Stats

• Census


  Recording of information of an entire population
• Sample survey

  A method of systematically gathering information on a segment of the population, for the purpose of inferring quantitative descriptors of the attributes of the population
• Sample

  The fraction of the population being studied
• Reasons for Sampling

  • Cost
  • Timeliness
  • Accuracy
  • Detailed information
  • Destructive testing
• Types of Sampling

  • Probability Sampling
  • Non-probability Sampling
• Probability Sampling


  • Allows every member of the population to have a known, nonzero chance of being selected into the sample
  • Meant to ensure that the segment taken is representative of the entire population
• Non-probability Sampling

  • Some units in the population do not have the chance to be selected in the sample, or the inclusion probabilities cannot be computed
• Basic Types of Probability Sampling

  • Simple random sampling (SRS)
  • Stratified sampling
  • Systematic sampling
  • Cluster sampling
• Basic Types of Non-Probability Sampling

  • Haphazard or accidental sampling
  • Convenience sampling
  • Volunteer sampling
  • Purposive sampling
  • Quota Sampling
  • Snowball Sampling
• Hypothesis testing


  A statistical method applied in making decisions using experimental data
• Hypothesis


  A proposed explanation, assertion, or assumption about a population parameter or about the distribution of a random variable
• Null Hypothesis


  An initial claim based on previous analyses, which the researcher tries to disprove, reject, or nullify. It shows no significant difference between two parameters.
• Alternative Hypothesis


  Contrary to the null hypothesis, which shows that observations are the result of a real effect.
• Example of Hypothesis Testing


  • The school record claims that the mean score in Math of the incoming Grade 11 students is 81. The teacher wishes to find out if the claim is true. She tests if there is a significant difference between the batch mean score and the mean score of students in her class.
• Level of Significance

  Denoted by alpha or α, refers to the degree of significance in which we accept or reject the null hypothesis. 100% accuracy is not possible in accepting or rejecting a hypothesis. The significance level α is also the probability of making the wrong decision when the null hypothesis is true.
• Two-Tailed Test vs One-Tailed Test

  Two-tailed test: Alternative hypothesis is two-sided like Ha: μ ≠ μ0. One-tailed test: The given statistics hypothesis assumes a less than or greater than value.
• Rejection Region

  The set of all values of the test statistic that causes us to reject the null hypothesis.
• Non-rejection Region


  The set of all values of the test statistic that causes us to fail to reject the null hypothesis.
• Critical Value


  A point (boundary) on the test distribution that is compared to the test statistic to determine if the null hypothesis would be rejected.
• Type I Error

  Rejecting the null hypothesis when it is true, with probability denoted by alpha (α).
• Type II Error

  Accepting the null hypothesis when it is false, with probability denoted by beta (β).
• The larger the value of alpha

  The smaller is the value of beta
• Standard Normal Distribution

  A normal distribution with a mean of 0 and a standard deviation of 1.
• Formula for the standard normal distribution
• Formula for the standard score