How to compare these two sets of data?

In summary, the conversation discusses two sets of data, with y as a function of x for two different experiments. The experiments were similar but yielded slightly different results. The speaker wants to compare the amount of error between the two sets of data and asks if there is a mathematical way to do so. The respondent mentions that the appropriate test depends on the data and suggests using a repetition test with the same instrument and concentration multiple times. They also mention that the data is not sufficient to draw specific conclusions and more data is needed. The speaker then clarifies the setup and the respondent suggests calculating the differences between measured values for each concentration to determine the standard deviation. They also mention that more repetitions and details about the setup would help in determining uncertainties and drawing
  • #1
Chemist125
16
0
Hi

I have two sets of data, y as a function of x, for two different experiments.

Y is the dependant variable, an instrument reading, x is the independant variable, a concentration of something in a solution.

Plotting the data in excel gives me 2 curves.

The experiments were essiantially the same, but the results are slightly different, I want to compare how much 'error' there is by comparing how close the data/curves from each experiment lie to each other. Is there some way I can do this mathematically?


Chem125
 
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  • #2
There are multiple tests, which test is appropriate here depends on the data.
 
  • #3
mfb said:
There are multiple tests, which test is appropriate here depends on the data.

I attached an excel sheet with example data.

What do you think?

Thanks
 

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  • #4
Chemist125 said:
I attached an excel sheet with example data.

What do you think?

Thanks
- the differences between the instruments are way smaller than the differences between the concentrations
- there is no repetition test where the same instrument was tested with the same concentration multiple times, therefore it is impossible to determine the accurary of the measurements based on that data alone. That would be really interesting.
- there is no clear systematic difference between the two instruments

The data is not sufficient to draw more specific conclusions, independent of the analysis method.
 
  • #5
mfb said:
- the differences between the instruments are way smaller than the differences between the concentrations
- there is no repetition test where the same instrument was tested with the same concentration multiple times, therefore it is impossible to determine the accurary of the measurements based on that data alone. That would be really interesting.
- there is no clear systematic difference between the two instruments

The data is not sufficient to draw more specific conclusions, independent of the analysis method.

That data shows a repetition test with the same concentrations...:confused: ...on the same instrument.

Sorry that I did not make this clear.
 
  • #6
Ah okay.
If we can assume the deviations are independent of the concentration, and there is no systematic difference between the two sets of measurements (unclear, but we don't have data to test this with any relevant precision), you can calculate all differences and find the standard deviation of them. This should be related to measurement uncertainties in some way. You would need more data to tell more.
 
  • #7
mfb said:
Ah okay.
If we can assume the deviations are independent of the concentration, and there is no systematic difference between the two sets of measurements (unclear, but we don't have data to test this with any relevant precision), you can calculate all differences and find the standard deviation of them. This should be related to measurement uncertainties in some way. You would need more data to tell more.

Yes, we can make those assumptions.

What do you mean calculate the differences?
 
  • #8
For concentration 1, take "measured value 1" - "measured value 2", repeat for all other concentrations. Something that would be 0 in the ideal case, if I understood your data.
 
  • #9
mfb said:
For concentration 1, take "measured value 1" - "measured value 2", repeat for all other concentrations. Something that would be 0 in the ideal case, if I understood your data.

Oh, I see what you mean. What extra data would I need to tell more?
 
  • #10
More repetitions would certainly help.

Some uncertainties or other issues could come from details of your setup, which is impossible to estimate without knowing the setup.
 

1. What is the purpose of comparing two sets of data?

The purpose of comparing two sets of data is to identify any similarities or differences between the data points. This can help in understanding patterns, trends, or relationships between the two sets and can provide insight into the underlying factors that may be influencing the data.

2. How do I choose which statistical test to use for comparing two sets of data?

The choice of statistical test depends on several factors such as the type of data, the number of groups being compared, and the research question being addressed. Some commonly used tests for comparing two sets of data include t-test, ANOVA, and Chi-square test. Consulting with a statistician or conducting a literature review can help in selecting the appropriate test.

3. What is the difference between descriptive and inferential statistics when comparing two sets of data?

Descriptive statistics involves organizing, summarizing, and presenting data in a meaningful way. It is useful for understanding the characteristics of the data. On the other hand, inferential statistics involves making conclusions or predictions about a larger population based on a sample of data. When comparing two sets of data, descriptive statistics can be used to summarize and visualize the data, while inferential statistics can be used to determine if there are significant differences between the two sets.

4. How do I interpret the results of a comparison between two sets of data?

The interpretation of the results will depend on the statistical test used. In general, the results will provide information about the significance of the differences between the two sets of data. For example, a p-value less than 0.05 indicates that there is a significant difference between the two sets, while a p-value greater than 0.05 suggests that there is no significant difference. It is important to also consider the effect size and the context of the data when interpreting the results.

5. What are some common pitfalls to avoid when comparing two sets of data?

One common pitfall is using the wrong statistical test or not understanding the assumptions of the test being used. It is also important to have a large enough sample size to ensure the results are representative of the larger population. Other pitfalls include not considering potential confounding variables or not properly interpreting the results. It is important to carefully plan and design the study and to seek guidance from a statistician when needed.

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