Statistics Question, any math people?

Question

My stats is a little rusty. I need to know the difference between piared and unpaired data. For my experiment, I'm comparing the size of plants under two different growing conditions. So there is two columns of data, each representing the weight of each plant under two kinds of conditions.

So all the the data in 1 column represent multiple trials of the same condition.

Answer 1

If the two numbers across a row refer to the same plant then you have paired data. You can think of it as "before and after." So if you have

x_1 | y_1
x_2 | y_2
...
x_N | y_N

this is paired data and you can replace it with a single variable which is the difference:

w_1 = x_1 - y_1
w_2 = x_2 - y_2
...
w_N = x_N - y_N

Now you can do a standard statistical test on w. For example

h0 : mean of w = 0
ha: mean of w is not 0

(If mean w < 0 then mean x < mean y)

On the other hand, if the two sets of numbers are for two different sets of plants then you do not have paired data. To make matters confusing, in this case you have to used a paired t-test! (The worst thing about statistics is the language.)

For example, if you have a set of plants, x, that you raise in one condition, and another set of plants, y, that you raise in a different set of conditions then you do not have paired data and have to look at the difference in the means,

Let w = x-y
then the mean of the sample mean of w = mean x - mean y
std dev of the sample mean of w = sqrt( var(x)/N_x + var(y)/N_y)

Now you do your statistical test on w,