stats

• Sampling Error


  The discrepancy between a sample statistic and its corresponding population parameter
• Samples provide an incomplete picture of the population. Although we try to make our sample representative of the population, there will always be some segments of the population that are not included in the sample
• Sampling error


  Also sometimes referred as margin of error (in election polls)
• Sampling Distribution of Sample Means


  A frequency distribution of a large number of random sample means that have been drawn from the same population
• The sampling distribution of means approximates a normal curve
• Central Limit Theorem


  • The mean of a sampling distribution of means (mean of means) is equal to the true population mean
• Bernoulli's Law of Large Numbers


  • The standard deviation of a sampling distribution of means is smaller than the standard deviation of the population
• Standard Error of the Mean


  The error of the mean measures the standard amount of difference between the sample X and μ that is reasonable to expect simply by chance
• Estimations


  • One aspect of inferential statistics
  • The process of estimating the value of a parameter from information obtained from a sample
• Interval Estimates


  The interval or a range of values used to estimate the parameter. This estimate may or may not contain the value of the parameter being estimated
• Confidence interval


  A specific interval estimate of a parameter determined by using data obtained from a sample and the specific confidence level of the estimate
• Confidence level


  The probability that the interval estimate will contain the parameter
• Population or universe


  A group or set of individuals that share at least one characteristic
• Samples


  Drawn by researchers to maximize time and efficiency, generalizations are made based on the samples for the population
• Sampling Methods


  • Simple random sampling
  • Systematic sampling
  • Stratified sampling
  • Cluster (multistage) sampling
  • Accidental sampling
  • Quota sampling
  • Judgment (purposive) sampling
• Sample members should be representative of the entire population in order to facilitate generalizations for the entire population
• Random sampling allows for equal chance for every member of the population to be selected in the sample
• Greek symbols


  Typically represent population parameters (e.g. μ for mean, σ for standard deviation)
• English symbols


  Represent sample statistics (e.g. x)
• Sampling error


  Discrepancy between a sample statistic and its corresponding population parameter
• Samples provide an incomplete picture of the population, there will always be some segments of the population that are not included in the sample
• Sampling Distribution of Sample Means


  A frequency distribution of a large number of random sample means that have been drawn from the same population
• Characteristics of Sampling Distribution of Sample Means


  • Approximates a normal curve (Central Limit Theorem)
  • Mean of means is equal to the population mean (Bernoulli's Law of Large Numbers)
  • Standard deviation is smaller than the population standard deviation (standard error of the mean)

  
• Standard Error of the Mean

  The error of the mean measures the standard amount of difference between the sample mean and population mean that is reasonable to expect simply by chance

  
• Estimations


  The process of estimating the value of a parameter from information obtained from a sample

  
• Point Estimates


  The specific numerical value estimate of a parameter, implies the sample mean is the population mean
• Interval Estimates


  The interval or range of values used to estimate the parameter, may or may not contain the true parameter value
• Confidence Interval (CI)


  A specific interval estimate of a parameter determined by using data from a sample and a specific confidence level

  
• Confidence Level


  The probability that the interval estimate will contain the parameter

  
• Greater confidence level leads to wider confidence interval and larger z-score

  
• Hypothesis Testing


  A statistical method that uses sample data to evaluate a hypothesis about a population
• Steps in Hypothesis Testing


  • Define the population
  • State the hypotheses
  • Give the significance level
  • Select the sample
  • Collect the data
  • Perform calculations
  • Reach a conclusion
• Null Hypothesis (H0)


  Prediction of "no difference" between groups or parameters
• Alternative Hypothesis (Ha)


  Prediction of real difference between groups or parameters
• To support the alternative hypothesis, we need to falsify the null hypothesis (Falsifiability criterion)
• Alpha level/Significance level


  Probability value used to define the very unlikely sample outcomes if the null hypothesis is true

  
• Critical region


  Extreme sample values that are very unlikely to be obtained if the null hypothesis is true
• Type I error


  Rejecting the null hypothesis when it is true
• Type II error


  Retaining the null hypothesis when it is false
• Critical region


  Composed of extreme sample values that are very unlikely to be obtained if the null hypothesis is true