Hat Graphs 1 Running Header - OSF

Hat Graphs 1

Running Header: INTRODUCING HAT GRAPHS

Introducing Hat Graphs

Jessica K. Witt

Colorado State University

Under review at Cognitive Research: Principles and Implications

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Visualizing data through graphs can be an effective way to communicate one’s results. A ubiquitous

graph and common technique to communicate behavioral data is the bar graph. The bar graph was first

invented in 1786 and little has changed in its format. Here, a replacement for the bar graph is proposed.

The new format, called a hat graph, maintains some of the critical features of the bar graph such as its

discrete elements, but eliminates redundancies that are problematic when the baseline is not at 0. Hat

graphs also include elements designed to improve Gestalt grouping principles and engage object-based

attention. The effectiveness of the hat graph was tested in two empirical studies for which participants

had to find and identify the condition that lead to the biggest improvement from baseline to final test.

Performance with hat graphs was 30 - 40% faster than with bar graphs.

Key words: Information visualization; graphs

Significance Statement: Visualizations are an important way to communicate results from data. As Big

Data has increased impact on daily life, communication of data is of critical importance. The bar graph is

ubiquitous and yet has not been fundamentally updated since its inception in the 18th century. The hat

graph is offered as a modernized version that more effectively communicates differences across

conditions. Hat graphs increased the speed to find the condition associated with the biggest difference

by 30-40% relative to bar graphs. Hat graphs can significantly improve how scientists communicate their

data.

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Introducing Hat Graphs

Bar graphs are a common technique to visualize data in psychology. In a recent issue of

Psychological Science, 50% of the articles included a bar graph (2018, v 29, issue 12). The bar graph

dates back to 1786 (Playfair, 1786), and the first bar graph bares great resemblance to typical bar graphs

used today. Bar graphs are problematic for behavioral research. Bar graphs depict differences in two

ways: one is by the relative position of the end of each bar and the other is by length of each bar (and,

perhaps a third, is by area of each bar). If the baseline of the graph is not set to 0, these various sources

of information will be inconsistent with each other. The relative position of the bar ends will accurately

reflect the differences between the bars, but the relative difference in length will be exaggerated (in

cases for which the baseline is greater than 0 and the bars are positive) or understated (in cases for

which the baseline is less than 0 and the bars are positive). For this reason, users are encouraged to

always use a baseline of 0 for bar graphs (Pandey, Rall, Satterthwaite, Nov, & Bertini, 2015). However,

this baseline creates large biases in readers’ perceptions of the size of effects depicted in bar graphs

(Witt, in press). Even big effects appear small with a baseline at 0. An ideal baseline is one that is at

least 0.75 standard deviations (SDs) below the general mean so as to maximize compatibility between

the visual size of the effect and the effect size being depicted. Given that effect size in psychology is

often measured in terms of SDs, and an effect size of 0.8 is considered “big” (Cohen, 1988), it is sensible

to set the range of the y-axis to be 1.5 SDs. This range is problematic when using bar graphs, however,

given the mixed meanings across the different features when the baseline is not set to 0.

Alternatives to bar graphs include point graphs and line graphs. Point graphs have the

advantage that only one feature specifies the data, namely relative position. Thus, inconsistencies are

not created by non-zero baselines. But point graphs do not have as strong Gestalt grouping principles to

help facilitate perceptual grouping of pairs of data points. This grouping problem can be solved by

connecting the points with a line, thus making the graph a line graph. Line graphs are a natural choice

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when communicating trends, such as differences in a dependent variable across a continuous

independent. Line graphs are not, however, a natural choice when communicating discrete values.

They can even lead to misinterpretations of discrete variables, such as when comparing across distinct

groups like construction workers versus librarians.

