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I keep seeing this in my econometrics book. "The t-statistic is -1.06 which is not significant at even the x% level against the two-sided alternative". This happens at exercises for which I have to do the calculations by hand. How can I find the p-value by hand. My idea is that if I have t-stat of -1.06 I go in the z-table and look at -1.0 and 6 (in the column) but how do I know the 2-sided value and what happens if the t-stat is -1.055?

Also, totally unrelated to the questions. I find it quite difficult to study for my econometrics exam. Like I read, but nothing stays with me. I would really appreciate any advice on how you guys are studying for exams (I have a more humanistic background and I am not used to study numerical subjects).

Thank you!

Michael R. Chernick
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user91991993
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    The second half of your question is not really on-topic here. I'm not sure there is an SE that could help you. But suggestions on exam preparation and study habits are just a Google search away. – Sycorax Apr 03 '17 at 19:04
  • You can't do it by hand unless you have the t table memorized. – Michael R. Chernick Apr 03 '17 at 19:16
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    @Michael It's easy enough to do with pencil and paper in just a minute or two using various techniques, such as Simpson's Rule. One can even test against critical values almost instantly, using mental arithmetic and a minimum of memorization. Consider the 68-95-99.7 rule, which provides lower bounds for the p-value. In this case, the t-statistic of -1.06 already indicates that the p-value is close to or greater than 100-68 = 32%, regardless of the number of degrees of freedom. (In fact, computer calculation shows the correct value is between 29% and 40%.) – whuber Apr 03 '17 at 19:38
  • I don't think it can be done exactly. – Michael R. Chernick Apr 03 '17 at 19:49
  • Your question is really unclear, but you seem to me to be asking about how to interpolate in tables. Is that the kind of thing you're after? Your unrelated question should be removed; it's a completely separate issue (and probably not suitable to our site as Sycorax suggests) – Glen_b Apr 03 '17 at 23:01
  • @Michael Any calculation of a p-value will be an approximation. Looking up tables certainly isn't exact either. As long as it's done to sufficient accuracy for the purpose at hand, there's no difficulty with approximation. [It's not all that difficult to compute bounds on the error should that prove necessary, but it's usually not needed. If one computes the p-value to be 0.231, it really doesn't matter if the exact answer would have been 0.22873472... ; there's rarely any benefit in knowing more than a couple of figures unless you're near a significance level] – Glen_b Apr 03 '17 at 23:03

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To get the two sides $\alpha$, divide by 2. If you want the p value for - 1.055 check the value for 1.055 since t-table is symmetric.

Edit: I guess there are no. 005 values in the table so just take the the two next to 1.055 and divide by 2.

Fisher_incarnated
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  • This might be right but it depends on the particular table you are using. The correct answer is to use the t distribution table with the appropriate number of degrees of freedom which would be n-2 where n is the sample size. – Michael R. Chernick Apr 03 '17 at 19:14
  • Oh right was reading too fast. Change normal to t-dist. – Fisher_incarnated Apr 03 '17 at 19:18
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    @MichaelChernick: Take care not to assume a particular application when the OP hasn't mentioned one - $n-2$ wouldn't be the correct no. degrees of freedom to use in a one-sample t-test for example. – Scortchi - Reinstate Monica Apr 03 '17 at 19:45