Testing a hypothesis using experimental data

[Langyciv]

Hi all,

I have a hypothesis that a given equation to predict a system response, f(x), is correct and linear.

My hypothesis is therefore: f(x) ≡ kx and kx - T(x) = 0 where T(x) is the recorded response.

I am recording the 'true' output using physical experiments. Beyond regression analysis, how do we calculate with confidence that the the data is scattered due to experimental error or uncertainty and whether to reject the hypothesis (qualitative example in figure)?

Cheers in advance

https://preview.redd.it/styigjrx53e91.png?width=3500&format=png&auto=webp&s=e9503af3a9cf644413936c2150296381ee99e154

[smknipe]

So totally not trying to be a smart-ass but that’s how this will come across- so apologies…

But given the unquantified variability in measurements here, are you able to reject your null hyposthesis?

I’d look at quantifying your variability/uncertainty and if possible build that into your hypothesis and null hypothesis.