The goal here was to create a new kind of graph that had the strong grouping properties of bar

and line graphs, the natural discrete interpretations of bar graphs, and the flexibility to have a

standardized y-axis range with a non-zero baseline. The new graph format, called hat graphs, is a simple

modification from the bar graph (see Figure 1). The “brim” of the hat is the top border of the bar of the

first of a pair of conditions. The “crown” of the hat is the portion of the bar from the second of the pair

that is different from the first. Thus, the information contained in the hat graph is the same as the

information in the bar graph. Now, however, the length of the bar (i.e., the size of the hat) corresponds

to the difference between the two conditions. Typically it is differences between two conditions that

represents the main finding in a paper, so the hat graph also has the advantage of emphasizing the key

result. Because the data are no longer represented as bars themselves, a non-zero baseline will not

create conflicting interpretations of the data. Because the pieces of the hat are connected, the hat will

benefit from some of the strongest Gestalt grouping principles (connectedness, proximity) and likely be

seen as a single object.

Figure 1. Illustration of the format of the hat graph as it relates to a bar graph.

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To corroborate these theoretical advantages for hat graphs, empirical studies were conducted

to explore the relative benefits of hat graphs versus bar graphs. In three experiments, participants

made judgments about the best advertisement on change in attitudes from baseline to final test based

on information displayed in bar graphs or hat graphs.

Experiment 1

Participants were shown images depicting attitude scores on baseline and final tests for 3 or 6

advertisements. Their task was to indicate which advertisement produced the largest improvement in

attitude at final score over baseline.

Method

Participants. Twenty-two participants volunteered in exchange for course credit. Given the

theoretical reasons to think hat graphs would have an advantage over bar graphs, a large effect was

assumed. A power analysis for a paired-samples t-test with an effect size of d = 0.80 and alpha = 0.05

(two-tailed) showed that 14 pairs are needed to achieve 80% power. Data collection was scheduled to

stop on a day for which this number was likely to be achieved, although more participants were

collected than needed, resulting in 95% power to find an effect size of d = 0.80.

Ethics, Consent and Permissions. All participants provided informed consent, and the protocol

was approved by Colorado State University’s IRB (protocol number 12-3709H).

Stimuli and Apparatus. Stimuli were displayed on computer monitors. The stimuli were

created using data simulated and plotted in R (R Core Team, 2017). Four factors were manipulated.

One factor was graph type (hat graph versus bar graph). Each set of simulated data were plotted with a

hat graph and with a bar graph. Another factor was number of advertisements (3 or 6). A third factor

was the position of the target (best) advertisement. These were evenly distributed across the locations,

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and target position was repeated for the graphs with only 3 advertisements. The fourth factor was the

alignment across advertisements. One third of the graphs were aligned to have similar baselines, so the

target advertisement also had the highest final score. One third were aligned to have similar final

scores, so the target advertisement had the lowest baseline score. The final third were aligned at the

center or middle value between baseline and final score (see Figure 2). Each graph style was repeated 4

times to have several variants to show to the participants. This resulted in 288 unique graphs (288 = 2 x

2 x 6 x 3 x 4).

A B

C D

Figure 2. Sample graphs from Experiment 1. Panels A and B show the hat graph version and the bar graph version of the same data. Panels A, C, and D show the 3 types of alignment (baseline, final, center, respectively).

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Data for the graphs were created from simulations. As noted below, the task for participants

was to indicate which advertisement produced the largest change in attitude, so the critical data are the

differences between conditions. For the non-target advertisements, the differences between baseline

and final scores were the mean value of 100 samples from a normal distribution with a mean of 1 and a

SD of 2. For the target advertisements, the differences between baseline and final scores were the

mean value of 100 samples from a normal distribution with a mean of 2.5 and a SD of 1. Thus, the

target advertisement produced a bump in attitude scores 2.5 times more than the non-target

advertisements. These difference scores were added to the baseline scores for the baseline aligned and

center aligned graphs. For these graphs, the baseline scores were the mean value of 100 samples from

a normal distribution with a mean of 3 and a SD of 1. For the final align graphs, the final scores were the

mean value of 100 samples from a normal distribution with a mean of 5.5 and a SD of 1, and the

difference score were subtracted from the final scores. The process was the same for the target

conditions with the exception that .5 was subtracted from the baseline condition so that it would not

align with the other baseline conditions.

