# Help on selecting 2 tests - unsure if they are paired or non-paired statistical test

I have data that measures the temperature of flowers and leaves on different plant species. These are the comparisons I am trying to make:

1. Comparing the flower and leaf of the same plant at the same time of day
2. Comparing the flower or leaf of a plant to the same flower or leaf at different times of day - on the same plant

My current interpretation is that 1 is an independent statistical test because while they are both on the same individual plant, they are separate "individuals" themselves. For 2 I believe it is a paired test as it is measuring the same flower or leaf at different times of day.

What is confusing me is that I have been taught that if it is the same "individual" then it should be paired, therefore 1 should be a paired test. However my interpretation is that "individual" means something different in the mathematical reality of the tests, where they are seen as different pools in this instance.

Am I correct in my thought? Or completely wrong?

Thank you

Edit: Maybe some clarification to my thought: The difference between my 2 tests is that one uses the same repeated leaf or flower (referring to case 2) at different times of day (therefore it is paired as it is a measurement of the same thing twice at different times). This contrasts with case 1 as this is comparing 2 different objects at the same time of day. The confusion for me comes in when case 2 is still on the same individual - they are related in a way, but I'm unsure if this is relevant to the test.

• I'm voting to close this question as off-topic because it is a question of statistics, not biology. Have a look at stats.SE Sep 12 '19 at 4:39
• I would argue that statistics is the core of Biology! The whole of the empirical method underlying biology is founded in statistics. Even high school level biology uses statistics. Thank you for your opinion either way. Sep 12 '19 at 10:03
• @s33ds Welcome to Bio.SE. You are right that biology relies on statistics! Remi.b isn't trying to say this is a bad question, but you would get a much better answer on stats.SE. For me the question is missing a few details that are important for the statistical analysis. For example in scenario 1: Are you only counting one leaf and one flower per plant? This might cause different sample sizes in the data. Sep 12 '19 at 14:42
• There may or there may not be any correlation between the flower and the leaf of a plant. If you think there might, you ought to account for that. Switching to mixed-effects (or multi-level) models will induce the change in mentality that will make the task of modelling such experimental designs easier. Sep 12 '19 at 18:28

I imagine that for case 1 you have data of the type:

Plant1, $$t_f$$, $$t_l$$;

Plant2, $$t_f$$, $$t_l$$;

etc.

If you are interested in comparing the mean temperatures between flowers and leaves, your data would consist of n measurements coming from flowers and n measurements from leaves. You may surely try a t-test for independent samples, especially if you have some missing data in one column or the other. However, I find it reasonable to think that the values of flower and leaves are correlated within plant (possibly because of different background exposures of different plants). If this correlation is strong, you are at risk of not registering a true effect (a significant temperature difference between leaves and flowers).

Therefore, I would opt for a paired test even for case1.

• Welcome to Biology.SE! ——— Please take the time to go through the tour and the help pages starting with How to Answer questions effectively on this site. Thanks! 😊 Nov 5 '19 at 23:28