# T-Test of two independent sets of samples

I have a total of 29 data points for each sample. In addition, each sample value was independently generated.

From researching on google, I have come across the t-test to determine if these two independent sets of samples have any similarities. Hence my null hypothesis is that and my alternative is the two sets of samples have no similarities.

My question is how do I go about using the t-test to either reject or accept the null hypothesis when from google they are so many different ways to calculate it?

Secondly, I assume the samples are independent because the second sample was obtained on a theoretical basis using a mathematical equation, the distance in meters is varied in steps of 1m from 1m to 29m in the Lfs term and the power is then recorded and shown in the figure below:

The second sample was determined by actual experimentation in the real world, where I purchased the equipment to actually see what results I obtained in the real world condition but the variables are not the same i.e. the GTX,GRX. The power received is also recorded in steps of 1m from 1m to 29m and is then shown in sample 1, is my assumption correct?

Below are the two sets of samples obtained.

• Basic Principle: "Sample 2 (dBm) Theoritical" cannot be treated as random variable in the analyses, because they are not random. – user158565 Aug 5 '19 at 15:05

1. If your experimental setup uses the same initial conditions as in your theoretical calculations, this is definitely a case of pairing.

2. This is not a standard setup for a t-test where the observations in each group are supposed to have the same distribution. You know that you will not have the same distribution of $$P_{RX}$$ when $$G_{TX} = 2$$ as when when $$G_{TX} = 5$$.

What I'm wondering now is if the best way to proceed is to do this as a regression problem where your regression equation includes the $$P_{TX}$$, $$G_{TX}$$, $$L_{TX}$$, $$L_{FS}$$, $$L_M$$, $$G_{RX}$$, and $$L_{RX$$} variables; an intercept term; and a categorical term that is 0 if the observation comes from the theoretical calculation and 1 if the observation comes from the experiment. You would then do your significance test on the parameter of the categorical variable.

OLD:

The "t-test" that you mean is the two-sample t-test. If you can assume the populations have the same variance, you use the vanilla two-sample t-test. If you cannot make this assumption, you would use the Welch test, which is the default in R (common statistical software package). The one-sample t-test does not apply, since you are comparing two groups, and the paired t-test does not apply, since your two groups are independent of one another. A paired t-test would be used in a situation where you measure 29 subjects before and then again after a treatment (for example), which it does not sound like you did.

However, the t-test only examines means. That may be what you intend to examine, but it sounds more like your null hypothesis is that the distributions are the same, and you want to check if you have evidence of any kind to dispute that. For instance, if you have 29 subjects from N(0,1) and 29 subjects from N(0,2), the t-test would be inappropriate for determining if there are differences.

• I assume the samples are independent because the first sample was obtained on a theoretical basis while the second sample was determined by actual experimentation in the real world, is my assumption correct? – Joey Aug 5 '19 at 14:06
• @Joey You'd have to describe your process of generating data based on a theory. Depending on how you do it, I could believe either paired or unpaired testing. – Dave Aug 5 '19 at 14:10
• theoretically being I used a mathematical equation to get the data. While the second sample I went out and purchased the equipment and tested it and recorded the data. Now I want to compare the two samples. – Joey Aug 5 '19 at 14:13
• @Joey So you set it up with 29 different initial conditions to calculate the theoretical outcomes? It would be helpful if you could edit your original post to give more detail about how you collected the data, as the paired vs unpaired issue is important. – Dave Aug 5 '19 at 14:18
• I have updated it. – Joey Aug 5 '19 at 14:31