I need to check if there is a significant difference in recorded level values between the two decades. I have a data that includes both of the decades.
I decided to use a t-test and was thinking using the two-sample t test but the definition of 2-sample t tests are that they are from 2 different samples and are independent which is not true in my case.
Can I assume they are 2 different samples or should I use something else?
You are interested in seeing if there is significant difference in recorded level values between the two decades.
I'd like to start with what are dependent or independent samples are and which tests to use for each case.
Dependent samples are such data that are 'related' to each other. For example, let's say you are interested in the drug effect on blood pressure(bp) level and would like to compare the bp level measured before taking the drug and bp level measured after taking the drug. 'BP level BEFORE taking drug' gives you some information about 'BP level AFTER taking drug', which means BP level is dependent on the existence of drug in each patient's body(same to say that the bp level of the 'Group Before taking drug' is dependent on bp level of the 'Group After taking drug'). In other words, two groups are related in regards to the bp level. Obviously, we have the same patient for each pair of Before/After BP level measurement, this would give us the idea about the effect of the drug, which again, Before group will give us information about After group about drug effects on BP level and vice versa.
Thus,'paired t-test' would be appropriate for the dependent sample above. You are looking at the paired observation(BP Before and After taking the drug) and testing to see if there's any significant mean difference between these paired dependent samples. The null hypothesis would be "paired difference(Before - After) is significantly different from 0"
(You are most likely to use paired t-test when the same subjects are measured on the two different things - like same patient's bp is measured before/after the drug. However, there are exceptions too. If we are looking at the twins and the difference of heights between twins it's the two different individuals that we're looking at. However, again, since they share the gene, diets, etc, they are dependent samples. I'm brining up this example to say that study subjects that are NOT the same individual can also be the dependent samples, depending on how the one group of sample is related to another group of the sample.)
Moving onto the independent samples. independent samples of first group does not give such information to the second group. Let's say we're interested in measuring the difference of height in people in France and Nepal. Two populations are independent of each other because people in France does not really give information about people in Nepal.
In this case, two sample t-test will be appropriate.
Now, in your case of recorded 'level values between the two decades'. I cannot tell much about which one you should use because I do not have much information about the data.
However, if you are certain that the first decade somehow gives information about the second decade or if the first decade is related to the second decade, use the paired t-test.
However, if you find that the first decade is totally independent to the second decade, please use the two sample t-test. It really depends on the description of the data and I do not have much information of each decade so please look into how the data was collected and interpreted to determine if the two decades are related or not.
Thank you.