Before conducting a significance test, the statistician will choose an alpha level. Depending upon the severity of having type I or type II error, the statistician will make the alpha level higher or lower. Generally in courts, the alpha level is .05. The other common alpha levels for significance tests are .10 and .01.
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You select the alpha level based on a number of factors. One consideration is the variability of the characteristic which you are trying to measure. Another, very important criterion is the importance of the decision to be made. If the consequences of the wrong decision are dire then you want a very high alpha, otherwise you may prefer a lower alpha.
Ratio level of measurement is the highest in statistics.
Alpha is not generally used in regression analysis. Alpha in statistics is the significance level. If you use a TI 83/84 calculator, an "a" will be used for constants, but do not confuse a for alpha. Some may, in derivation formulas for regression, use alpha as a variable so that is the only item I can think of where alpha could be used in regression analysis. Added: Though not generally relevant when using regression for prediction, the significance level is important when using regression for hypothesis testing. Also, alpha is frequently and incorrectly confused with the constant "a" in the regression equation Y = a + bX where a is the intercept of the regression line and the Y axis. By convention, Greek letters in statistics are sometimes used when referring to a population rather than a sample. But unless you are explicitly referring to a population prediction, and your field of study follows this convention, "alpha" is not the correct term here.
Cronbach's alpha refers to a coefficient of reliability. This can be written as a purpose of the number of test items and its average inter-correlation. Cronbach's alpha commonly increases as the correlation of the items increase.
Level of measurement most inferential statistics rely upon is ratio.