Do you want to calculate the average for each group of trials, or summarize the results in some other way such as ratios, percentages, or error and significance for really advanced students? Or, is it better to display your data as individual data points?
Do any calculations that are necessary for you to analyze and understand the data from your experiment. Graphs are often an excellent way to display your results. In fact, most good science fair projects have at least one graph. The example line graph shows three different brands of batteries in color coded lines and measures the voltage remaining as the battery is used over time.
A key to the right of the graph shows Duracell represented by a red line, Energizer represented by a green line and Panasonic represented by a blue line. All batteries start at 1. After around 5 hours the Panasonic battery is drained completely while the Energizer and Duracell batteries drain at a very similar rate, lasting for hours. Different types of graphs are appropriate for different experiments.
These are just a few of the possible types of graphs:. A bar graph might be appropriate for comparing different trials or different experimental groups. It also may be a good choice if your independent variable is not numerical. In Microsoft Excel, generate bar graphs by choosing chart types "Column" or "Bar.
A time-series plot can be used if your dependent variable is numerical and your independent variable is time. In Microsoft Excel, the "line graph" chart type generates a time series. By default, Excel simply puts a count on the x-axis. To generate a time series plot with your choice of x-axis units, make a separate data column that contains those units next to your dependent variable.
Then choose the "XY scatter " chart type, with a sub-type that draws a line. An xy-line graph shows the relationship between your dependent and independent variables when both are numerical and the dependent variable is a function of the independent variable.
In Microsoft Excel, choose the "XY scatter " chart type, and then choose a sub-type that does draw a line. Rather, they found that high graphicacy students were only influenced by format expectations when the graph depicted data from a known domain.
Specifically, high graphicacy students were more likely to identify main effects in bar graphs only when the subject matter was familiar to them. When the domain was unfamiliar, there was no difference in performance between graph formats.
The authors did find however that the identification of interactions from both high and low graphicacy participants was affected by graph format in the predicted way i. While it is unclear to what extent high graphicacy students can be considered experts, Shah and Freedman's experiment can be seen as providing at least tentative evidence that could challenge previous recommendations to use line graphs because of experts' ability to recognize interactions using common patterns created by the lines e.
Shah and Freedman found no effect of graph skill on interaction descriptions and while they did show that both high and low graphicacy participants were affected by graph format, they found no evidence that line graphs supported identification of interactions more than bar graphs in either group.
It may be the case therefore, that once users have obtained a certain level of graphical literacy, they are able to apply their knowledge to override differences in Gestalt grouping or visual salience between graph types to interpret data appropriately whatever graph they use. The experiment reported here aims to answer the questions raised in the above discussion by focusing more closely on the types of individuals we study. Unlike previous research in this area including our own that has predominantly used undergraduate students, we recruited participants from academic faculty in the areas of scientific psychology and cognitive science who have sufficient experience either through teaching or research or a combination of both of ANOVA designs to be considered expert users of interaction graphs.
The sample was representative of the range of expertise typically found in academia and ranged from early career researchers and assistant professors to full professors. Experience in the field at post-doctoral level ranged from a few years to decades. The sample was gathered from multiple centers and participants included British and international academics who could be considered experts in the field.
Using this participant group, we aim to determine whether experts' interpretations of unfamiliar data differ depending upon whether the data is presented in bar or line graph form. In so doing we also aim to ascertain the relative effects of bottom-up and top-down processes i. This will allow us to quantify the amount of benefit, if any, that line graphs provide for expert users as suggested by Kosslyn, and to determine whether this is outweighed by other factors e.
The second aim of this experiment is to determine whether the processes by which experts achieve their interpretations differ using the two graphs. Although it may be the case that experts are able to produce accurate and roughly equivalent interpretations of bar and line graphs, the processes by which they do so may be quite different and affected significantly by graphical features.
Specifically, previous studies using non-expert samples have shown that graph format affects the order in which people interpret the graph; people typically interpret the legend variable before the x axis variable when using line graphs Shah and Carpenter, but the opposite order when using bar graphs Peebles and Ali, In addition, line graphs may facilitate pattern recognition processes that bar graphs do not which may lead to more rapid identification of interaction effects.
