2. Hypothesis Testing Concepts and Terminology
|H0 is Actually True||H0 is Actually False|
|Experimental conclusion: reject H0||Type I error is committed||Experimental conclusion is correct|
|Experimental conclusion: do not reject H0||Experimental conclusion is correct||Type II error is committed|
3. Contemporary Textbooks’ Misinterpretations of Hypothesis Testing Concepts
3.1. Erroneous Interpretations of α
In the example at hand, the null hypothesis was rejected and the probability that this decision was incorrect is 0.05.
As zobt > 2.33, you would reject the null hypothesis, knowing there is a 1 in 100 chance that you are making the wrong the decision (Type I error).
3.2. Erroneous Interpretations of p-Value
Sir Ronald A. Fisher, established the basic guidelines for significance testing. He said that a statistical result may be considered significant if it can be shown that the probability of it being rejected due to chance is 5% or less. In inferential statistics, this probability is called the p-value, 5% is called the significance level (α), and the desired relationship between the p-value and α is denoted as: p ≤ 0.05. The significance level is the maximum level of risk that we are willing to accept as the price of our inference from the sample to the population. If the p-value is less than 0.05 or 5%, it means that we have a 5% chance of being incorrect in rejecting the null hypothesis or having a Type I error.
4. Analysis of Causes of Erroneous Interpretations
If we set our alpha level to the conventional .05, then the probability that we will reject the null hypothesis wrongly, that is, make a Type I error, is also .05. After all, by setting the alpha level to .05 for a statistical test we commit ourselves to rejecting the null hypothesis if the result we obtain would occur 5% of the time or less given that the null hypothesis is true. If we did the same experiment again and again, and in fact there is no effect in the population, over the long run 95% of the time we would correctly claim no effect. But 5% of the time, just by the luck of the draw, we would wrongly claim an effect.
Appendix A: Conditional Probability Calculations
= α·Pr[H0 is true in the experiment]
Appendix B: Textbooks Examined in the Study
Conflicts of Interest
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