STATISTICS

• Parameter


  A measure that describes a population
• Statistic


  A measure that describes a sample
• Sampling


  The process of selecting units, such as people, organizations or objects from a population of interest in order to come up with a fair generalization of the population from which the sample was chosen
• Statisticians


  Use different methods of sampling to obtain samples that give each element in the population an equal chance of being selected
• Census or complete enumeration


  The process of gathering information from every unit in the population
• Advantages of Sampling


  • Reduced Cost
  • Greater Speed
  • Greater Scope
  • Greater Accuracy
• Probability sampling


  A sampling procedure that gives every element of the population a nonzero (known) chance of being selected/included in the sample
• Simple Random Sampling (SRS)


  • A method of selecting n units out of N units in the population in such a way that every distinct sample size n has an equal chance of being drawn
  • It may be simple random sampling with replacement (SRSWS) or simple random sampling without replacement (SRSWOR)
• Stratified Random Sampling


  • The population of N units is first divided into subpopulations called strata. Then, a sample random sample is drawn from each stratum, the selection being made independently in different strata
  • Equal allocation: The sample sizes from the different strata are equal
  • Proportional allocation: The sample sizes from the different strata are proportional to the sizes of the strata
• Systematic Sampling (1 - in - k)


  • A method of selecting a sample by taking every k^tℎ unit from an ordered population, the first unit being selected at random. Here, k is called the sampling interval, the reciprocal 1/k is the sampling fraction
• Cluster Sampling


  • The population is divided into clusters. A sample of clusters is selected, and all the elements in the selected clusters are observed
• Methods of Non-Probability Sampling

  • Purposive Sampling
  • Quota Sampling
  • Accidental, Haphazard, or Convenience Sampling
  • Expert or Judgement Sampling
  • Modal Instance Sampling
  • Diversity of Heterogeneity Sampling
  • Snowball Sampling
• Parameter


  A characteristic of the population which is usually unknown and needs to be estimated
• Estimator


  Formula used in coming up with the estimated
• Estimate


  A numerical value that you arrived at when you apply the estimator using the sample data
• Point estimate


  A specific numerical value of a population parameter
• Interval estimate


  A range of values that may contain the parameter of a population
• Characteristics of a Good Estimator


  • Accurate: A measure of how close the estimates are to the actual value of the parameter being estimated
  • Precise: A measure of how close the estimates are with each other
• Unbiased estimator


  An estimator with zero bias
• The t-distribution was formulated in 1908 by an Irish brewing employee named W.S. Gosset
• When n≥30 and σ is unknown, the sample standard deviation s can be substituted for σ
• Assumptions for computing the population mean when σ is unknown: The sample is a random sample, and either n≥30 or the population is normally distributed when n<30
• Proportion


  A fraction expression where the favorable response is in the numerator and the total number of respondents is in the denominator
• Steps for Point Estimate for the Population Proportion

  1. Determine what is asked in the problem

  2. Specify the given information

  3. Write the representations for computing the desired proportions

  4. Write a formula for computing the proportions

  5. Substitute the given values in the computing formula and then solve

  6. Answer the questions raised in the problem
• Hypothesis testing


  A decision-making process for evaluating claims about a population based on the characteristics of a sample purportedly coming from that population
• Null hypothesis (H0)


  A statistical hypothesis that says, there is no difference between a parameter and a specific value, or that there is no difference between two parameters
• Alternative hypothesis (H1)


  A statistical hypothesis that says, there is a difference between a parameter and a specific value, or that there is difference between two parameters
• The null hypothesis is the starting point of investigation
• Non-directional test


  A test where the alternative hypothesis utilizes the ≠ symbol
• Directional test


  A test where the alternative hypothesis utilizes the > or the < symbol
• In hypothesis testing, we determine the probability of obtaining the sample results if the null hypothesis is true
• One-tailed test


  A test of statistical hypothesis in which the alternative hypothesis specifies a direction (either greater than or less than)
• One-tailed test


  A test of statistical hypothesis where the region of rejection is only one side of the sampling distribution
• Two-tailed test


  A test of statistical hypothesis where the region of rejection is on both sides of the sampling distribution
• In hypothesis testing, we make decisions about the null hypothesis
• Decisions about the H0

  • If the null hypothesis is true and accepted, or if it is false and rejected, the decision is CORRECT
  • If the null hypothesis is true and rejected, the decision is incorrect and this is a Type I error
  • If the null hypothesis is false and accepted, the decision is incorrect and this is a Type II error
• Type I error


  Occurs when the researcher rejects a null hypothesis when it is true
• Significance level


  The probability of committing a Type I error, often denoted by α
• Type II error


  Occurs when the researcher fails to reject a null hypothesis that is false
• Power of the statistical test

  The probability of not committing a Type II error