Question

discuss why practicing scientists (e.g. you in the physics labs) need to design at least two independent experiments to test one theory (hypothesis)

Answer 1

The discussion begins, implementing the scientific method to an experiment. When designing an experiment, measures will be developed, which will have results.
When we consider independent experiments, the results of the measurements do not have to affect the result of the other.
In physics and science in general, we have a hypothesis, which can be refuted (null hypothesis) and an alternative hypothesis, which is proven by independent experiments. Now, at least we have to maintain two independent experiments to make the respective relevant comparisons. Statistically speaking, we have the T-Student test to assess whether one or more independent experiments test a null or alternative hypothesis.

If we consider two independent experiments A and B, then for independent experiments, the T-student is expressed based on the average values, standard deviations, obtained in the measurements of each experiment.

where

x_{1}: is the average value for an experiment A

x_{2}: is the average value for an experiment B

and

is the standard error

Then to prove the null or alternative hypothesis the value of t has to be for a significant level of confidence

In conclusion, because it is necessary to consider independent experiments, it is reflected in adopting independent variables, which are subject to measurement. In fact, two experiments with independent variables are considered to compare their results, which are statistically calculated through the T-Student