I have a data set assume as shown below:
I wanted to know that can I use a paired T-Test to test if the average time spent is different Pre and Post change? (I am a little unsure because the each data point is an average in itself)
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This question came back in the list. It is an old question, but to ensure that it is not misleading for the reader, I feel that it is important to stress that the answer really depends on the very nature of the data. Doing so requires to be sure that the person analyzing the data understand the data and has clear objectives in mind. For instance, with the information provided, we do not know why the data has been grouped by day. Does the specificity of each day explain the significant differences that we can observe from one day to another? Indeed, a lot of information is hidden when averaged by day... It is possible that the average for day 5 is 107 for Pre and 76 for Post, but this very same day, most of time "Post" data were greater than "Pre" data for the majority except for some cases that were surprisingly low and produced this average. Frequency of the visits per day is another aspect to consider to avoid a Simpson paradox.
So, I do not think the short answer should be yes without knowing more about the data and the goal of the analysis.
The short answer is yes. The slightly longer answer is that if this is a real data set, then at some point someone compressed a number of raw data into a mean, reducing the amount of information and power you have. There are techniques that can handle that slightly more complicated type of data. And they would be better.