# Tito Andrei Fontanos

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Tito Andrei Fontanos
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The p-value is the smallest alpha level at which you declare significance when in fact there is none. Looking at your nomal curve, if you see that your p-value is more extreme than your alpha value (in other words, it is smaller in area than your alpha value) you reject your null hypothesis and accept your alternative. Makes sense since you already set your alpha to be small, say .01. An even smaller p-value would lead you to accept or declare significance.
But you must be careful when testing for rho greater than 0. Remember that it is easy to declare or reject significance if you have a few points sampled. Imagine you have just 3 points and judging from the way they are placed on a scatter plot, they lie in a relatively straight line. Would you be accepting this as having a linear relationship? What if you had a few more points? A good approach is to use a scatter plot in conjunction with your formal test (i.e. t-test).

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