For each set of data, two graphs were created. One was a bar graph and one was a hat graph.

Thus, the data contained in the graphs were identical across graph types. For the bar graph, the

baseline condition was white and the final condition was black. For the hat graphs, the lines were black

and the crown was white. The y-axis ranged from 1 to 8 on every graph. Advertisements were labeled A

– F and were always in alphabetical order.

Procedure. Participants completed two blocks of trials, one with bar graphs and one with hat

graphs. Start order was counterbalanced across participants. For the hat graphs, they were shown

these initial instructions: “An advertising company is interested in which ads lead to the biggest changes

in attitude. They ran a study testing several different ads. In each study, they measured attitude at

BASELINE (before seeing any ads) and again at the FINAL test (after seeing the ads). All of the ads

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increased attitude. Your task is to determine which ad produced the BIGGEST increase in attitude. The

baseline attitude will be shown as a horizontal line. The final attitude is shown as the top of the box. The

height of the box shows the change in attitude from baseline to final test. Which ad produces the

biggest change? Enter your response for each graph on the keyboard. Respond as fast and accurately as

possible. Press ENTER to begin”. For the bar graphs, the instructions were the same except instead of

describing the hat graph, they were told the following: “The baseline attitude will be shown in white

boxes. The final attitude will be shown in black boxes. The difference between the white and black

boxes shows change in attitude from baseline to final test.”

On each trial, after a fixation screen of 500ms, a graph was shown and participants entered a

response A-C (for graphs with 3 advertisements) or A-F (for graphs with 6 advertisements). The graph

remained visible until participants made their response. At which point, a blank screen was shown for

500ms before the next trial began. Participants completed 144 trials with one type of graph before

switching to the block of trials with the other graph type. Order within block was randomized.

Results and Discussion

The data were initially explored for outliers. Reaction times (RTs) beyond 1.5 times the

interquartile range (IQR) for each subject for each condition were excluded (6.2% of the data). Next,

median RTs and mean accuracy scores were calculated for each subject and each condition and

submitted to separate boxplots. No participants were beyond the IQR on the RTs but four were beyond

1.5 times the IQR for accuracy scores. These participants were excluded. For remaining participants,

accuracy was nearly perfect (M = 98.9%, SD = 1.2%), so the analysis focused on RTs.

RTs are positively skewed, so they were log-transformed. Data were analyzed with linear mixed

models using the LME4 and LMERTEST packages in R (Bates, Machler, Bolker, & Walker, 2015;

Kuznetsova, Brockhoff, & Christensen, 2017). A linear mixed model was run with the log RTs as the

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dependent factor. The independent factors were graph type (bar or hat), number of advertisers (3 or 6;

entered as a factor), graph alignment (baseline, final, center), and start condition. Only two-way

interactions with graph type were included in the model. Random effects were included for participant

including intercepts and slopes for graph type and number of advertises. The model did not converge

with the inclusion of a random slope for graph alignment. Random intercepts were also included for

each set of simulated data that was plotted in both the hat and bar graphs. The main effect of graph

type was significant, t = 12.66, p < .001, estimate = 0.48, SE = .04. Relative to hat graphs, responses to

bar graphs were 38% slower (see Figure 3).

Figure 3. Reaction time is plotted as a function of number of items and graph type for Experiment 1. The brim of the hat corresponds to the RTs for the hat graph condition, and the top of the crown of the hat corresponds to RTs for the bar graph condition. The size of the crown indicates the difference in RTs between the two conditions. Error bars are 1 SEM calculated within-subjects. The range of the y-axis is 4 within-subjects SDs.

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The main effect of number of items was significant, t = 5.90, p < .001, estimate = .13, SE = .02.

