning curve for many. The program can seem clunky and intimidating, and the output includes too much noise. This can interfere with students deciphering the signal. Intellectus Statistics exists to overcome these challenges. However, some faculty worry that too much interpretation may hinder students learning of statistics. 

Faculty want their students to turn raw output into written results. But where do students learn to write? Some faculty provide journal articles with written results while some use examples from textbooks. Intellectus’ AutoDrafting technology is simply another way to exemplify how to interpret and report quantitative results.

How to integrate Intellectus into statistics learning

When teaching statistics to students, use the “whole picture, then practice, practice, practice” approach. Students need to see the whole picture of an analysis and the reporting. These pieces include an introduction to the analysis, the correct assumptions conducted and interpreted, the analysis interpreted with recommendations to retain or reject the null hypotheses, the appropriate tables and figures for that analysis, and in-text citations and references. This is precisely what Intellectus provides under the interpreted output view. The first step to acquiring statistical competence is to let Intellectus show students the whole picture of that analysis. Below is an interpreted output view of a paired t-test.

Two-Tailed Paired Samples t-Test: Interpreted Output View


A two-tailed paired samples t-test is conducted to examine whether the mean difference of Knowledge Pretest and Knowledge Posttest is significantly different from zero.


Normality. A Shapiro-Wilk test is conducted to determine whether the differences in Knowledge Pretest and Knowledge Posttest could have been produced by a normal distribution (Razali & Wah, 2011). The results of the Shapiro-Wilk test are significant based on an alpha value of 0.05, W = 0.90, p < .001. This result suggests the differences in Knowledge Pretest and Knowledge Posttest are unlikely to have been produced by a normal distribution, indicating the normality assumption is violated.

Homogeneity of Variance. Levene’s test is conducted to assess whether the variances of Knowledge Pretest and Knowledge Posttest are significantly different. The result of Levene’s test is significant based on an alpha value of 0.05, F(1, 98) = 15.86, p < .001. This result suggests it is unlikely that Knowledge Pretest and Knowledge Posttest are produced by distributions with equal variances, indicating the assumption of homogeneity of variance was violated.


The result of the two-tailed paired samples t-test is significant based on an alpha value of 0.05, t(49) = -12.20, p < .001, indicating the null hypothesis can be rejected. This finding suggests the difference in the mean of Knowledge Pretest and the mean of Knowledge Posttest is significantly different from zero. The mean of Knowledge Pretest was significantly lower than the mean of Knowledge Posttest. Find the results in Table 1 and a bar plot of the means in Figure 1.

Table 1

Two-Tailed Paired Samples t-Test for the Difference Between Knowledge Pretest and Knowledge Posttest

Snapshot of t-Test results

Note. N = 50. Degrees of Freedom for the t-statistic = 49. d represents Cohen’s d.

Figure 1

The means of Knowledge Pretest and Knowledge Posttest with 95% CI Error Bars

Bar graph of KnowledgePre and KnowldgePost t-Test

The next step is to take the same statistical test with different data and provide students with only the raw output view. The students must then interpret and write-up the results, create the appropriate tables and figures, and reference the assumptions. Below is the raw output view of a paired t-test.

Two-Tailed Paired Samples t-Test: Raw Output View

Paired t-Test for Knowledge Pretest and Knowledge Posttest

The students can then independently do a knowledge check by comparing their write-up to the interpreted output view and edit as necessary. Faculty can use the numerous datasets to allow the students to practice, practice, practice. 

Intellectus Statistics and its Autodrafting technology offer a different mode of learning and teaching. Students who use Intellectus are much less frustrated when they see that an analysis includes easily digested data. They gain the skill of writing the results themselves as well as the competence and confidence to conduct data analyses without being a statistician.

“How do I drive students to successful learning?” is a question confronting educators, from provosts, deans, department chairs, to faculty.  When combined with moving learning online, using technologies, and adding a challenging subject like statistics, driving students to success becomes an obstacle course. 

Intellectus Statistics AutoDrafting technology analyzes data and automatically generates a written interpretation of statistical output for students. The technology can help students and instructors navigate the learning and teaching of statistics by building bridges over knowledge gaps, accelerating learning by reducing cognitive loads for novices, and avoiding putting the brakes on learning with embedded support throughout the journey.

Scaffolding Designs for Novice Learners

Learning differs between novices and experts. Novices depend on concept formation, whereas experts use concept integration (Daley, 1999). Concept formation is accelerated by guiding learners through step-by-step tasks that illustrates and demonstrates how components of statistical analysis become integrated.    

Intellectus’ AutoDrafting technology facilitates concept formation through step-by-step guidance and examples of how to conduct and understand statistical analyses and interpretations. By comprehensively including the components of an analysis in the output, including automated interpreted assumptions, automated interpreted output in plain English narrative, automatically generating appropriate tables and figures, as well as presenting worked-through examples of how the findings and tables are reported.  Intellectus creates conceptual landmarks for the novice learner’s journey where there are gaps in students’ knowledge. Intellectus also provides context-sensitive help that can bridge the knowledge gaps and drive them to the solution. Together, these features allow novice students to form the concept of how data analyses are conducted, what they mean, and how they are written.

Managing Cognitive Loads

Being overwhelmed is a common obstacle for novices learning statistics. With so many new concepts, mixing with some less-than optimal math skills, novices cannot organize their learning into meaning chunks/concepts. According to Cognitive Load theory (Sweller, 1988), there are three types of cognitive load: intrinsic load (task complexity), extraneous load (features that are not beneficial for learning), and germane load (features that are beneficial for learning). Novice learners learn better from worked examples (Cooper & Sweller, 1987; Paas & Van Merriënboer, 1994; Sweller & Cooper, 1985) by reducing task complexity on intrinsic load. Intellectus reduces task complexity with a simple user-interface, useful default settings, and fully worked examples. Extraneous load is minimized by stripping away irrelevant options and unnecessary, confusing output; Intellectus only provides information relevant for presentation and understanding. Germane load is enhanced in Intellectus by providing instructional features such as scroll-overs that immediately explain statistical figures, terms, and symbols. Intellectus manages these cognitive load types in a way that optimizes cognitive resources.

To the left is a linear regression Q-Q scatter- plot, automatically generated in the output, to assess normality. 

The right side of the image shows the scroll-over to help students decide whether the data is from a normal distribution. 

Supporting Retention

Repetition and meaning are keys to long-term memory. For example, introduction to statistics terms just once is subject to primacy and recency effects, while seeing terms a third time increases the retention of structurally important information. Increased repetition allows for important information to be remembered (Bromage & Mayer, 1986).  Intellectus’ built-in datasets, textbook, and videos provide novices numerous complete examples. These examples produce and explain relevant terms and symbols that provide meaningful encoding and retrieval opportunities, and champions retention and understanding.

Synergizing Accelerators

Intellectus accelerates statistics learning by supporting students’ ability to form statistical concepts, managing cognitive load, and promoting retention opportunities. To learn more about Intellectus Statistics click here.


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