A third, related aim of the experiment is to determine whether interpretation order is affected significantly by the relative size and as a result salience of the patterns formed by the various relationships in the data. By recording a range of behavioral measures such as the number of correct interpretations, the sequential order of interpretations, and task completion times, together with concurrent verbal protocols, we aim to construct detailed hypotheses relating to the processes underlying expert graph comprehension and to use the information obtained to evaluate the assumptions of the cognitive model, specifically the hypothesis that expert performance can be accounted for by a sequence of pattern recognition and knowledge retrieval processes.
Verbal protocol analysis is a technique widely used in cognitive science to obtain information about the processes being employed to perform tasks Newell and Simon, ; Ericsson and Simon, which has successfully brought to light a wide range of phenomena including nonverbal reasoning Carpenter et al. Taken as a whole, the verbal protocol and other behavioral data will allow us to determine the extent to which experts' performance differs from the optimal predictions of the model and provide valuable information to inform revisions of the currently assumed mechanisms and processes.
The participants were 42 11 female, 31 male university faculty i. Forty were educated to PhD level while two were in the latter stages of working toward a PhD while being employed as university teaching fellows. Participants were gathered from three locations. The majority of participants were faculty specializing in cognitive psychology and quantitative research methods from the universities of Keele and Huddersfield in the UK. The remaining participants were cognitive scientists attending an international conference on cognitive modeling.
The experiment was an independent groups design with one between-subject variable: the type of diagram used bar or line graph and 21 participants were allocated to each condition using a random process.
The stimuli were 16 three-variable interaction graphs—eight line and eight bar—depicting a wide range of fictional content using variables taken from a variety of non-psychology related sources.
The data sets were generated to create the main effects and interactions commonly encountered in these designs in a range of sizes. The y axis for all graphs started at zero and had the same 11 tick marks in the same locations although the values on the scales varied and data values were chosen so that all plotted points corresponded to a tick mark.
To classify the size of the effects we used the same procedure as used in the ACT-R model of Peebles The resulting classifications of the eight graphs are shown in Table 1. When matching data sets to graph content, care was taken to ensure that the effects depicted did not corresponded to commonly held assumptions about relationships between the variables although this would be unlikely given the specialized nature of the graphs' subject matter.
The graphs were presented on A4 laminated cards and were drawn black on a light gray background with the legend variable levels colored green and blue. A portable digital audio recorder was used to record participants' speech as they carried out the experiment.
The study was carried out in accordance with the ethical conduct recommendations of the British Psychological Society and was approved by the University of Huddersfield's School of Human and Health Sciences Research Ethics Committee. All subjects gave written informed consent in accordance with the Declaration of Helsinki. Participants were seated at a table with eight bar or line graphs randomly ordered and face down in front of them and informed that their task was to try to understand each one as fully as possible while thinking aloud.
In addition to concurrent verbalization during interpretation, participants were also asked to summarize the graph before proceeding to the next one. During the experiment, if participants went quiet the experimenter encouraged them to keep talking.
When participants had interpreted and summarized a graph, they were instructed to place the graph face down to one side and continue by turning over the next graph. Participants were not allowed to revisit graphs. Data analysis involved coding whether each of the effects was identified and noting the time taken to interpret each graph.
Audio recordings were transcribed prior to data coding with information identifying graph format being removed to ensure that coders were blind to graph format. To meet the requirements for identification of main effects, participants had to state explicitly that there was an effect e. To meet the requirements for identification of an interaction effect a participant had to state that there was an interaction effect e. To illustrate the general speed and efficiency of many of the expert participants' interpretations, the example verbal protocol below is a verbatim transcription of a not atypical expert participant interpreting the line graph version of Figure 1G.
Alright, so we have…you're either fasting or you're not. You have relaxation training or you don't. And so…not fasting…er…. So there's a big effect of fasting.
Very little glucose uptake when you're not fasting. And lots of glucose uptake when you are fasting. And a comparatively small effect of relaxation training. That actually interacts with fasting. The protocol which lasted 43 s reveals the speed with which the variables and their levels are established and the key relationships within the data identified.
Accuracy is not always perfect however; in addition to correctly identifying the main effect of the x variable and the interaction between the two IVs, the participant also incorrectly states that there is a small main effect of the legend variable. When disagreements were found the raters came to a consensus as to the correct code.
