The situation I have encountered is a simple statistical comparison of the experimental data, which accepted as correct, with the results obtained via six theoretical models. In the experimental data, there exist y values corresponding to x values and also the measurement errors of y values.
Before formally analyzing the experimental data, it is important that we visualize it. Visualization is a powerful tool to spot any unconvincing situations — such as a failed randomization, a failed manipulation, or ceiling and floor effects — and to have an initial sense of the effect ’s direction.
In the experimental data, there exist y values corresponding to x values and also the measurement errors of y values. In theoretical values, there exist y values corresponding to the same x values as the experimental data. Theoretical values are calculated with six different models. I've uploaded an excel file as an example.
The main feature of an experiment that ensures the estimate of a causal effect is that people are randomly allocated to an experimental condition. This feature is called “ randomization ” and it prevents people with certain characteristics from self-selecting into the Treatment and the Control group.
(2nd Edition), Pierre Gy's theory and Sampling Practice, Vol. I. Heterogeneity and Sampling, CRC Press Inc, Florida (USA) (1989)
As with all research designs, the first step is to formulate the hypothesis or pose the research question. This leads to formulating the experimental design, which provides guidelines for planning and performing the experiment as well as analyzing the collected data.
Sandra Slutz, PhD, Staff Scientist, Science Buddies Kenneth L. Hess, Founder and President, Science Buddies Introduction. Whether your goal is to present your findings to the public or publish your research in a scientific journal, it is imperative that data from advanced science projects be rigorously analyzed.
The main advantage of using an experiment compared to observational data is that well-designed experiments allow you to measure causal effects.
We also need to remove the answers that were given in any “ Preview ” mode or “Test” mode, because those were not generated from your experimental sample. (Note: in our case, all answers were generated in “Test” mode).
It is good practice to check whether the participants allocated in the Treatment or in the Control have the same completion rate. If this is not the case, the internal validity of your experiment might be in danger.
Alternatively, we can directly plot the mean by group, along with the bootstrapped standard errors for the means:
This is the first form of plot typically scientists do, just to visualize where their data is, how does it look like, whether you're working in the right dynamic range or not. So this kind of information is very critical at this point, so that you don't spend effort in analyzing your data even before you understand whether your experiment has actually been somewhat successful.
So to plot any error bars in MATLAB, you can use this Error Bar function and specify the x data on y data, and the standard deviation, and the plot type. So here, this all specifies the circle that is being plotted over here. Similarly, you can get various types of markers, like square, triangle. Whatever marker you want, you can specify that. And we have the error bars. I have grid on here. But if you don't like or don't want to have grid, you can just specify it as grid off command. And again, x-label, y-label, and, of course, the title of this plot is essential.
This is a standard experiment, which perhaps many experimentalists do in your own research. That is, you will have to generate a calibration curve. You'll have to correlate your output variable, which, in my case, which was the absorbance of my spectrometer, versus is the dependent variable, which is the alkali concentration that I was using.
And you can learn more about it there. Overall, MATLAB is a very powerful environment for researchers and scientists, so that they can quickly churn out data and quickly plot plots and have a script which can represent your entire task in the form of a live editor.
The main advantage of using an experiment compared to observational data is that well-designed experiments allow you to measure causal effects.
We also need to remove the answers that were given in any “ Preview ” mode or “Test” mode, because those were not generated from your experimental sample. (Note: in our case, all answers were generated in “Test” mode).
It is good practice to check whether the participants allocated in the Treatment or in the Control have the same completion rate. If this is not the case, the internal validity of your experiment might be in danger.
Alternatively, we can directly plot the mean by group, along with the bootstrapped standard errors for the means: