Choosing the Best Error Bars to Use on a Graph

A workshop brought to you by Kristen Dotti of Catalyst Learning Curricula

 

Full recording of the same workshop presented on March 15, 2021. Note: this is not the live version presented. We forgot to record that one :)

 

Thank you so much for registering for Choosing the Best Error Bars to Use on a Graph

We had a great workshop with Kristen Dotti on Monday. Whether or not you were in attendance we want you to have access to the workshop because you reserved a ticket. We were thrilled to sponsor the event and wanted to follow up with some of the questions that were asked in the chat.

Here are questions we received during the workshop and via email.

Questions

 

  1. Is there a tutorial for adding error bars on DataClassroom?

    Yes! Here is the quick tutorial on adding visuals for descriptive stats from our How To series of YouTube videos useful for teachers or students.

  2. Can we get links to the datasets and slides that Kristen used in her presentation? 

    Here they are:   

    Kristen’s presentation slides

    Dataset: Impact of sample Size on SD, SEM, and 95CI

    Dataset: example experiment (breath holding pre and post relaxation)

  3. What is the difference between 2SEM and the 95%CI? Are these really the same thing?

    This is such a tough question to answer succinctly because in practice they really are almost the same thing. However, there is a difference and I think understanding what those numbers represent is the best way to understand that subtle difference. I think the best place to start is by understanding the relationship of the standard deviation to the true mean of a population.

 
68.2% of the observations fall within one standard deviation of the mean in a normally distributed population while 95.4% of all observations are expected within two standard deviations of the mean.

68.2% of the observations fall within one standard deviation of the mean in a normally distributed population while 95.4% of all observations are expected within two standard deviations of the mean.

 

This figure above shows normally distributed values for an entire population. For the sake of example let's say it is wing length in sparrows. 68.2% (34.1% x 2) of all sparrows in the population will have wing length measurements within 1 standard deviation from the population mean. 95.4% of all sparrows will have wing length measurements within 2 standard deviations from the mean ((34.1% x 2)+(13.6% x 2)). These are the assumptions we can make because we know the shape of a normal distribution.

Just as these measurements of wing length are normally distributed, if we take multiple samples from this population (say 10 birds at a time out of a population of 1,000) and calculate a mean for each sample of 10 birds, we expect the distribution of those sample means to be normally distributed. This is shown to be true even if the distribution of wing measurements is not normal; we always expect the distribution of sample means to be normally distributed around the true population mean. This is the central limit theorem.

With that in mind it is best to think of SEM as a sort of standard deviation of sample means (whereas the SD is a measure of variation for measurements). We expect 68.2% of all sample means to fall within 1 SEM of the true population mean. We expect 95.4% of all sample means to fall within 2 SEM of the true population mean.

The 95% confidence interval is the range where we would expect 95% of all sample means to fall within. Thus we are very confident that the true population mean falls within the 95% CI.

We don't often see 2SEM appear in scientific literature. 1 SEM is the most commonly seen error bar on a graph in my scientific field (evolutionary biology) and you see 95%CI when researchers really have a great sample size and want to show off how small their 95% CI is :) I think that 2SEM has been popular with AP bio because it is just a bit easier to calculate by hand than the 95%CI is (maybe?). I agree that it's use is confusing for learners trying to to understand the new vocabulary

To sum it up I would say that we expect 95.0% of all calculated means from population samples to fall within 95%CIs. We expect 95.4% of all calculated means from population samples to fall within 2 SEM of the true population mean. Thus the true population mean is very likely (you might say we are 95% confident) to fall within that range as defined by either 95%CI or 2SEM.

4. Are there more workshops by Kristen Dotti of Catalyst learning?

Click the CLC logo below to see upcoming workshops by Kristen Dotti of Catalyst Learning Curricula.

 

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