Going from 3 to 6 items was associated with a 14% increase in reaction time. The interaction between

graph type and number of items was not significant, t = -0.27, p = .78, estimate < .01, SE = .01. Thus, hat

graphs made people faster at finding the target item but not necessarily more efficient given the similar

search slopes (see Figure 3). Graph alignment had a significant effect on RTs. RTs were 5% slower when

the final scores were aligned than when the baseline scores were aligned, t = 2.23, p = .027, estimate =

.054, SE = .02. RTs were just less than 5% slower when the center of both scores were aligned than

when the baseline scores were aligned, t = 1.97, p = .050, estimate = .048, SE = .02. The interaction

between graph type and graph alignment was significant. RTs were 6% faster with hat graphs than with

bar graphs when the baseline scores were aligned than when the final score were aligned, t = 3.88, p <

.001, estimate = .06, SE = .02, and were less than 3% faster with hat graphs than with bar graphs when

baseline scores were align than when center values were aligned, though this did not reach statistical

significance, t = 1.67, p = .096, estimate = .026, SE = .015 (see Figure 4).

Figure 4. Reaction time is plotted as a function of number of items and graph type for Experiment 1. The brim of the hat corresponds to the RTs for the hat graph condition, and the

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top of the crown of the hat corresponds to RTs for the bar graph condition. The size of the crown indicates the difference in RTs between the two conditions. Error bars are 1 SEM calculated within-subjects. The range of the y-axis is 4 within-subjects SDs.

There was a significant interaction between graph type and start condition, t = 4.74, p < .001,

estimate = .26, SE = .06 (see Figure 5). Hat graphs had a bigger advantage over bar graphs for people

who started with the bar graphs than for people who started with the hat graphs. Another way to

interpret this pattern, however, is that both groups got faster in the second block, and there was also a

main effect of graph type (see Figure 5).

Figure 5. Reaction time is plotted as a function of graph type and start condition (left panel) or block (right panel) for Experiment 1. The brim of the hat corresponds to the RTs for the hat graph condition, and the top of the crown of the hat corresponds to RTs for the bar graph condition. The size of the crown indicates the difference in RTs between the two conditions. In the left panel, error bars are 1 SEM calculated within-subjects for each start condition. In the right panel, the error bars are 1 SEM calculated between-subjects. The range of the y-axis is 6 within-subjects SDs.

Hat graphs improved speed to find the advertisement that produced the biggest boost in

attitude relative to bar graphs.

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Experiment 2

Experiment 2 serves as a replication of Experiment 1. The effect size depicted in the graphs was

slightly smaller than in Experiment 1.

Method

Seventeen students volunteered in exchange for course credit. Everything was the same as in

Experiment 1 except the target difference was simulated as a magnitude of 2 (rather than 2.5).

Results and Discussion

Data were analyzed as before, and 5% of trials were excluded because the RT was beyond 1.5

times the IQR for that participant for that condition. RTs were then summarized for each participant for

each condition, and 3 participants were identified as having a median RT greater than 1.5 times the IQR

for the group and 4 participants had mean accuracy scores less than 1.5 times the IQR for the group. All

7 were excluded. This eliminated a large portion of the data, but resulted in the inclusion of 10

participants, which was sufficient to achieve 95% power to find an effect of d = 1.28 (as a one-sample t-

test). For the included participants, mean accuracy was 98.9% (SD = 1.2%).

The data were submitted to a linear mixed model with the log of the reaction times as the

dependent factor, graph type and number of items as independent factors, and subject and graph image

as random effects (including random slopes for subject for both independent factors). The main effect

for graph type was significant, t = 12.46, p < .001, estimate = 0.37, SE = .03 (see Figure 6). Participants

were 31% slower to respond to bar graphs than to hat graphs. The main effect for number of items was

significant, t = 7.16, p < .001, estimate = .17, SE = .02. Participants were 15% slower to respond to 6

items than to 3 items. The interaction between graph type and number of items was not significant, t =

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0.46, p = .64, estimate < .01, SE = .02. Hat graphs lead to faster response times but not more efficient

search slopes.


