I in deciding what my error bars should be

In summary: It is a good thing to check for yourself, and be able to explain to others who ask you about it.In summary, the conversation discussed an experiment on dissolved oxygen concentration in a stirred tank reactor at different flow rates and agitator speeds. They did not do any repeat measurements and are unsure of what error bars to include on their graph. They considered using standard errors of the mean or instrumental uncertainties, but both have limitations. The expert suggests that repeating measurements under the same conditions is necessary for reasonable estimates on the uncertainties. They also briefly discussed how uncertainties propagate in calculations.
  • #1
jb95
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So, we did an experiment to find the dissolved oxygen concentration in % over time in a stirred tank reactor at 2 different flow rates and at 3 different agitator speeds. We did not do any repeat measurements, it was just one reading per condition. Now I am confused what sort of error bars I could include on my graph. I have fitted a line of best fit for the data. Error bars are usually standard errors of the mean but no repeats were done and hence I have no mean value to base it on. Should the error bars in this case be uncertainties in the variable arising from measuring instruments. Are there curve fitting error bars I could use here? If yes, what could they be?
Btw I am plotting 3 graphs in total. In the first graph, I am plotting three sets of data, each set representing the particular agitator speed, of DO% against time. The first one is for flow rate of 5L/min. The second graph is for flow rate of 10 L/min, and again there are 3 sets of data of DO against time. The 3rd graph is of Mass transfer coefficient*Area (Kla) vs agitator speed. There would be 2 lines on the same graph because each line corresponds to a flow rate condition. I have fitted a best fit line on the first two graphs to calculate the gradient and hence Kla. I think I will put a trendline for Kla vs speed graph too.
 
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  • #2
In most cases, an experimenter needs repeated measurements under the same conditions to have error bars, and the standard error of the mean is used to estimate the uncertainties. https://en.wikipedia.org/wiki/Standard_error

Occasionally, one does include instrumental uncertainties to the standard error of the mean by adding the uncertainties in quadrature, but using only the instrumental uncertainties is equivalent to assuming the standard error of the mean is zero, which isn't really right either.

I think the bottom line is you need to repeat measurements under the same conditions to have reasonable estimates on the uncertainties.
 
  • #3
Dr. Courtney said:
In most cases, an experimenter needs repeated measurements under the same conditions to have error bars, and the standard error of the mean is used to estimate the uncertainties. https://en.wikipedia.org/wiki/Standard_error

Occasionally, one does include instrumental uncertainties to the standard error of the mean by adding the uncertainties in quadrature, but using only the instrumental uncertainties is equivalent to assuming the standard error of the mean is zero, which isn't really right either.

I think the bottom line is you need to repeat measurements under the same conditions to have reasonable estimates on the uncertainties.
Thank you Dr. Courtney. I just had one more thing to check with you for this lab report. If a quantity x is some function of 1/y^3 (y is being measured), the percentage uncertainty in y is 0.7%, then the would the percentage uncertainty propagated in x be 3*0.7?
 
  • #4
jb95 said:
Thank you Dr. Courtney. I just had one more thing to check with you for this lab report. If a quantity x is some function of 1/y^3 (y is being measured), the percentage uncertainty in y is 0.7%, then the would the percentage uncertainty propagated in x be 3*0.7?

There are many times when uncertainties propagate like this.
 

1. What are error bars and why are they important in scientific research?

Error bars are graphical representations of uncertainty in data. They show the range of values within which the true value is likely to fall. They are important because they provide a visual representation of the reliability and accuracy of the data, allowing researchers to assess the precision of their results and draw meaningful conclusions.

2. How do I determine the appropriate length of error bars for my data?

The length of error bars is determined by the type of data and the statistical analysis being performed. Generally, error bars represent either the standard error or the confidence interval of the data. The standard error is calculated by dividing the standard deviation of the data by the square root of the sample size. The confidence interval is determined by the desired level of confidence, typically 95%. Consult a statistician or statistical software for assistance in determining the appropriate length of error bars for your data.

3. Can I use error bars for any type of data?

Error bars are commonly used in scientific research, but they may not be appropriate for all types of data. They are most useful for representing continuous data with a normal distribution. If your data is categorical or non-normal, alternative methods such as box plots or violin plots may be more suitable for displaying uncertainty.

4. How do I interpret error bars on a graph?

The length of the error bars represents the amount of uncertainty in the data. The longer the error bars, the greater the uncertainty. If the error bars overlap between two groups, it suggests that there is no significant difference between the two groups. If the error bars do not overlap, it indicates a significant difference between the groups. It is important to also consider the size of the error bars in relation to the size of the data points on the graph.

5. Are error bars the only way to represent uncertainty in data?

No, there are other methods for representing uncertainty in data, such as confidence intervals, standard deviation, and standard error. Depending on the type of data and the specific research question, other graphical representations such as box plots, violin plots, or histograms may also be more appropriate. It is important to choose the method that best represents the data and accurately conveys the level of uncertainty to the audience.

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