Naked Science Forum
Non Life Sciences => Physics, Astronomy & Cosmology => Topic started by: EthanElijah on 07/01/2021 08:35:52

Hey there, so recently I did an experiment where the expected results i should get would be a linear graph. However, after plotting my data, the graph more closely follows a polynomial curve. Based on the theory, the quantity i wanted to find should be the gradient of a straight line, so how can i interpret my results? Thanks in advance!

Hey there, so recently I did an experiment where the expected results i should get would be a linear graph.
Can you describe the experiment, set up, results and how you analysed them compared to expectation.

Based on the theory, the quantity i wanted to find should be the gradient of a straight line, so how can i interpret my results?
In real experiments, the results rarely lie exactly on a straight line. You can expect:
 Randomness in the results (ie results above and below the trend line)
 Some systematic errors in the results (eg a trend line that should go through the origin actually passes through some non0 value. Or the results may not lie on a straight line, but appear "bent")
 Could you be be plotting the data on linear axes, but it only forms a straight line with loglinear or loglog axes?
 Or you may just be plotting the wrong thing. If you plot the kinetic energy of a particle instead of its velocity, the results would lie on a parabola where you expect a straight line.
A common technique to reduce the impact of random errors is to use a "Least Squares" fit to the data.
 This adjusts the equation of the trend line to minimize the errors (squared)
 This function is available in many maths packages
 I sometimes use this function in the EXCEL spreadsheet, as follows:
 Enter the observed X & Y values in a table and then plot it on a graph.
 Add a trendline to the graph.
 You can specify whether you want to trend line to be a straight line, parabola, etc, and see how well it matches the data
 For a straight line, you can specify that you expect it to pass through the origin
 You can display the equation of the trend line. For a straight line, you can read the slope straight out of this equation.
 You can add a measure of how closely the trend fits the data
 Beware of "overfitting": If you have 10 data points, a 10th degree polynomial will fit it exactly  but be totally useless at predicting the result of a new measurement
 This method is less successful at reducing the impact of systematic errors...
See: https://en.wikipedia.org/wiki/Least_squares

Beware of "overfitting": If you have 10 data points, a 10th degree polynomial will fit it exactly
So will a 9th order one.*
I'm fairly sure the term in x^10 should be zero.
* a zero order polynomial i.e. a constant can be plotted exactly through 1 point.
If you have two points you can draw a straight line through them, so a first order polynomial will exactly fit 2 points and so on.
If the OP shows us what the graph looks like that will be very helpful.
It's possible that he has transformed that data to linearise it, that's generally a god thing but, if the transform is wrong, you end up with a curve.

Based on the theory, the quantity i wanted to find should be the gradient of a straight line, so how can i interpret my results?
Do it again. If you get the same result, the theory is wrong, or you made the same mistake in the experiment.

The distinction between informational and computational equivalence of representations, first articulated by Larkin and Simon (1987) has been a fundamental principle in the analysis of diagrammatic reasoning which has been supported empirically on numerous occasions. We present an experiment that investigates this principle in relation to the performance of expert graph users of 2 × 2 “interaction” bar and line graphs. The study sought to determine whether expert interpretation is affected by graph format in the same way that novice interpretations are. The findings revealed that, unlike novices—and contrary to the assumptions of several graph comprehension models—experts' performance was the same for both graph formats, with their interpretation of bar graphs being no worse than that for line graphs. We discuss the implications of the study for guidelines for presenting such data and for models of expert graph comprehension.

Little confused after reading this post.

Hello EE!
Welcome to the Forum.
If you'd wish to post the Graph in here...
Just click on..
 Attachments and other options
Then Choose File...
& then (Insert Attachment 0)
[ Invalid Attachment ]
Ps  Hello Rebecca & Welcome.
Hopeful that Confusion will turn into Clarity.

First, share the experiment set up with us, then we can help you.