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How do we (MIS)interpret graphs?

Learn how to correctly interpret histograms and box plots while avoiding common misconceptions in data analysis. Understand Tversky's graph design principles and the challenges university students face in interpreting graph data. Discover the importance of spatial metaphors and directionality in accurate graph analysis.

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How do we (MIS)interpret graphs?

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  1. How do we (MIS)interpret graphs? Nataly Beribisky

  2. Interpreting graphs • Commonly used graphs such as histograms and boxplots are often a cleaner and more accessible way to present data. • However, although graphs may help us in interpreting data, we may sometimes misinterpret them.

  3. Tversky’s graph design principles • (1) the use of spatial metaphors • Natural use of space • Area of a graphical element should correspond to its property like proportion or frequency • (2) the use of directionality. • We focus more on vertical dimensions than horizontal ones •  ”the top is naturally viewed as more or better than the bottom”

  4. On the misinterpretation of histograms and box plotsLem, onghena, Lieven, verschaffel & Van dooren (2012) N = 125 university students in an educational science course. Participants were asked to respond to statements made about four different items.

  5. iTEM 1: comparing SAMPLE SIZE

  6. TWO CHILDREN ASKED THEIR FRIENDS HOW MANY PETS THEY HAD. both CHILDREN THEN PRESENTED THEIR DATA WITH THE REPRESENTATION BELOW B A 2 4 6 8 10 12 14 16 18 2 4 6 8 10 12 14 16 18 ITEM 1 - B asked more children about their pets than A: TRUEFALSEINDETERMINABLEI DON’T KNOW

  7. TWO CHILDREN ASKED THEIR FRIENDS HOW MANY PETS THEY HAD. both CHILDREN THEN PRESENTED THEIR DATA WITH THE REPRESENTATION BELOW 987654321 987654321 B A 2 4 6 8 10 12 14 16 18 2 4 6 8 10 12 14 16 18 ITEM 1 - B asked more children about their pets than A: TRUEFALSEINDETERMINABLEI DON’T KNOW

  8. TWO CHILDREN ASKED THEIR FRIENDS HOW MANY PETS THEY HAD. both CHILDREN THEN PRESENTED THEIR DATA WITH THE REPRESENTATION BELOW ITEM 1 - B asked more children about their pets than A: TRUEFALSEINDETERMINABLEI DON’T KNOW

  9. IN WHICH CASE DID Participants HAVE THE MOST TROUBLE?

  10. Results to item 1 • “According to design principle on the use of space in graphs, people will try to interpret space between elements in a graph, but also area, in a natural way. In the case of the box plot, this means that students can be expected to interpret the area of the box as representing frequency or proportion of observations. As it is in fact not possible to derive from the box plot the number of observations on which it is based, this is likely to lead to an incorrect conclusion.”

  11. iTEM 2: comparing MEANS

  12. TWO CHILDREN ASKED THEIR FRIENDS HOW MANY PETS THEY HAD. both CHILDREN THEN PRESENTED THEIR DATA WITH THE REPRESENTATION BELOW B A 2 4 6 8 10 12 14 16 18 2 4 6 8 10 12 14 16 18 ITEM 2 – The mean number of pets is the same in both figures: TRUEFALSEINDETERMINABLEI DON’T KNOW

  13. TWO CHILDREN ASKED THEIR FRIENDS HOW MANY PETS THEY HAD. both CHILDREN THEN PRESENTED THEIR DATA WITH THE REPRESENTATION BELOW 987654321 987654321 B A 2 4 6 8 10 12 14 16 18 2 4 6 8 10 12 14 16 18 ITEM 1 - The mean number of pets is the same in both figures: TRUEFALSEINDETERMINABLEI DON’T KNOW

  14. TWO CHILDREN ASKED THEIR FRIENDS HOW MANY PETS THEY HAD. both CHILDREN THEN PRESENTED THEIR DATA WITH THE REPRESENTATION BELOW ITEM 1 - The mean number of pets is the same in both figures: TRUEFALSEINDETERMINABLEI DON’T KNOW

  15. IN WHICH CASE DID Participants HAVE THE MOST TROUBLE?

  16. Results to item 2 • Possible misconceptions: (coming from directionality principle) • For histograms: would think that figure with higher bars would make participants believe that means was higher. • For boxplots: expected that students might interpret the higher box as representing a higher mean • Results: • Students comparing descriptive statistics all got the correct answer. • When students answered the histogram response incorrectly, they often stated that the mean was not the same. • Boxplot confusion occurred much less frequently

  17. other misinterpretations • Evidence that participants may not view the whiskers of the boxplots as containing data. • Illusion that we know specific values from graphs and from descriptive statistics • When asked about a specific value, participants stated that it was possible to tell that it was in the dataset from reading boxplots, histograms, and descriptive statistics.

  18. Conclusions • In these instances, descriptive statistics were easier to interpret than graphs. • When using graphs to communicate, we should try to implement good design principles, so that interpretations are as clear as possible.

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