I have two datasets, dataset A going from 1980 to 1990, and dataset B going from 1990 to 2000. I wanted to check if there is a significant difference between the two datasets so I ran a t-test. The result is not statistically significant (t-stat: -1.02), but I'm not sure on how to interpret that.

From what I understand, the null hypothesis is that the difference between the averages is 0 (in this case the null hypothesis is that there is no difference between the two datasets) and if the result of the t-test is statistically significant we reject the null hypothesis (meaning that the two datasets are statistically different).

Since in this case the t-stat is not statistically significant should I say that there is no statistically significant difference between the two datasets?

I'm wondering if my writeup is correct. What I've currently written is:

After running a t-test I find that the difference is not statistically significant (t-stat of -1.02) so the 1980 – 1990 performance is not statistically different from the 1990 – 2000 one.

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    $\begingroup$ What do you mean by "going from 1980 to 1990" & "going from 1990 to 2000"? Is this a time series, & you're wondering it the values (of what?) are higher in later years than earlier? It seems a t-test is not likely to be appropriate here. $\endgroup$ – gung - Reinstate Monica Jun 4 '19 at 19:03
  • $\begingroup$ Thank you for the answer. I have this investment strategy that gives me a time serie with all the returns. In 1990 an asset was removed and I want to check if this fact changed the returns of the strategy from the first to the second period. $\endgroup$ – Lorenzo Jun 4 '19 at 19:53
  • $\begingroup$ Wouldn't it make sense to just assess that single asset to see if it's a net positive or negative? In general, you need to account for the non-independence of the data. This requires time series methods. $\endgroup$ – gung - Reinstate Monica Jun 4 '19 at 20:00
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    $\begingroup$ But I removed the asset because I didn't have the data anymore not because I chose to do that, so it's impossible for me to check if in the second decade this asset would have been a net positive or negative (if I'm understanding correctly what you are suggesting) $\endgroup$ – Lorenzo Jun 4 '19 at 20:10

This seems correct assuming your t-statistic is correct as well (that you have the correct degrees of freedom, etc.). I would, however, specify to what level $\alpha$ your hypothesis can be rejected. Generally, statisticians/econometricians use $\alpha=0.05$ which yields the 1.96 threshold for most test statistics. If this is specified by a problem prompt, then this is not a problem, but if you are forming an original hypothesis you need to include your significance level. I hope that helps.

  • $\begingroup$ Thank you Arthur! $\endgroup$ – Lorenzo Jun 4 '19 at 19:54

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