Theory revision 4

Hypothesis Testing

• Testing hypothesis is an essential part of statistical inference.
• A statistical hypothesis is an assumption about a population. This assumption may or may not be true.
• For example, claiming that a new drug is better than the current drug for treatment of the same symptons.
• The best way to determine whether a statistical hypothesis is true would be to examine the entire population.
• Since that is often impractical, researchers examine a random sample from the population.If sample data are consistent with the statistical hypothesis, the hypothesis is accepted if not, it is rejected.
• Null Hypothesis: the null hypothesis denoted by H0 is usually the hypothesis that sample observations result purely from chance.
• Alternative Hypothesis: The alternative hypothesis denoted by H1 is the hypothesis that sample observations are influenced by some non random cause.
• Statisticians follow a formal process to determine whether to accept or reject a null hypothesis based on sample data. This process, called hypothesis testing consists of five steps.
1. State null and alternative hypothesis
2. write down relevant data, select a level of significance
3. Identify and compute the test statistic, Z to be used in testing the hypothesis.
4. Compute the critical values Zc.
5. Based on the sample arrive a decision.
• Decision errors
• Type I error: A type I error occurs when the null hypothesis is rejected when it is true. Type I error is called the significance level. This probability is also denoted by Alpha. α
•  Type II error: A type II error occurs when the researcher accepts a null hypothesis that is false.
•  One-tailed and two-tailed tests
• A test of a statistical hypothesis, where the region of rejection is on only one side of the sampling distribution is called a one tailed test.
• For example, suppose the null hypothesis states that the mean is equal to or more than 10. The alternative hypothesis would be that the mean is less than 10.
• The region of rejection would consist of a range of numbers located on the left side of sampling distribution that is a set of numbers less than 10.
• A test of a statistical hypothesis where the region of rejection is on both sides of the sampling distribution is called a two tailed test.
• For example, suppose the null hypothesis would be that the mean is equal to 10, the alternative hypothesis would be that the mean is less than 10 or greater than 10.
• The region of rejection would consist of a range of numbers located on both sides of sampling distribution; that is the region of rejection would consist partly of numbers that were less than 10 and partly numbers that were greater than 10.
• Degree of freedom
• The concept of degree of freedom is central to the principle of estimating  Statistics of population from samples of them.
• It is the number of scores that are free to try.