MODULE 1

• Hypothesis Testing

  • Claims need to be backed up with valid and authentic evidence. We do not need to be believe everything we are told. Statistics provide us with a powerful tool in hypothesis testing. Here, we can actually verify claims made about the population through some systematic approach.
• Statistical Hypothesis

  • A claim or assertion concerning one or more population.
• Null Hypothesis

  • Denoted by Ho
  • This is the hypothesis being tested
  • This is a statement that usually shows no difference between a parameter of interest and an expected value.
  • No difference between several populations or no relationship between variables.
• Alternative Hypothesis

  • Denoted by Ha
  • This is the hypothesis proven to be true by providing sufficient evidence to show it is true.
• One-Tailed Test

  • The alternative hypothesis shows only one direction for the other possible values of the parameter of interest.
• Two-Tailed Test

  • The alternative hypothesis shows two directions for the other possible values of the parameter of interest.
• To reject the null hypothesis:

  • When sufficient evidence are presented to show that the alternative hypothesis is true.
  • This decision is more conclusive, since this decision is based on evidence.
• To fail to reject the null hypothesis:

  • When there are insufficient evidence to show that the alternative hypothesis is true.
• Type 1 Error

  • The rejection of a true null hypothesis. When this type of error is committed, there must be irregularities in the accepted evidence, since we can only reject the null hypothesis if there is sufficient evidence to show that it is false.
• Type 2 Error

  • The failure to reject a false null hypothesis. Here insufficient evidence presented to show that the alternative hypothesis is true.
• The type 1 error is the bigger mistake to commit, since to reject the null hypothesis, there must be sufficient evidence presented. So it means that the presented evidence is also questionable or false.
• Level of Significance

  • The probability of committing a type 1 error.
  • This is the chance we are willing to take of rejecting a true null hypothesis.
  • It is usually a value that range from 0.01 to 0.10. It is the size of the critical region. It is denoted by α.
• Test Statistic

  • A value that is calculated from sample data and used to determine whether to reject null hypothesis. The test statistic compares your data with what is expected under the null hypothesis.
  • The formula used in determining the test statistic depends on the type of test of hypothesis being performed. ( Z- test, t-test, χ2-test, ANOVA, etc.)
• Critical Region

  • Also called the Rejection Region
  • The possible values of the test would lead to the rejection of the null hypothesis.
  • The size of the critical region is equal to the level of significance, α.
• Population

  • Collection of all units concerned in a statistical way.
• Parameter

  • Numerical characteristic of population. Value computed from population data.
• Sample

  • A part or subset of population.
• Data

  • Individual pieces of factual information recorded and used for the purpose of analysis.
• Statistic

  • Numerical characteristic of a sample. The result of data analysis— its interpretation and presentation.
• Variable

  • Characteristic or attribute which takes on different values or labels for different persons.