Hi, can someone explain to me how to interpret the p-value?
say, the t-stat is 0.981919 n the p-value is 0.330289
does th mean there is a 33% chance of rejecting th null?
It means there’s approximately a 33% chance that we see a result at least as unusual (contradicting to the null) than the current result (assuming the null is true).
Here is another thread. If you scroll to the last post I made, I gave a longer explanation of the p-value. Hope this helps! http://www.analystforum.com/forums/cfa-forums/cfa-level-ii-forum/91340224
Also, the smaller the p-value the more unusual (significant) the results. Again, this is correct assuming that the null is true. This is (partly) why we compare p-values to alpha when making a decision to reject (alpha > p-values) or fail to reject H0 (alpha < p-value).
It means that the smallest α for which you would reject the null hypothesis is 33%.
In other words, in the real world, you won’t reject the null hypothesis.
Respectively, I think this definition is incomplete and doesn’t generate much intuition as to what a p-value is (creates a mechanical view, in my opinion). This is correct, though, but I don’t particularly like it as it probably influences “cherry picking” in practice. “Oh p-value is 0.033? I’ll reduce the threshold probability of a Type I error (alpha) from 0.05 to 0.033! Now, it’s more likely I’m not making a mistake!” – doesn’t really work that way, unfortunately.
t -stat = -1.293
p-value = 0.199
lower 95% = -0.159
upper 95% = 0.034
cannot reject the Ho because the p value is 0.199?
First, define H0 and Ha. I’m assuming H0 is b1=0 for your example.
In either case, from the p-value, we can see .199> any alpha you would pick (say 0.05), so you are correct. Fail to reject H0. Note, you can obtain the identical (and even more) information from that confidence interval. Since 0 is contained within the confidence interval, it is possible the parameter is equal to zero. Therefore, we say the parameter value is not statically different from zero (or any of the values of the interval). In short, if a number falls inside the CI, then the parameter is not statistically different from that value (at the given confidence level). So, fail to reject H0.
But the t stat falls outside of CI… th is how I got it wrong
Right, but you should be comparing the hypothesized parameter value, 0 (if you’re testing b1=0), to the confidence interval. The t-statistic should only be compared to critical t-values. The p-value should only be compared to alpha. Hypothesized values for the parameter (for example, b1=0) should be compared with the confidence interval. The confidence interval is a range of values for which we are X% confident that the true value of the parameter (true value of b1) will fall within. The confidence interval isn’t comparable to a calculated test statistic.