STAT 101

• Statistics


  science of decision making in a world full of uncertainties.
• Science


  Singular sense
• processed data


  plural sense
• Population


  collection of set (who or what)

  set of all entities under study (that we want to study)
• Variable


  characteristics that can assume different values for different elements
• sample


  subset of population
• Nominal 


  weakest of level of measurement
• Ratio


  highest
• Nominal


  names, label, categories

  equal importance
• Ordinal


  implied ordering
• Interval


  zero does not mean absence
• Ratio


  with true zero point
• Probability samples


  obtained using a randomization procedure , requires a sampling frame, with known & non zero chance of selection, statistical inference is valid
• Non-probability samples


  obtained haphazardly, selected purposively or taken as volunteers

  unknown chance of selection

  statistical inference is not valid
• the two most common in inferential is estimation and test of hypothesis
• Estimation

  • concerned with finding a value or range of value for an unknown parameter of interest
  • providing a single or range of values
  • in inferential, it is the parameter
• Test of Hypothesis


  statement that we want to test

  claim or guess about the parameter because the parameter is unknown
• Simple Random Sampling


  equal chance of being selected
• Type I error


  Reject Ho if Ho is True
• Correct Decision


  Reject Ho if Ho is false
• Correct decision


  Fail to reject Ho if Ho is true
• Type II error


  Fail to reject Ho if Ho is false
• the probability of a type I error is usually denoted by a.
• Stratified Random Sampling


  when the population can be divided into a set pf non-overlapping subgroups (strata)
• Stratified Random Sampling


  simple random samples are independently selected from each strata
• Systematic Sampling


  population can be viewed as a list
• Systematic sampling


  every kth unit in the sequence is included in the sample
• Cluster sampling

  • clusters
  • cluster are selected at random
  • all units in that cluster is the sample
• Parameter


  summary measure based on the entire population
• statistic


  summary measure based on the sample
• Estimator 


  formula for computing the statistic using sample data
• Estimate


  numerical value (realization) of the estimator
• alpha 


  level of significance
• p-value


  significance probability
• Parametric Test

  • At least interval scale
  • normality of data
  • homogeneity of variances
• Normality (via graph)

  • histogram
  • Q-Q plot
• Normality ( via statistical test)


  Shapiro-Wilk
• P-value is greater than Alpha. We Fail to Reject Ho, normality is satisfied.
• Homogeneity in two population


  F-Test

  Ho: The variances of the two groups are equal

  Ha: The variances of the two groups are not equal
• Descriptive Statistics


  tool used to describe a mass of data in a clear way, through organizing, summarizing, and presenting data