# t-test and p-value from processed data (mean, SD, sample number)

#### walfrieda

##### New Member
Hi all,
I am new to this forum and would greatly appreciate your help. I know how to do a t-test for significance when I have simple sets of raw data. Now, however, I have to do it on already "processed" data, and in a more difficult way (at least for me).

What I have is the following: I have two sets of measurements of a parameter over time. For each time point, data from around 20 individual measurements were taken and processed to obtain the mean and the standard deviation; of course I also know the number of samples for each data point.

I would like to know how to perform a kind of t-test and how to calculate p-values to tell me whether the two sets of data ("curves" when plotted) are significantly different. In principle I think it should be possible to perform a t-test on the two data points (for which I have the mean, the SD and the sample size) for each time point.
But
(1) I don't know how to do a t-test on processed data, and
(2) I don't know how to get a (kind of) p-value for the two data sets over time, to show whether they are significantly different.

Could anybody help me with this problem?

#### JohnM

##### TS Contributor
You can "back into it" by squaring the SD to get the variance, then multiplying that by degrees of freedom (i.e., n1+n2-2) to get the sum of squares (SS), then using the SS in the t-test computation....

I have attached an Excel file that I've used to do this.

#### walfrieda

##### New Member
You can "back into it" by squaring the SD to get the variance, then multiplying that by degrees of freedom (i.e., n1+n2-2) to get the sum of squares (SS), then using the SS in the t-test computation....

I have attached an Excel file that I've used to do this.
thanks a lot, especially for the excel file. I have tested it on two data points from the sets, and it works great. I now have to go into the detail to understand what it does - your explanation is a bit too short for me but I think I can figure out the rest myself.
Now, is there any way to statistically evaluate whether the two "time curves" in total are significantly different? I could do the t-test for all individual time points (comparing two sets of data, "treated" versus "non-treated") - but then I end up with approximately 400 p-values (or "yes"/"no" values from your excel sheet). I am sure there is some great way to statistically handle these values, but I have no idea how...

#### walfrieda

##### New Member
hmmm, seems to be difficult. As it is not really a "homework"-related question (I just posted it here because I thought it is possibly too trivial for the more advanced parts of the forum), I consider to shift the second part of my question to the "statistical consulting" forum. Is that allowed?

#### mvinces

##### New Member
You can "back into it" by squaring the SD to get the variance, then multiplying that by degrees of freedom (i.e., n1+n2-2) to get the sum of squares (SS), then using the SS in the t-test computation....

I have attached an Excel file that I've used to do this.
Thanks very much JohnM! That was very useful.

#### juan2osteo

##### New Member
I am sorry to ask a silly question but how do you determine the SD if I only have the mean?

thanks

#### Squall

##### New Member
Hi all,

Very new to this forum and found the excel sheet posted by JohnM very useful for simplifying t-test calculations for my colleagues.

I was wondering if anyone could suggest to me how to adjust appropriate calculations within the file to allow an option to treat the data as paired or unpaired?

I am quite novice at stats (although I am very eager to learn), so I don't know if this is a ridicules query.

Many thanks to all.