Responses were faster to graphs with aligned baselines than to graphs with aligned centers, t =

2.18, p = .031, estimate = .05, SE = .02. Participants were marginally faster to graphs with aligned

baselines than to graphs with aligned final scores, t = 1.61, p = .110, estimate = .04, SE = .02. The

interaction between graph type and alignment was significant for the comparison between baseline

aligned and final score aligned graphs, t = 2.10, p = .036, estimate = .05, SE = .02, but not for the other

comparisons, ps > .40 (see Figure 7).

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The interaction between graph type and start condition was significant, t = 7.02, p < .001,

estimate = .25, SE = .04. Participants who started with bar graphs were even faster with hat graphs

relative to bar graphs compared with participants who started with hat graphs (see Figure 8). An

alternative explanation is that both groups got faster from block 1 to block 2, and there was also a main

effect of graph type.

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Figure 8. Reaction time is plotted as a function of graph type and start condition (left panel) or block (right panel) for Experiment 2. The brim of the hat corresponds to the RTs for the hat graph condition, and the top of the crown of the hat corresponds to RTs for the bar graph condition. The size of the crown indicates the difference in RTs between the two conditions. In the left panel, error bars are 1 SEM calculated within-subjects for each start condition. In the right panel, the error bars are 1 SEM calculated between-subjects. The range of the y-axis is 6 within-subjects SDs.

The results replicate those found in Experiment 1 and show a large advantage for the hat graphs

over the bar graphs.

General Discussion

Hat graphs were designed based on principles of Gestalt grouping, graph design, and object-

based attention as a better alternative to bar graphs. The current experiments showed that

performance on detecting differences across pairs of conditions was 20% faster for hat graphs than for

bar graphs. In a 2 x N design for which comparisons across pairs of conditions is of interest, a graph of

the data is easier to read when the pairs are visually-grouped together. Such grouping can be readily

achieved through the principles of Gestalt grouping (Wagemans et al., 2012; Wertheimer, 1912). Hat

graphs leverage two of the strongest principles, namely connectedness and proximity. Because the brim

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of the hat is close to and physically connected to the crown, the hat should be seen as a grouped object.

This is likely to have contributed to why performance was better with the hat graphs than the bar

graphs.

Graph design principles also contributed to the creation of the hat graphs. According to graph

design, discrete elements (like in bar graphs) are more likely to be interpreted as a discrete effect (e.g.

“males are taller than females”) whereas continuous lines (like in line plots) are more likely to be

interpreted as a continuous effect even when such an interpretation is in appropriate (e.g. “the more

male a person is, the taller he is”, Zacks & Tversky, 1999). Although not directly tested here, the hat

graphs bare more of a resemblance to the discrete elements of the bar graph than the continuous

elements of the line graph. It is recommended that hat graphs be used instead of bar graphs for plotting

discrete data, whereas line graphs continue to be used for continuous data.

In addition to performance being better with hat graphs than with bar graphs, hat graphs have

another advantage related to graph design in that they are not restricted to having a baseline at zero.

Bar graphs should always have a zero baseline so that the impression given by the length of the bars is

consistent with the differences between the values of the various conditions (e.g., Pandey et al., 2015).

Hat graphs do not have the same restriction because they do not contain the misleading element within

bar graphs, namely bar length. It is important to not have the baseline be restricted to zero because

graph design indicates that for behavioral studies for which effect size is measured in terms of standard

deviations, the range of the y-axis should be 1.5 standard deviations (Witt, in press). Setting the y-axis

in this way helps to maximize compatibility between the visual impression of the effect and the size of

the effect. Small effects will look small and big effects will look big. In cases for which the size of the

effect is too big to fit within 1.5 SDs (as was the case in the current studies), the y-axis should be

expanded and its range noted in the figure caption.

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Another graph design principle concerns the data-to-ink ratio (Tufte, 2001). According to this

principle, redundant ink should be minimized within reason. For the bar graph, both the length of the

two side lines and the position of the top of the bar are all redundant, so to minimize redundant ink, one

could remove two of the three indicators. The hat graph has a higher data-to-ink ratio than the bar

graph, which could be one of the factors contributing to its advantage. The hat graph still contains

redundant elements (such as the brim of the hat). However, sometimes redundancy can be

advantageous for reading graphs, so it is important to not take the data-to-ink ratio too far (Carswell,

1992; Gillan & Richman, 1994). Future studies could determine whether adding or deleting ink from hat

graphs improves performance.

