Formative Use of Intuitive Analysis of Variance

Trumpower, David L.

doi:10.1080/10986065.2013.830952

Cited by 5 publications

(6 citation statements)

References 24 publications

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“…In both experiments described here, we found no predictive effect of the level of statistical education that participants had previously received, or their knowledge of specific statistical terms, in line with previous research (Trumpower, 2015;Trumpower & Fellus, 2008;Trumpower et al, 2009). For Experiment 1, we attempted to represent a variety of ages and education levels in our sample, but the majority of participants reported mathematics/statistics education at the level of secondary school (i.e., until approximately 18 years of age).…”

Section: Discussionsupporting

confidence: 77%

“…While such information may be perceived more easily than when simple lists of numbers were presented in previous work (Trumpower, 2015;Trumpower & Fellus, 2008;Trumpower et al, 2009), we did not make this comparison directly. It is worth noting that, even if variability information is made salient, participants are still required to understand the inverse relationship between within-group variability and effect size (i.e., larger spreads equate to smaller Brain Juice effects).…”

Section: Discussionmentioning

confidence: 87%

“…In addition, researchers have shown that between-group variability (the difference between the means) influences decisions when displaying raw data but participants did not respond to changes in within-group variability (each group's spread) when comparing groups (Masnick & Morris, 2008). Even experience with introductory-level statistics did not guarantee that within-group variability would be given sufficient consideration (Trumpower, 2015;Trumpower & Fellus, 2008;Trumpower, Hachey, & Mewaldt, 2009). In fact, after extensive training, secondary-school mathematics teachers continued to show difficulties with the concept of sampling distributions in the context of comparing two groups (Makar & Confrey, 2004).…”

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confidence: 99%

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Visual comparison of two data sets: Do people use the means and the variability?

Kramer¹,

Telfer²,

Towler³

2017

J. Numer. Cogn.

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In our everyday lives, we are required to make decisions based upon our statistical intuitions. Often, these involve the comparison of two groups, such as luxury versus family cars and their suitability. Research has shown that the mean difference affects judgements where two sets of data are compared, but the variability of the data has only a minor influence, if any at all. However, prior research has tended to present raw data as simple lists of values. Here, we investigated whether displaying data visually, in the form of parallel dot plots, would lead viewers to incorporate variability information. In Experiment 1, we asked a large sample of people to compare two fictional groups (children who drank 'Brain Juice' versus water) in a one-shot design, where only a single comparison was made. Our results confirmed that only the mean difference between the groups predicted subsequent judgements of how much they differed, in line with previous work using lists of numbers. In Experiment 2, we asked each participant to make multiple comparisons, with both the mean difference and the pooled standard deviation varying across data sets they were shown. Here, we found that both sources of information were correctly incorporated when making responses. Taken together, we suggest that increasing the salience of variability information, through manipulating this factor across items seen, encourages viewers to consider this in their judgements. Such findings may have useful applications for best practices when teaching difficult concepts like sampling variation.Keywords: informal inferential reasoning, comparing groups, mean difference, pooled standard deviation, variability When deciding whether two groups are different on some measure, one of the most important concepts to understand is the mean or "average". Indeed, many teachers have focussed on determining the best ways to convey this idea to students at an early age, both through calculation and visual impression (Gal, 1995;Watson & Moritz, 1998). Even in adulthood, we are often presented with mean values in newspapers or television adverts (e.g., comparing the miles per gallon of two car models or the battery life of two smartphones) and expected to decide whether there is a meaningful difference. Problematically, research suggests that we place more weight than we should on these types of average ratings (e.g., de Langhe, Fernbach, & Lichtenstein, 2016). Statistically, information about the means alone is insufficient for making such decisions. One also requires knowledge of the variances (or some other measure of the "spread" of the two groups) in order to determine the size and importance of any difference. Unfortunately, understanding the concept of sampling distributions is both difficult for people (delMas, Garfield, &Chance, 1999) and under-researched (Meletiou, 2000). Journal of Numerical Cognition jnc.psychopen.eu | 2363-8761For several years, studies have investigated what has been termed 'informal inferential reasoning', where judgements are made...

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Section: Discussionsupporting

confidence: 77%

Section: Discussionmentioning

confidence: 87%

mentioning

confidence: 99%

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Visual comparison of two data sets: Do people use the means and the variability?

Kramer¹,

Telfer²,

Towler³

2017

J. Numer. Cogn.

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“…Product of perceptual and cognitive mechanisms Implicit grouping of numbers that yields summary values (e.g., mean, variance) [25,27,28,[41][42][43] Data Reasoning Detecting Patterns Detecting covariation between variables [3,11,44,45] Detecting Differences Noticing differences between sets [28,[41][42][43]46] Scientific…”

Section: Data Sensemaking Summarizationmentioning

confidence: 99%

“…Additional work has examined how college students compute analyses of variance (ANOVAs) intuitively, in which they are comparing four columns of data [46]. The data varied in their within-group variance and between-group variance, though students only saw raw data and this variance was not summarized.…”

Section: Sensemaking Of and Reasoning With Group Comparisonsmentioning

confidence: 99%

A Model of Scientific Data Reasoning

Masnick

Morris

2022

Education Sciences

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Data reasoning is an essential component of scientific reasoning, as a component of evidence evaluation. In this paper, we outline a model of scientific data reasoning that describes how data sensemaking underlies data reasoning. Data sensemaking, a relatively automatic process rooted in perceptual mechanisms that summarize large quantities of information in the environment, begins early in development, and is refined with experience, knowledge, and improved strategy use. Summarizing data highlights set properties such as central tendency and variability, and these properties are used to draw inferences from data. However, both data sensemaking and data reasoning are subject to cognitive biases or heuristics that can lead to flawed conclusions. The tools of scientific reasoning, including external representations, scientific hypothesis testing, and drawing probabilistic conclusions, can help reduce the likelihood of such flaws and help improve data reasoning. Although data sensemaking and data reasoning are not supplanted by scientific data reasoning, scientific reasoning skills can be leveraged to improve learning about science and reasoning with data.

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Aspects of first year statistics students’ reasoning when performing intuitive analysis of variance: effects of within- and between-group variability

Trumpower

2014

Educ Stud Math

Self Cite

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Making inferences about population differences based on samples of data, that is, performing intuitive analysis of variance (IANOVA), is common in everyday life. However, the intuitive reasoning of individuals when making such inferences (even following statistics instruction), often differs from the normative logic of formal statistics. The present study examined the reasoning used by several cohorts of first year statistics students when performing IANOVA. In general, participants perceived datasets representing larger but less reliable group differences as stronger evidence of a population effect than datasets representing smaller yet more reliable differences, across various data formats (Experiment 1) and datasets (Experiment 2). Qualitative results revealed several distinct patterns of reasoning between participants which was associated with performance. Implications for instruction are discussed.

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Formative Use of Intuitive Analysis of Variance

Cited by 5 publications

References 24 publications

Visual comparison of two data sets: Do people use the means and the variability?

Visual comparison of two data sets: Do people use the means and the variability?

A Model of Scientific Data Reasoning

Aspects of first year statistics students’ reasoning when performing intuitive analysis of variance: effects of within- and between-group variability

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