Hypothesis Testing

Ronald Fisher, Jerzy Neyman, Karl Pearson, and Egon Pearson introduced hypothesis testing.  Researchers use hypothesis testing as a statistical method to make decisions based on experimental data.  Hypothesis Testing is basically an assumption that we make about the population parameter.

Key terms and concepts

• Null hypothesis: Null hypothesis assumes that the observation is due to a chance factor.  The null hypothesis, denoted as H0: μ1 = μ2, states that there is no difference between the two population means.
• Alternative hypothesis: Contrary to the null hypothesis, the alternative hypothesis shows that observations are the result of a real effect.
• Level of significance: Refers to the degree of significance in which we accept or reject the null-hypothesis.  100% accuracy is not possible for accepting or rejecting a hypothesis, so we therefore select a level of significance that is usually 5%.
• Type I error: When we reject the null hypothesis, although that hypothesis was true.  We denote Type I error by α.  In hypothesis testing, we call the normal curve showing the critical region the alpha region.
• Type II errors: When we accept the null hypothesis but it is false.  We denote Type II errors by beta. In hypothesis testing, we call the normal curve showing the acceptance region the beta region.
• Power: Usually known as the probability of correctly accepting the null hypothesis.  We call 1-beta the power of the analysis.
• A one-tailed test occurs when the given statistical hypothesis has one value, like H0: μ1 = μ2.
• A two-tailed test occurs when the statistical hypothesis assumes a less than or greater than value.