Our initial analysis sought to determine whether experts' identification of main and interaction effects was affected by graph format. Figure 2. The effect sizes vary from very small for main effect z to approaching medium for the interaction effect.
In all cases, the pattern of responses was in favor of the bar graph condition but, in general, the results indicate that any bottom-up or top-down effects that may exist are not strong enough to bias experts' interpretations significantly in favor of one graph format over another. The present study therefore has not detected any effect of graph format on experts' ability to identify the key relationships in the data.
Another measure of the effect of graph format on performance is task completion time because this may indicate differences in interpretation strategy. A t -test on the mean task completion time for bar graphs 1 min, 25 s and line graphs 1 min, 11 s showed that this was not the case however [ t Although graph format does not lead to significant differences in the number of effects and interactions identified or the time taken to interpret a graph, it may be the case that the format of the graph affects the processes by which experts interpret them.
For example, Shah and Carpenter found that people's understanding of the x-y relationship in three-variable line graphs was more comprehensive than their understanding of the z-y relationship due to the action of Gestalt processes whereas Peebles and Ali found the reverse effect in bar graphs. This typically leads to users focusing initially on the legend variable in line graphs and the x axis variable in bar graphs.
If expert users are susceptible to the same visual influences as novices, then it could be expected that they would be more likely to identify the main effect of the legend first in the line graph but the x axis main effect first in the bar graphs.
Alternatively, experts' well-practiced strategies may override any such influences. The two graph formats also differ in terms of the perceptual cues they provide to indicate the existence of an interaction. Line graphs provide a salient perceptual cue cross pattern or non parallel lines which is not as salient in bar graphs Pinker, ; Kosslyn, In addition, there may be an expectation effect—experts may be influenced by their knowledge that line graphs are most often used to represent interactions and may therefore be primed to look for them Shah and Freedman, If this is the case, it could be expected that experts will identify interaction effects first in line graphs but main effects first in bar graphs.
As with the previous analyses, there was no significant difference in the order of interaction and main effect identification between graph format conditions. This shows that experts are influenced neither by an expectation that certain effects will be present in particular formats nor the more salient perceptual line graph cue indicating an interaction effect.
Although we have found no differences in the patterns of identification due to Gestalt principles, user expectations, or different visual cues, the different perceptual cues in the two graphs may result in different patterns of inference to establish the existence of an interaction effect in bar graphs compared to line graphs. Specifically, interaction identification in line graphs may be triggered by the rapid identification of a salient pattern such as a cross and parallel lines [as assumed in the ACT-R model Peebles, ] whereas in bar graphs this pattern recognition process may not be as prevalent or influential.
To determine whether this is the case, we counted whether experts described the nature of the interaction prior to identifying the interaction effect in bar graphs and vice versa in line graphs. An example verbal protocol illustrating the first case recorded from a participant using the bar graph version of the graph in Figure 1B is presented below. When plant density is compact maize yield is higher. Otherwise it's the same in all other conditions. So it's an interaction between nitrogen level and plant density.
In contrast, an example verbal protocol illustrating the latter case recorded from a participant using the line graph in Figure 1E is listed below. Straight away I see an interaction. The effect of this factor is opposite depending on the rock type conditions. If you have bead diamond type cutting tool wear is highest under limestone whereas bead under granite condition cutting tool wear is lower. Bead works best in limestone and worse in granite. In the wire it's the opposite trend.
Cutting tool wear is lower in limestone and much higher in the granite. Definite interaction. The other thing is the effect is very consistent; the two higher bars are 8 and the lower ones are at 5. My summary is that if you're cutting limestone you want a bead type cutter, if it's granite then wire. Only trials where participants described both the nature of the interaction and stated explicitly the existence of the interaction were included in the analysis. Analysis of the verbal protocols revealed that expert line graph users predominantly state the interaction immediately and then continue to describe the nature of the interaction whereas expert bar graph users would be equally likely to ascertain the nature of the relationship between the variables through a process of interrogation and reasoning followed by an explicit identification of the interaction.
Explaining this variance in behavior in terms of experts' different expectations is implausible as the previous process analysis found no differences in preference for identification of main effect and interaction order between the graph formats.
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