A third cognitive principle at play with hat graphs relates to attention. Attention can be

deployed spatially or towards a particular object (e.g., Posner, 1980; Scholl, 2001). With hat graphs, the

difference between conditions is itself an object and thus could benefit from object-based attention,

whereas the difference in spatial location between the brim of the hat and the crown of the hat could

benefit from spatial attention. With hat graphs, either type of attention would result in the same

outcome. Neither bar graphs nor point graphs would likely benefit as much as hat graphs from object-

based attention. The added benefit of the difference between conditions being represented as an

object and thus engaging object-based attention could contribute to the advantage for hat graphs over

bar graphs.

When researchers want to emphasize differences across two conditions (such as difference in

RTs), there is a dilemma whether to highlight the differences themselves by plotting those differences in

a bar graph versus plotting the raw RTs and having the reader infer the differences between the bars or

the points. Hat graphs solve this dilemma by plotting both at the same time. One disadvantage to the

hat graphs compared with plotting the differences themselves is that the crowns in the hat graphs are

unlikely to be perfectly aligned. The relative lengths of aligned bars are easier to discriminate than the

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relative lengths of misaligned bars (Cleveland & McGill, 1985). Thus, researchers will have to decide if

the added benefit of more precise estimate of length outweighs the benefit of showing both the

differences (as misaligned bars in the crown of the hat) and the raw scores. Of course, if precision is an

important goal for the researcher, the researcher could put the actual number corresponding to the

differences in or near the crown of the hat or in the text itself.

Hat graphs have a number of limitations and future research questions. One question concerns

the best way to add error bars. The figures here show one way to do so, but this format was not

empirically tested. Another limitation is how best to signal when the direction of the hat is reversed

from one condition to another (such as would be found in a crossed interaction). Perhaps filling in

crowns of hats that are “upside-down” would be beneficial, but reversing the hat so the brim points to

the right is another alternative. The Appendix provides R code for creating hat graphs, which can be

manipulated to try various options.

A critical limitation is that hat graphs are limited to 2 x N designs for which comparisons across

pairs are the critical comparisons. It is unclear how to expand hat graphs to allow comparison across 3

or more conditions. Many reported studies involve designs with factors that have 2 levels, so there is

plenty of room for hat graphs to exert their advantage even if they are not generalizable to all research

scenarios.

An unknown factor, and potential limitation, is that the current studies focused on a task for

which participants had to identify differences between baseline and final scores. The nature of the task

dictates which graph will be most appropriate (e.g., Gillan, Wickens, Hollands, & Carswell, 1998). For

finding differences, hat graphs proved to be more effective than bar graphs. However, if the task is

instead to ignore differences and identify the precise value of a given condition or identify the baseline

with the highest value, another format may prove more effective than hat graphs. According to the

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proximity compatibility principle (Wickens & Carswell, 1995), the greater proximity achieved in the hat

graphs should improve performance on an information integration task (such as finding the biggest

difference) but should decrease performance on a focused attention task (such as finding the precise

value of a particular condition).

In conclusion, hat graphs resulted in better performance than bar graphs. Hat graphs show that

design principles based on the nature of cognitive processes (e.g., Gestalt grouping principles, object-

based attention) can significantly improve how researchers visualize and communicate their data.

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Author Note

Jessica K. Witt, Department of Psychology, Colorado State University.

Data, scripts, and supplementary materials available at https://osf.io/khjb9/. For peer-review

process, use this link: https://osf.io/khjb9/?view_only=6c453d634ee24b019d1b247c5be14b6b. This

work was supported by a grant from the National Science Foundation (BCS-1632222). Author has no

competing interests to declare.

