Web Visualization: Confidence intervals for the mean

Students often have trouble interpreting confidence intervals and hold some common misconception. For instance, many students believe, for the same data and parameter of interest, a 90% confidence interval is wider than a 95% confidence interval. This visualization was designed to help mitigate some of these misconceptions with confidence intervals.

Comments about what we learned from trialing the resource:

• Students need clear instructions when taking repeated samples. Some students were confused about the sampling process, such as how long to keep sampling and when they should stop (“The part that really didn’t work well is the creating repeated samples…otherwise we don’t know when to click on ‘stop’… worried and stuff…”). Clearer instructions were provided to prevent the student from moving away from repeated sampling process too soon, and helped them gauge how long to keep sampling.
• Some students found the repeated sampling too slow. The sampling process was adjusted to hit the right balance in terms of speed to allow enough time for students to grasp what was happening on the screen, but without letting the sampling run too long so that the student disengages.



“Kind of going on for too long. Should point out the stop button sooner. Kind of get the idea of what’s happening”

• Students liked the interactive, hands-on nature of visualizations. Most of the students commented that the simulation was good for visualizing the effect the confidence level, standard deviation and sample size had on the width of the confidence intervals.



“Cool. Never seen anything like it! Pretty straight forward. Like how fish changes to bar graph, sliders, drop down thing. … [Repeated Sampling Process] Really liked it. Good that they have slower and faster buttons.”




“Creating all of the samples is fun to watch”

• We recommend that the “Sampling from a Normally distributed population” web visualization be used as a primer for the Confidence Interval web visualization. From our interviews, we found students who interacted with the Sampling from Normal web visualization prior to the Confidence Interval web visualization had a better understanding of the context of these proceeding simulations (i.e. how the samples are drawn, what the population mean represents with respect to the example). Students using only the Confidence Interval applet requested more explanation about the population mean and standard deviation. For instance, one student commented that he did not understand what represented with respect to the example, which suggests that he did not understand the basic premise of the simulation.



“Confidence interval part was much more difficult than the sampling distribution of means… sampling distribution of means was more clear. Sampling distribution of means… there was more section of how sampling is really happening…. More instruction in the sampling part is helpful.”