Address correspondence to JKW, Department of Psychology, Colorado State University, Fort

Collins, CO 80523, USA. Email: [email protected]

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Appendix: R Code for Creating Hat Graphs # Note: You can run code as is to get random data and see how graphs work # Instructions how to implement with your data below - see [1] # Instructions for how to add error bars - see [2] # Instructions for how to shade in upside-down hats - see [3] dt <- data.frame(subjectID = seq(1,30),DV = rnorm(30,50,20),IV1 = rep(c(1,2),15), IV2 = c(rep(1,15),rep(2,15))) #dt <- read.csv("YourDataHere.csv",header=T) #### [1] - HOW TO IMPLEMENT WITH YOUR DATA #### # Replace DV with your dependent measure (or name your dependent measure "DV") # Replace IV1 with your independent measure that you want paired in your hats (or name this measure "IV1") # Assumes only two levels of IV1 # Replace IV2 with your independent measure that you want spaced across the x-axis (or name this measure "IV2") # # Also replace label names here to match how you want your axes labeled: xLab <- "Independent Variable 2" yLab <- "Dependent Variable" legendLab <- c("IV1: Level 1","IV1: Level 2") upsideDownColor <- "black" #[3] Color to fill hat crown when second part is less than first part - set to "white" if you do not want shading ## Computes means for plotting # Also computes SD for setting y-axis range and for error bars # If your design involves within-subjects, see Loftus & Masson (1994) for computing SEM within-subjects dtMeans <- aggregate(DV ~ IV1 + IV2, dt, mean) dtSEM <- aggregate(DV ~ IV1 + IV2, dt, sd) #assumes between-subjects effects only dtMeans$SEM <- dtSEM$DV / sqrt(length(unique(dt$subjectID))) dtMeans$hatPos <- as.integer(as.factor(dtMeans$IV1)) dtMeans$xPos <- as.integer(as.factor(dtMeans$IV2)) ## Values for setting the range of the y-axis # Based on recommendations from Witt (in press) # If data do not fit in graph with this value, increase .75 to greater number # Should not decrease .75 grandMean <- mean(dtMeans$DV) grandSD <- mean(dtSEM$DV) * .75 # produces y-axis range of 1.5 SDs (see Witt (in press) for details) hatWidth <- .25

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plot(dtMeans$IV1,dtMeans$DV,ylim=c(grandMean - grandSD,grandMean + grandSD),xlim=c(min(dtMeans$xPos) - (2 * hatWidth),max(dtMeans$xPos) + (2 * hatWidth)),xaxt="n",col="white",bty="l",xlab=xLab,ylab=yLab) axis(side = 1, at=dtMeans$xPos,labels = dtMeans$IV2) for (i in unique(dtMeans$xPos)) { m1 <- which(dtMeans$xPos == i & dtMeans$hatPos == 1) m2 <- which(dtMeans$xPos == i & dtMeans$hatPos == 2) segments(i-hatWidth,dtMeans$DV[m1],i,dtMeans$DV[m1],lwd=3) # Brim of the hat if (dtMeans$DV[m2] > dtMeans$DV[m1]) { rect(i,dtMeans$DV[m1],i+hatWidth,dtMeans$DV[m2],lwd=3) # Crown of the hat } else { rect(i,dtMeans$DV[m1],i+hatWidth,dtMeans$DV[m2],lwd=3, col=upsideDownColor) # Crown of the hat } } # [2] - Add error bars dtMeans$semPos <- ifelse(dtMeans$hatPos == 1, dtMeans$xPos - (hatWidth/2), dtMeans$xPos + (hatWidth/2)) for (i in 1:length(dtMeans$semPos)) { segments(dtMeans$semPos[i],dtMeans$DV[i] - dtMeans$SEM[i],dtMeans$semPos[i],dtMeans$DV[i] + dtMeans$SEM[i]) } # Add Legend legend("topleft",pch=c(NA,0),lwd=c(3,NA),pt.cex=c(NA,3),cex=1.5,legend=legendLab,bty="n")

Hat Graphs 23

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